TSTP Solution File: LCL800-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL800-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 13:05:27 EDT 2022
% Result : Unknown 39.17s 39.33s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL800-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 09:11:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 38.95/39.06 ----- Otter 3.3f, August 2004 -----
% 38.95/39.06 The process was started by sandbox2 on n021.cluster.edu,
% 38.95/39.06 Wed Jul 27 09:11:38 2022
% 38.95/39.06 The command was "./otter". The process ID is 9906.
% 38.95/39.06
% 38.95/39.06 set(prolog_style_variables).
% 38.95/39.06 set(auto).
% 38.95/39.06 dependent: set(auto1).
% 38.95/39.06 dependent: set(process_input).
% 38.95/39.06 dependent: clear(print_kept).
% 38.95/39.06 dependent: clear(print_new_demod).
% 38.95/39.06 dependent: clear(print_back_demod).
% 38.95/39.06 dependent: clear(print_back_sub).
% 38.95/39.06 dependent: set(control_memory).
% 38.95/39.06 dependent: assign(max_mem, 12000).
% 38.95/39.06 dependent: assign(pick_given_ratio, 4).
% 38.95/39.06 dependent: assign(stats_level, 1).
% 38.95/39.06 dependent: assign(max_seconds, 10800).
% 38.95/39.06 clear(print_given).
% 38.95/39.06
% 38.95/39.06 list(usable).
% 38.95/39.06 0 [] A=A.
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)=c_HOL_Otimes__class_Otimes(V_b,V_a,T_a).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)=c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_x,V_y,T_a)=c_HOL_Otimes__class_Otimes(V_y,V_x,T_a).
% 38.95/39.06 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a)=V_a.
% 38.95/39.06 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),T_a).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat),tc_nat).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),T_a).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat)=c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat)=c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)|V_c=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a)=V_d.
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_i,V_m,tc_nat)),tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_i,tc_nat)),tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(V_m,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat)),tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_y,tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_z,tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(V_i,V_k,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)=c_HOL_Oplus__class_Oplus(V_c,V_a,T_a).
% 38.95/39.06 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)=c_HOL_Oplus__class_Oplus(V_b,V_a,T_a).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)=c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat)!=c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat)| -c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(V_x,V_y,T_a)=c_HOL_Oplus__class_Oplus(V_y,V_x,T_a).
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.06 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).
% 38.95/39.06 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.
% 38.95/39.06 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|V_x!=c_HOL_Oplus__class_Oplus(V_x,V_a,T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)!=V_m|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 0 [] V_x!=c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat)|V_a=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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.
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 0 [] c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 0 [] c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=V_m.
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)!=c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)|V_m=V_n|V_k=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)!=c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)|V_k=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=V_n.
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat)!=c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat)|V_k=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=V_n.
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,V_a,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oring__no__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ono__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_Suc(V_m),tc_nat).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a).
% 38.95/39.06 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a)=c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),T_a).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat),tc_nat).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat)=c_HOL_Oplus__class_Oplus(V_m,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat).
% 38.95/39.06 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a).
% 38.95/39.06 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)=c_HOL_Oplus__class_Oplus(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a).
% 38.95/39.06 0 [] -class_OrderedGroup_Oab__semigroup__add(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_d,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a)=c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a).
% 38.95/39.06 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),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat).
% 38.95/39.06 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a)!=c_HOL_Oplus__class_Oplus(V_y,V_u,T_a)|c_HOL_Oplus__class_Oplus(V_x,V_z,T_a)=V_u.
% 38.95/39.06 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 38.95/39.06 0 [] c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 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,c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat).
% 38.95/39.06 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.
% 38.95/39.06 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.
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)!=c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)|V_m=V_n.
% 38.95/39.06 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat)=c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat).
% 38.95/39.06 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat).
% 38.95/39.06 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_k,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_u,tc_nat),V_k,tc_nat).
% 38.95/39.06 0 [] -class_Ring__and__Field_Osemiring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a).
% 38.95/39.06 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).
% 38.95/39.06 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),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat).
% 38.95/39.06 0 [] 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),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat).
% 38.95/39.06 0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 38.95/39.06 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.
% 38.95/39.06 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.
% 38.95/39.06 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.
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(V_k,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat).
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat).
% 38.95/39.06 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).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat)!=c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat)|V_y=V_z.
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat)!=c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat)|V_m=V_n.
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat)!=c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat)|V_m=V_n.
% 38.95/39.06 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(V_x,V_y,T_a)!=c_HOL_Oplus__class_Oplus(V_x,V_z,T_a)|V_y=V_z.
% 38.95/39.06 0 [] -class_OrderedGroup_Ocancel__ab__semigroup__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)!=c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)|V_b=V_c.
% 38.95/39.06 0 [] -class_OrderedGroup_Ocancel__semigroup__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)!=c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)|V_b=V_c.
% 38.95/39.06 0 [] -class_OrderedGroup_Ocancel__semigroup__add(T_a)|c_HOL_Oplus__class_Oplus(V_b,V_a,T_a)!=c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)|V_b=V_c.
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)!=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).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)!=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)).
% 38.95/39.06 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).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a).
% 38.95/39.06 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).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_j,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_k,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__comm__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)=V_x.
% 38.95/39.06 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=V_a.
% 38.95/39.06 0 [] V_x=c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=V_n.
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=V_m.
% 38.95/39.06 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|V_x=c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 38.95/39.06 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=V_a.
% 38.95/39.06 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=V_a.
% 38.95/39.06 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=V_a.
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=V_a.
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=V_a.
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),T_a).
% 38.95/39.06 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_n,tc_nat)=V_m.
% 38.95/39.06 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_n,tc_nat)=V_m.
% 38.95/39.06 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a)=V_a.
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat).
% 38.95/39.06 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a).
% 38.95/39.06 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ono__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 38.95/39.06 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 38.95/39.06 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.06 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)| -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).
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(V_m,c_Suc(V_n),tc_nat)=c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat).
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat)=c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a)=c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)|V_y=V_z|V_w=V_x.
% 38.95/39.06 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_d,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)|V_c=V_d|V_a=V_b.
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_d,tc_nat),tc_nat)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_d,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat)|V_c=V_d|V_a=V_b.
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_y,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),tc_nat)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_z,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat)|V_y=V_z|V_w=V_x.
% 38.95/39.06 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).
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_ry,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oring__no__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oring__no__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Omult__zero(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Omult__zero(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 38.95/39.06 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).
% 38.95/39.06 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 38.95/39.06 0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 38.95/39.06 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.
% 38.95/39.06 0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)| -c_HOL_Oord__class_Oless(V_c,V_d,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_l,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat).
% 38.95/39.06 0 [] -class_OrderedGroup_Oab__semigroup__idem__mult(T_a)|c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_x,V_y,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)=c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Otimes__class_Otimes(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 38.95/39.06 0 [] -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_i,tc_nat).
% 38.95/39.06 0 [] -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_i,tc_nat).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_c,T_a),T_a)!=c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_d,T_a),T_a)|V_c=V_d|V_r=c_HOL_Ozero__class_Ozero(T_a).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_c,tc_nat),tc_nat)!=c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_d,tc_nat),tc_nat)|V_c=V_d|V_r=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat)| -c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat).
% 38.95/39.06 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(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat).
% 38.95/39.06 0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 38.95/39.06 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 38.95/39.06 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a).
% 38.95/39.06 0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 38.95/39.06 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 38.95/39.06 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.06 0 [] -class_OrderedGroup_Oab__semigroup__idem__mult(T_a)|c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)=V_x.
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat)!=c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat)|V_m=V_n.
% 38.95/39.06 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),T_a)=c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(V_n,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat)=V_m|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)!=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)).
% 38.95/39.06 0 [] c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)!=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).
% 38.95/39.06 0 [] -class_OrderedGroup_Oab__semigroup__mult(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)=c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a)=c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,V_rx,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ry,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a).
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_k,tc_nat)=c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat).
% 38.95/39.06 0 [] c_HOL_Otimes__class_Otimes(V_k,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat).
% 38.95/39.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 0 [] V_n!=c_Suc(V_n).
% 38.95/39.06 0 [] c_Suc(V_n)!=V_n.
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat).
% 38.95/39.06 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 38.95/39.06 0 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k)=V_t.
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat).
% 38.95/39.06 0 [] c_Suc(V_m)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 0 [] c_Suc(V_nat_H)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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.
% 38.95/39.06 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.
% 38.95/39.06 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.
% 38.95/39.06 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).
% 38.95/39.06 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.
% 38.95/39.06 0 [] c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k)=c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(V_i,V_n,tc_nat))|c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 38.95/39.06 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 38.95/39.06 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 38.95/39.06 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 38.95/39.06 0 [] -c_HOL_Oord__class_Oless(V_n,V_n,tc_nat).
% 38.95/39.06 0 [] -c_HOL_Oord__class_Oless(V_x,V_x,tc_nat).
% 38.95/39.06 0 [] V_m=c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__e_q__0__disj__1__1(V_m,V_n))|V_m=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 38.95/39.06 0 [] c_Suc(V_nat)!=c_Suc(V_nat_H)|V_nat=V_nat_H.
% 38.95/39.06 0 [] c_Suc(V_x)!=c_Suc(V_y)|V_x=V_y.
% 38.95/39.06 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_m).
% 38.95/39.06 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_nat_H).
% 38.95/39.06 0 [] V_n=c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(V_n))| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 38.95/39.06 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).
% 38.95/39.06 0 [] V_n=c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(V_n))| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xless__Suc__e_q__0__disj__1__1(V_m,V_n),V_n,tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 0 [] -c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 38.95/39.06 0 [] -c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat).
% 38.95/39.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 0 [] c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t))| -c_Lambda_Obeta(V_s,V_t).
% 38.95/39.06 0 [] V_s=c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s))| -c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r),V_s).
% 38.95/39.06 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)).
% 38.95/39.06 0 [] V_xs!=c_List_Olist_OCons(V_x,V_xs,T_a).
% 38.95/39.06 0 [] c_List_Olist_OCons(V_x,V_t,T_a)!=V_t.
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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.
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 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).
% 38.95/39.06 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OAbs(V_dB_H).
% 38.95/39.06 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).
% 38.95/39.06 0 [] c_Lambda_OdB_OAbs(V_dB)!=c_Lambda_OdB_OAbs(V_dB_H)|V_dB=V_dB_H.
% 38.95/39.06 0 [] c_Lambda_Obeta(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))).
% 38.95/39.06 0 [] -c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t).
% 38.95/39.06 0 [] c_Lambda_Obeta(V_r,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s))| -c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_r),V_s).
% 38.95/39.06 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)).
% 38.95/39.06 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).
% 38.95/39.06 0 [] c_List_Olist_OCons(V_a,V_list,T_a)!=c_List_Olist_OCons(V_a_H,V_list_H,T_a)|V_a=V_a_H.
% 38.95/39.06 0 [] c_List_Olist_OCons(V_a,V_list,T_a)!=c_List_Olist_OCons(V_a_H,V_list_H,T_a)|V_list=V_list_H.
% 38.95/39.06 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OVar(V_nat_H)|V_nat=V_nat_H.
% 38.95/39.06 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=c_Lambda_OdB_OVar(V_nat).
% 38.95/39.06 0 [] c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k)=c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)).
% 38.95/39.06 0 [] c_Lambda_OdB_OApp(V_dB1,V_dB2)!=c_Lambda_OdB_OAbs(V_dB_H).
% 38.95/39.06 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=c_Lambda_OdB_OApp(V_dB1,V_dB2).
% 38.95/39.06 0 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k)=V_u.
% 38.95/39.06 0 [] c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j))| -c_InductTermi_OIT(V_r).
% 38.95/39.06 0 [] c_Lambda_OdB_OApp(V_dB1,V_dB2)!=c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H)|V_dB1=V_dB1_H.
% 38.95/39.06 0 [] c_Lambda_OdB_OApp(V_dB1,V_dB2)!=c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H)|V_dB2=V_dB2_H.
% 38.95/39.06 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H).
% 38.95/39.06 0 [] c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))| -c_InductTermi_OIT(V_t).
% 38.95/39.06 0 [] v_n____=v_i____.
% 38.95/39.06 0 [] c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)).
% 38.95/39.06 0 [] c_Lambda_Olift(c_Lambda_OdB_OApp(V_s,V_t),V_k)=c_Lambda_OdB_OApp(c_Lambda_Olift(V_s,V_k),c_Lambda_Olift(V_t,V_k)).
% 38.95/39.06 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).
% 38.95/39.06 0 [] c_InductTermi_OIT(v_ua______).
% 38.95/39.06 0 [] c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))| -c_InductTermi_OIT(V_r).
% 38.95/39.06 0 [] c_Lambda_Obeta(c_Lambda_OdB_OApp(V_u,V_s),c_Lambda_OdB_OApp(V_u,V_t))| -c_Lambda_Obeta(V_s,V_t).
% 38.95/39.06 0 [] c_Lambda_Obeta(c_Lambda_OdB_OApp(V_s,V_u),c_Lambda_OdB_OApp(V_t,V_u))| -c_Lambda_Obeta(V_s,V_t).
% 38.95/39.06 0 [] c_InductTermi_OIT(v_u____).
% 38.95/39.06 0 [] c_Lambda_Oliftn(V_n,c_Lambda_OdB_OApp(V_s,V_t),V_k)=c_Lambda_OdB_OApp(c_Lambda_Oliftn(V_n,V_s,V_k),c_Lambda_Oliftn(V_n,V_t,V_k)).
% 38.95/39.06 0 [] c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k)=V_t.
% 38.95/39.06 0 [] v_rs____=c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB).
% 38.95/39.06 0 [] c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i)))| -c_InductTermi_OIT(V_t).
% 38.95/39.06 0 [] c_Lambda_Osubstn(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k)=c_Lambda_OdB_OApp(c_Lambda_Osubstn(V_t,V_s,V_k),c_Lambda_Osubstn(V_u,V_s,V_k)).
% 38.95/39.06 0 [] c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H)!=c_Lambda_OdB_OVar(V_nat).
% 38.95/39.06 0 [] c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))).
% 38.95/39.06 0 [] -c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))).
% 38.95/39.06 0 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 38.95/39.06 0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 38.95/39.06 0 [] class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat).
% 38.95/39.06 0 [] class_Ring__and__Field_Oordered__semiring__strict(tc_nat).
% 38.95/39.06 0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 38.95/39.06 0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 38.95/39.06 0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 38.95/39.06 0 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 38.95/39.06 0 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 38.95/39.06 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 38.95/39.06 0 [] class_OrderedGroup_Oab__semigroup__mult(tc_nat).
% 38.95/39.06 0 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 38.95/39.06 0 [] class_Ring__and__Field_Ocomm__semiring(tc_nat).
% 38.95/39.06 0 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 38.95/39.06 0 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 38.95/39.06 0 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 38.95/39.06 0 [] class_Ring__and__Field_Osemiring(tc_nat).
% 38.95/39.06 0 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 38.95/39.06 0 [] class_Nat_Osemiring__char__0(tc_nat).
% 38.95/39.06 0 [] class_Orderings_Opreorder(tc_nat).
% 38.95/39.06 0 [] class_Orderings_Olinorder(tc_nat).
% 38.95/39.06 0 [] class_Orderings_Oorder(tc_nat).
% 38.95/39.06 end_of_list.
% 38.95/39.06
% 38.95/39.06 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 38.95/39.06
% 38.95/39.06 This ia a non-Horn set with equality. The strategy will be
% 38.95/39.06 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 38.95/39.06 deletion, with positive clauses in sos and nonpositive
% 38.95/39.06 clauses in usable.
% 38.95/39.06
% 38.95/39.06 dependent: set(knuth_bendix).
% 38.95/39.06 dependent: set(anl_eq).
% 38.95/39.06 dependent: set(para_from).
% 38.95/39.06 dependent: set(para_into).
% 38.95/39.06 dependent: clear(para_from_right).
% 38.95/39.06 dependent: clear(para_into_right).
% 38.95/39.06 dependent: set(para_from_vars).
% 38.95/39.06 dependent: set(eq_units_both_ways).
% 38.95/39.06 dependent: set(dynamic_demod_all).
% 38.95/39.06 dependent: set(dynamic_demod).
% 38.95/39.06 dependent: set(order_eq).
% 38.95/39.06 dependent: set(back_demod).
% 38.95/39.06 dependent: set(lrpo).
% 38.95/39.06 dependent: set(hyper_res).
% 38.95/39.06 dependent: set(unit_deletion).
% 38.95/39.06 dependent: set(factor).
% 38.95/39.06
% 38.95/39.06 ------------> process usable:
% 38.95/39.06 ** KEPT (pick-wt=11): 1 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,C,A)=c_HOL_Otimes__class_Otimes(C,B,A).
% 38.95/39.06 ** KEPT (pick-wt=11): 2 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.06 Following clause subsumed by 1 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,C,A)=c_HOL_Otimes__class_Otimes(C,B,A).
% 38.95/39.06 ** KEPT (pick-wt=11): 3 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,C,A),C,A)=B.
% 38.95/39.06 ** KEPT (pick-wt=25): 4 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(B,C,A),A).
% 38.95/39.06 Following clause subsumed by 4 during input processing: 0 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(B,C,A),A).
% 38.95/39.06 ** KEPT (pick-wt=26): 6 [copy,5,flip.2] -class_Ring__and__Field_Oring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,B,A),C,A),E,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,C,A),E,A).
% 38.95/39.06 Following clause subsumed by 6 during input processing: 0 [] -class_Ring__and__Field_Oring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,B,A),C,A),E,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,C,A),E,A).
% 38.95/39.06 ** KEPT (pick-wt=29): 7 [] -class_Ring__and__Field_Oring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A)|D=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,A),C,A),F,A).
% 38.95/39.06 ** KEPT (pick-wt=29): 8 [] -class_Ring__and__Field_Oring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,A),C,A),D,A)=F.
% 38.95/39.06 ** KEPT (pick-wt=11): 9 [] c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=11): 10 [] c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=11): 11 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,C,tc_nat),B,tc_nat).
% 38.95/39.06 Following clause subsumed by 9 during input processing: 0 [] c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 38.95/39.06 Following clause subsumed by 10 during input processing: 0 [] c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=11): 12 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(B,C,A)=c_HOL_Oplus__class_Oplus(C,B,A).
% 38.95/39.06 ** KEPT (pick-wt=11): 13 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oplus__class_Oplus(B,C,A)=c_HOL_Oplus__class_Oplus(C,B,A).
% 38.95/39.06 ** KEPT (pick-wt=17): 14 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=c_HOL_Oplus__class_Oplus(C,D,tc_nat)| -c_HOL_Oord__class_Oless(C,B,tc_nat)|c_HOL_Oord__class_Oless(A,D,tc_nat).
% 38.95/39.06 Following clause subsumed by 12 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(B,C,A)=c_HOL_Oplus__class_Oplus(C,B,A).
% 38.95/39.06 ** KEPT (pick-wt=13): 15 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.06 ** KEPT (pick-wt=13): 16 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.06 ** KEPT (pick-wt=18): 17 [] 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).
% 38.95/39.06 ** KEPT (pick-wt=12): 18 [] -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.
% 38.95/39.06 ** KEPT (pick-wt=14): 20 [copy,19,flip.3] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(B,C,A)!=B|C=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.06 ** KEPT (pick-wt=10): 21 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 Following clause subsumed by 21 during input processing: 0 [flip.1] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=9): 22 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.06 ** KEPT (pick-wt=9): 23 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.06 ** KEPT (pick-wt=9): 24 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 38.95/39.06 Following clause subsumed by 23 during input processing: 0 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.06 ** KEPT (pick-wt=11): 25 [] -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).
% 38.95/39.06 ** KEPT (pick-wt=16): 26 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Otimes__class_Otimes(A,C,tc_nat)|B=C|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 Following clause subsumed by 26 during input processing: 0 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Otimes__class_Otimes(A,C,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=C.
% 38.95/39.06 ** KEPT (pick-wt=16): 27 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Otimes__class_Otimes(C,B,tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat)|A=C.
% 38.95/39.06 ** KEPT (pick-wt=11): 28 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=11): 29 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=13): 30 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oplus__class_Oplus(B,B,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.06 ** KEPT (pick-wt=31): 31 [] -class_Ring__and__Field_Opordered__ring(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A),A)| -c_HOL_Oord__class_Oless(D,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,A),C,A),F,A),A).
% 38.95/39.06 ** KEPT (pick-wt=31): 32 [] -class_Ring__and__Field_Opordered__ring(A)|c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,D,A),E,A),F,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,E,A),B,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,E,A),F,A),A).
% 38.95/39.06 ** KEPT (pick-wt=31): 33 [] -class_Ring__and__Field_Opordered__ring(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,A),C,A),D,A),F,A).
% 38.95/39.06 ** KEPT (pick-wt=31): 34 [] -class_Ring__and__Field_Opordered__ring(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),D,A),E,A),F,A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),E,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,A),F,A),A).
% 38.95/39.06 ** KEPT (pick-wt=17): 35 [] -class_Ring__and__Field_Oring__no__zero__divisors(A)|c_HOL_Otimes__class_Otimes(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.06 ** KEPT (pick-wt=17): 36 [] -class_Ring__and__Field_Ono__zero__divisors(A)|c_HOL_Otimes__class_Otimes(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.06 ** KEPT (pick-wt=17): 38 [copy,37,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A).
% 38.95/39.06 ** KEPT (pick-wt=17): 39 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A)=c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A).
% 38.95/39.06 ** KEPT (pick-wt=17): 40 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A).
% 38.95/39.06 ** KEPT (pick-wt=17): 41 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A)=c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A).
% 38.95/39.06 ** KEPT (pick-wt=17): 42 [] -class_OrderedGroup_Oab__semigroup__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A).
% 38.95/39.06 Following clause subsumed by 38 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A).
% 38.95/39.06 ** KEPT (pick-wt=17): 43 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,D,A),C,A).
% 38.95/39.06 ** KEPT (pick-wt=17): 44 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A)=c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A).
% 38.95/39.06 Following clause subsumed by 38 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A).
% 38.95/39.06 ** KEPT (pick-wt=18): 45 [] 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),c_HOL_Oplus__class_Oplus(B,A,tc_nat),tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=20): 46 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A)!=c_HOL_Oplus__class_Oplus(C,E,A)|c_HOL_Oplus__class_Oplus(B,D,A)=E.
% 38.95/39.06 ** KEPT (pick-wt=14): 47 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,D,A)|B=C.
% 38.95/39.06 ** KEPT (pick-wt=14): 48 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)!=c_HOL_Ominus__class_Ominus(C,D,A)|C=D.
% 38.95/39.06 ** KEPT (pick-wt=17): 49 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Otimes__class_Otimes(A,C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|B=C.
% 38.95/39.06 ** KEPT (pick-wt=17): 50 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Oplus__class_Oplus(A,B,tc_nat)|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=17): 51 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Oplus__class_Oplus(A,B,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.06 ** KEPT (pick-wt=15): 52 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,A,tc_nat),c_HOL_Otimes__class_Otimes(C,A,tc_nat),tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=15): 53 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=26): 55 [copy,54,flip.2] -class_Ring__and__Field_Osemiring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A),E,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,A),E,A),A).
% 38.95/39.06 ** KEPT (pick-wt=9): 56 [] -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).
% 38.95/39.06 ** KEPT (pick-wt=13): 57 [] 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),c_HOL_Otimes__class_Otimes(B,A,tc_nat),tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=13): 58 [] 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),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=20): 59 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 38.95/39.06 ** KEPT (pick-wt=14): 60 [] -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.
% 38.95/39.06 ** KEPT (pick-wt=12): 61 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 38.95/39.06 ** KEPT (pick-wt=12): 62 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 38.95/39.06 ** KEPT (pick-wt=10): 63 [] -class_Ring__and__Field_Oordered__ring__strict(A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Ozero__class_Ozero(A),A).
% 38.95/39.06 ** KEPT (pick-wt=16): 64 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(A),B,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(A),C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=16): 65 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(C),A,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(C),B,tc_nat),tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=12): 66 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=c_HOL_Oplus__class_Oplus(A,C,tc_nat)|B=C.
% 38.95/39.06 ** KEPT (pick-wt=12): 67 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=c_HOL_Oplus__class_Oplus(C,B,tc_nat)|A=C.
% 38.95/39.06 Following clause subsumed by 66 during input processing: 0 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=c_HOL_Oplus__class_Oplus(A,C,tc_nat)|B=C.
% 38.95/39.06 ** KEPT (pick-wt=16): 68 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(B,C,A)!=c_HOL_Oplus__class_Oplus(B,D,A)|C=D.
% 38.95/39.06 ** KEPT (pick-wt=14): 69 [] -class_OrderedGroup_Ocancel__ab__semigroup__add(A)|c_HOL_Oplus__class_Oplus(B,C,A)!=c_HOL_Oplus__class_Oplus(B,D,A)|C=D.
% 38.95/39.06 ** KEPT (pick-wt=14): 70 [] -class_OrderedGroup_Ocancel__semigroup__add(A)|c_HOL_Oplus__class_Oplus(B,C,A)!=c_HOL_Oplus__class_Oplus(B,D,A)|C=D.
% 38.95/39.06 ** KEPT (pick-wt=14): 71 [] -class_OrderedGroup_Ocancel__semigroup__add(A)|c_HOL_Oplus__class_Oplus(B,C,A)!=c_HOL_Oplus__class_Oplus(D,C,A)|B=D.
% 38.95/39.06 ** KEPT (pick-wt=17): 72 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=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).
% 38.95/39.06 ** KEPT (pick-wt=17): 73 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=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)).
% 38.95/39.06 ** KEPT (pick-wt=20): 74 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A)|B=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.06 ** KEPT (pick-wt=20): 75 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A)|C=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.06 ** KEPT (pick-wt=23): 76 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,E,A),A).
% 38.95/39.06 ** KEPT (pick-wt=9): 77 [] -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).
% 38.95/39.06 ** KEPT (pick-wt=22): 78 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 38.95/39.06 ** KEPT (pick-wt=20): 79 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A).
% 38.95/39.06 ** KEPT (pick-wt=22): 80 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Otimes__class_Otimes(D,B,A),A).
% 38.95/39.06 ** KEPT (pick-wt=20): 81 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 38.95/39.06 ** KEPT (pick-wt=19): 82 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=19): 83 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 38.95/39.06 Following clause subsumed by 83 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 38.95/39.06 Following clause subsumed by 82 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=19): 84 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat).
% 38.95/39.06 Following clause subsumed by 83 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=21): 85 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A)| -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A).
% 38.95/39.06 ** KEPT (pick-wt=21): 86 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(D,C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 38.95/39.06 ** KEPT (pick-wt=21): 87 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A).
% 38.95/39.06 ** KEPT (pick-wt=21): 88 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 38.95/39.06 Following clause subsumed by 86 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(D,C,A).
% 38.95/39.06 ** KEPT (pick-wt=21): 89 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(C,D,A).
% 38.95/39.06 Following clause subsumed by 88 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 38.95/39.06 Following clause subsumed by 86 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(D,C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 38.95/39.06 ** KEPT (pick-wt=21): 90 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(D,B,A).
% 38.95/39.06 ** KEPT (pick-wt=21): 91 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 38.95/39.06 ** KEPT (pick-wt=21): 92 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A).
% 38.95/39.06 Following clause subsumed by 90 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(D,B,A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A).
% 38.95/39.06 ** KEPT (pick-wt=21): 93 [] -class_Ring__and__Field_Oordered__comm__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(C,D,A).
% 38.95/39.06 ** KEPT (pick-wt=20): 95 [copy,94,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 38.95/39.06 ** KEPT (pick-wt=9): 96 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A)=B.
% 38.95/39.06 ** KEPT (pick-wt=9): 97 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A)=B.
% 38.95/39.06 ** KEPT (pick-wt=11): 99 [copy,98,flip.3] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 38.95/39.06 ** KEPT (pick-wt=9): 100 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 38.95/39.06 ** KEPT (pick-wt=9): 101 [] -class_OrderedGroup_Omonoid__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A)=B.
% 38.95/39.06 ** KEPT (pick-wt=9): 102 [] -class_OrderedGroup_Omonoid__add(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 38.95/39.06 ** KEPT (pick-wt=9): 103 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 38.95/39.06 Following clause subsumed by 96 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A)=B.
% 38.95/39.06 ** KEPT (pick-wt=20): 104 [] -class_Ring__and__Field_Oordered__ring__strict(A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A),A).
% 38.95/39.06 ** KEPT (pick-wt=11): 105 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,A),C,A)=B.
% 38.95/39.06 Following clause subsumed by 10 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 38.95/39.06 Following clause subsumed by 9 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=15): 106 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A).
% 38.95/39.06 ** KEPT (pick-wt=15): 107 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 38.95/39.06 Following clause subsumed by 36 during input processing: 0 [] -class_Ring__and__Field_Ono__zero__divisors(A)|c_HOL_Otimes__class_Otimes(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.06 ** KEPT (pick-wt=15): 108 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=15): 109 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 38.95/39.06 ** KEPT (pick-wt=15): 110 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A).
% 38.95/39.06 ** KEPT (pick-wt=15): 111 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A).
% 38.95/39.06 ** KEPT (pick-wt=15): 112 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 38.95/39.06 ** KEPT (pick-wt=18): 113 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Oplus__class_Oplus(A,B,tc_nat)|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.06 ** KEPT (pick-wt=16): 114 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Oplus__class_Oplus(A,B,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=20): 115 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A).
% 38.95/39.06 ** KEPT (pick-wt=20): 116 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A).
% 38.95/39.06 ** KEPT (pick-wt=20): 117 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 38.95/39.06 ** KEPT (pick-wt=20): 118 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 38.95/39.06 ** KEPT (pick-wt=18): 119 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),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),A,tc_nat).
% 38.95/39.06 ** KEPT (pick-wt=16): 120 [] -class_Ring__and__Field_Oordered__ring__strict(A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),c_HOL_Ozero__class_Ozero(A),A).
% 38.95/39.06 ** KEPT (pick-wt=17): 121 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(B,C,tc_nat),A)=c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A).
% 38.95/39.06 ** KEPT (pick-wt=31): 122 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A)|C=E|B=D.
% 38.95/39.06 Following clause subsumed by 122 during input processing: 0 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A)|C=E|B=D.
% 38.95/39.07 ** KEPT (pick-wt=27): 123 [] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,D,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)|B=D|A=C.
% 38.95/39.07 Following clause subsumed by 123 during input processing: 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,D,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)|B=D|A=C.
% 38.95/39.07 ** KEPT (pick-wt=23): 124 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,E,A),A).
% 38.95/39.07 ** KEPT (pick-wt=23): 125 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(D,E,A),A),A).
% 38.95/39.07 ** KEPT (pick-wt=23): 126 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)=c_HOL_Otimes__class_Otimes(D,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),E,A),A).
% 38.95/39.07 ** KEPT (pick-wt=10): 127 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.07 ** KEPT (pick-wt=10): 128 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.07 ** KEPT (pick-wt=10): 129 [] -class_Ring__and__Field_Oring__no__zero__divisors(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.07 ** KEPT (pick-wt=10): 130 [] -class_Ring__and__Field_Oring__no__zero__divisors(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.07 ** KEPT (pick-wt=10): 131 [] -class_Ring__and__Field_Omult__zero(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.07 ** KEPT (pick-wt=10): 132 [] -class_Ring__and__Field_Omult__zero(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.07 Following clause subsumed by 127 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.07 ** KEPT (pick-wt=11): 133 [] 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).
% 38.95/39.07 ** KEPT (pick-wt=20): 134 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 38.95/39.07 ** KEPT (pick-wt=17): 135 [] 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.
% 38.95/39.07 ** KEPT (pick-wt=20): 136 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A)| -c_HOL_Oord__class_Oless(C,E,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 38.95/39.07 ** KEPT (pick-wt=18): 137 [] c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(B,D,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=14): 138 [] -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).
% 38.95/39.07 ** KEPT (pick-wt=14): 139 [] -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).
% 38.95/39.07 ** KEPT (pick-wt=14): 140 [] -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).
% 38.95/39.07 ** KEPT (pick-wt=14): 141 [] -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).
% 38.95/39.07 ** KEPT (pick-wt=14): 142 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=14): 143 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=14): 144 [] -class_OrderedGroup_Oab__semigroup__idem__mult(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(B,C,A),A)=c_HOL_Otimes__class_Otimes(B,C,A).
% 38.95/39.07 ** KEPT (pick-wt=20): 145 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A).
% 38.95/39.07 ** KEPT (pick-wt=20): 146 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 38.95/39.07 Following clause subsumed by 145 during input processing: 0 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 38.95/39.07 ** KEPT (pick-wt=18): 147 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A).
% 38.95/39.07 ** KEPT (pick-wt=7): 148 [] -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),A,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=7): 149 [] -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),B,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=26): 150 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A)!=c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,E,A),A)|D=E|C=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.07 ** KEPT (pick-wt=22): 151 [] c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat)!=c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,D,tc_nat),tc_nat)|C=D|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=19): 152 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A)!=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.07 ** KEPT (pick-wt=19): 153 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.07 ** KEPT (pick-wt=14): 154 [] c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat)| -c_HOL_Oord__class_Oless(A,c_HOL_Ominus__class_Ominus(C,B,tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=14): 155 [] c_HOL_Oord__class_Oless(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,C,tc_nat),B,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=16): 156 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A)| -c_HOL_Oord__class_Oless(B,D,A).
% 38.95/39.07 ** KEPT (pick-wt=16): 157 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A)| -c_HOL_Oord__class_Oless(B,D,A).
% 38.95/39.07 ** KEPT (pick-wt=16): 158 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A).
% 38.95/39.07 ** KEPT (pick-wt=16): 159 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,A).
% 38.95/39.07 ** KEPT (pick-wt=16): 160 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,A).
% 38.95/39.07 ** KEPT (pick-wt=16): 161 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(D,B,A),c_HOL_Oplus__class_Oplus(D,C,A),A).
% 38.95/39.07 ** KEPT (pick-wt=14): 162 [] c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=14): 163 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(C,A,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=14): 164 [] c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=8): 165 [] -class_OrderedGroup_Oab__semigroup__idem__mult(A)|c_HOL_Otimes__class_Otimes(B,B,A)=B.
% 38.95/39.07 ** KEPT (pick-wt=12): 166 [] 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).
% 38.95/39.07 ** KEPT (pick-wt=12): 167 [] 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).
% 38.95/39.07 ** KEPT (pick-wt=19): 168 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A)=c_HOL_Ozero__class_Ozero(A).
% 38.95/39.07 ** KEPT (pick-wt=21): 169 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Otimes__class_Otimes(D,B,A),A).
% 38.95/39.07 ** KEPT (pick-wt=21): 170 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 38.95/39.07 ** KEPT (pick-wt=21): 171 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 38.95/39.07 ** KEPT (pick-wt=21): 172 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A).
% 38.95/39.07 ** KEPT (pick-wt=14): 173 [] c_HOL_Otimes__class_Otimes(c_Suc(A),B,tc_nat)!=c_HOL_Otimes__class_Otimes(c_Suc(A),C,tc_nat)|B=C.
% 38.95/39.07 ** KEPT (pick-wt=17): 174 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(B,C,tc_nat),A)=c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A).
% 38.95/39.07 ** KEPT (pick-wt=17): 175 [] 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).
% 38.95/39.07 ** KEPT (pick-wt=19): 176 [] -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).
% 38.95/39.07 ** KEPT (pick-wt=19): 177 [] -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).
% 38.95/39.07 ** KEPT (pick-wt=18): 178 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=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)).
% 38.95/39.07 ** KEPT (pick-wt=16): 179 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=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).
% 38.95/39.07 ** KEPT (pick-wt=17): 180 [] -class_OrderedGroup_Oab__semigroup__mult(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A).
% 38.95/39.07 ** KEPT (pick-wt=17): 181 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,D,A),C,A).
% 38.95/39.07 ** KEPT (pick-wt=17): 182 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A).
% 38.95/39.07 Following clause subsumed by 182 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A).
% 38.95/39.07 ** KEPT (pick-wt=17): 183 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A)=c_HOL_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(B,D,A),A).
% 38.95/39.07 Following clause subsumed by 182 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A).
% 38.95/39.07 Following clause subsumed by 95 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 38.95/39.07 ** KEPT (pick-wt=20): 184 [] -class_Ring__and__Field_Ocomm__semiring(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 38.95/39.07 ** KEPT (pick-wt=20): 185 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oplus__class_Oplus(C,D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 38.95/39.07 ** KEPT (pick-wt=10): 186 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 38.95/39.07 Following clause subsumed by 186 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 38.95/39.07 ** KEPT (pick-wt=10): 187 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 38.95/39.07 ** KEPT (pick-wt=10): 188 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 38.95/39.07 ** KEPT (pick-wt=13): 189 [] 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).
% 38.95/39.07 ** KEPT (pick-wt=14): 190 [] 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).
% 38.95/39.07 ** KEPT (pick-wt=9): 191 [] c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=9): 192 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=4): 194 [copy,193,flip.1] c_Suc(A)!=A.
% 38.95/39.07 Following clause subsumed by 194 during input processing: 0 [] c_Suc(A)!=A.
% 38.95/39.07 ** KEPT (pick-wt=19): 195 [] c_HOL_Oord__class_Oless(A,c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),A,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=19): 196 [] c_HOL_Oord__class_Oless(A,c_HOL_Otimes__class_Otimes(B,A,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),A,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=6): 197 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=14): 198 [] -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).
% 38.95/39.07 ** KEPT (pick-wt=14): 199 [] -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).
% 38.95/39.07 ** KEPT (pick-wt=13): 200 [] 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).
% 38.95/39.07 ** KEPT (pick-wt=5): 201 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.07 Following clause subsumed by 201 during input processing: 0 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=13): 202 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A).
% 38.95/39.07 Following clause subsumed by 202 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).
% 38.95/39.07 Following clause subsumed by 202 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.
% 38.95/39.07 Following clause subsumed by 202 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(C,B,A)|c_HOL_Oord__class_Oless(B,C,A).
% 38.95/39.07 ** KEPT (pick-wt=13): 203 [] -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.
% 38.95/39.07 ** KEPT (pick-wt=6): 204 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 38.95/39.07 ** KEPT (pick-wt=6): 205 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 38.95/39.07 ** KEPT (pick-wt=6): 206 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 38.95/39.07 ** KEPT (pick-wt=4): 207 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 38.95/39.07 Following clause subsumed by 207 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=15): 209 [copy,208,flip.1] c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__e_q__0__disj__1__1(A,B))=A|A=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=12): 210 [] A=B| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)|c_HOL_Oord__class_Oless(A,B,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=12): 211 [] A=B| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 38.95/39.07 Following clause subsumed by 210 during input processing: 0 [] A=B|c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=8): 212 [] c_Suc(A)!=c_Suc(B)|A=B.
% 38.95/39.07 Following clause subsumed by 212 during input processing: 0 [] c_Suc(A)!=c_Suc(B)|A=B.
% 38.95/39.07 Following clause subsumed by 201 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.07 Following clause subsumed by 201 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=10): 214 [copy,213,flip.1] c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(A))=A| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=10): 215 [] 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).
% 38.95/39.07 ** KEPT (pick-wt=10): 217 [copy,216,flip.1] c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(A))=A| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=15): 218 [] c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xless__Suc__e_q__0__disj__1__1(A,B),B,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=14): 219 [] -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).
% 38.95/39.07 ** KEPT (pick-wt=14): 220 [] -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).
% 38.95/39.07 ** KEPT (pick-wt=5): 221 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 38.95/39.07 Following clause subsumed by 221 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=21): 222 [] c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),A,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=13): 223 [] c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat)|c_Suc(A)=B| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=9): 224 [] -c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=10): 225 [] c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=10): 226 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat).
% 38.95/39.07 Following clause subsumed by 225 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).
% 38.95/39.07 ** KEPT (pick-wt=8): 227 [] c_Lambda_Obeta(c_Lambda_OdB_OAbs(A),c_Lambda_OdB_OAbs(B))| -c_Lambda_Obeta(A,B).
% 38.95/39.07 ** KEPT (pick-wt=10): 229 [copy,228,flip.1] c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(A,B))=B| -c_Lambda_Obeta(c_Lambda_OdB_OAbs(A),B).
% 38.95/39.07 ** KEPT (pick-wt=6): 231 [copy,230,flip.1] c_List_Olist_OCons(A,B,C)!=B.
% 38.95/39.07 Following clause subsumed by 231 during input processing: 0 [] c_List_Olist_OCons(A,B,C)!=B.
% 38.95/39.07 ** KEPT (pick-wt=10): 232 [] c_Lambda_Obeta(c_Lambda_Olift(A,B),c_Lambda_Olift(C,B))| -c_Lambda_Obeta(A,C).
% 38.95/39.07 ** KEPT (pick-wt=11): 233 [] c_Lambda_Olift(c_Lambda_OdB_OVar(A),B)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=12): 234 [] c_Lambda_Oliftn(A,c_Lambda_OdB_OVar(B),C)=c_Lambda_OdB_OVar(B)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=5): 235 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 38.95/39.07 ** KEPT (pick-wt=8): 236 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OAbs(B)|A=B.
% 38.95/39.07 ** KEPT (pick-wt=4): 237 [] -c_Lambda_Obeta(c_Lambda_OdB_OVar(A),B).
% 38.95/39.07 ** KEPT (pick-wt=9): 238 [] c_Lambda_Obeta(A,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(A,B))| -c_Lambda_Obeta(c_Lambda_OdB_OAbs(A),B).
% 38.95/39.07 ** KEPT (pick-wt=12): 239 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,C)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=12): 240 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_OCons(D,E,C)|A=D.
% 38.95/39.07 ** KEPT (pick-wt=12): 241 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_OCons(D,E,C)|B=E.
% 38.95/39.07 ** KEPT (pick-wt=8): 242 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OVar(B)|A=B.
% 38.95/39.07 ** KEPT (pick-wt=5): 243 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 38.95/39.07 ** KEPT (pick-wt=6): 244 [] c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OAbs(C).
% 38.95/39.07 ** KEPT (pick-wt=6): 245 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OApp(B,C).
% 38.95/39.07 ** KEPT (pick-wt=8): 246 [] c_InductTermi_OIT(c_Lambda_Osubst(A,c_Lambda_OdB_OVar(B),C))| -c_InductTermi_OIT(A).
% 38.95/39.07 ** KEPT (pick-wt=10): 247 [] c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OApp(C,D)|A=C.
% 38.95/39.07 ** KEPT (pick-wt=10): 248 [] c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OApp(C,D)|B=D.
% 38.95/39.07 ** KEPT (pick-wt=6): 249 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OApp(B,C).
% 38.95/39.07 ** KEPT (pick-wt=6): 250 [] c_InductTermi_OIT(c_Lambda_Olift(A,B))| -c_InductTermi_OIT(A).
% 38.95/39.07 ** KEPT (pick-wt=12): 251 [] c_Lambda_Obeta(c_Lambda_Osubst(A,B,C),c_Lambda_Osubst(D,B,C))| -c_Lambda_Obeta(A,D).
% 38.95/39.07 ** KEPT (pick-wt=5): 252 [] c_InductTermi_OIT(c_Lambda_OdB_OAbs(A))| -c_InductTermi_OIT(A).
% 38.95/39.07 ** KEPT (pick-wt=10): 253 [] c_Lambda_Obeta(c_Lambda_OdB_OApp(A,B),c_Lambda_OdB_OApp(A,C))| -c_Lambda_Obeta(B,C).
% 38.95/39.07 ** KEPT (pick-wt=10): 254 [] c_Lambda_Obeta(c_Lambda_OdB_OApp(A,B),c_Lambda_OdB_OApp(C,B))| -c_Lambda_Obeta(A,C).
% 38.95/39.07 ** KEPT (pick-wt=7): 255 [] c_InductTermi_OIT(c_Lambda_OdB_OApp(A,c_Lambda_OdB_OVar(B)))| -c_InductTermi_OIT(A).
% 38.95/39.07 ** KEPT (pick-wt=6): 256 [] c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OVar(C).
% 38.95/39.07 ** KEPT (pick-wt=7): 257 [] -c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))).
% 38.95/39.07 142 back subsumes 84.
% 38.95/39.07 142 back subsumes 65.
% 38.95/39.07 182 back subsumes 125.
% 38.95/39.07 183 back subsumes 126.
% 38.95/39.07 207 back subsumes 197.
% 38.95/39.07 Following clause subsumed by 243 during input processing: 0 [copy,235,flip.1] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 38.95/39.07 Following clause subsumed by 235 during input processing: 0 [copy,243,flip.1] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 38.95/39.07 Following clause subsumed by 245 during input processing: 0 [copy,244,flip.1] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OApp(B,C).
% 38.95/39.07 Following clause subsumed by 244 during input processing: 0 [copy,245,flip.1] c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OAbs(C).
% 38.95/39.07 Following clause subsumed by 256 during input processing: 0 [copy,249,flip.1] c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OVar(C).
% 38.95/39.07 Following clause subsumed by 249 during input processing: 0 [copy,256,flip.1] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OApp(B,C).
% 38.95/39.07
% 38.95/39.07 ------------> process sos:
% 38.95/39.07 ** KEPT (pick-wt=3): 305 [] A=A.
% 38.95/39.07 ** KEPT (pick-wt=9): 306 [] c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.07 ---> New Demodulator: 307 [new_demod,306] c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=9): 308 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)=c_HOL_Otimes__class_Otimes(B,A,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=21): 309 [] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat).
% 38.95/39.07 Following clause subsumed by 309 during input processing: 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=11): 310 [] c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.07 ---> New Demodulator: 311 [new_demod,310] c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.07 ** KEPT (pick-wt=11): 313 [copy,312,flip.1] c_Suc(c_HOL_Oplus__class_Oplus(A,B,tc_nat))=c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat).
% 38.95/39.07 ---> New Demodulator: 314 [new_demod,313] c_Suc(c_HOL_Oplus__class_Oplus(A,B,tc_nat))=c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=11): 316 [copy,315,demod,314] c_HOL_Oplus__class_Oplus(c_Suc(A),B,tc_nat)=c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=8): 318 [copy,317,demod,314] c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=8): 320 [copy,319,demod,314] c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,c_Suc(A),tc_nat),tc_nat).
% 38.95/39.07 Following clause subsumed by 318 during input processing: 0 [demod,314] c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=9): 321 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)=c_HOL_Oplus__class_Oplus(B,A,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=7): 322 [] c_HOL_Ominus__class_Ominus(A,A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=7): 323 [] c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 38.95/39.07 ---> New Demodulator: 324 [new_demod,323] c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 38.95/39.07 ** KEPT (pick-wt=8): 325 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_Suc(A),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=15): 326 [] c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=15): 327 [] c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat)=c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat).
% 38.95/39.07 ---> New Demodulator: 328 [new_demod,327] c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat)=c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=11): 330 [copy,329,flip.1] c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.07 ---> New Demodulator: 331 [new_demod,330] c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.07 ** KEPT (pick-wt=10): 332 [] c_HOL_Ominus__class_Ominus(A,c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=15): 333 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat).
% 38.95/39.07 Following clause subsumed by 316 during input processing: 0 [] c_HOL_Oplus__class_Oplus(c_Suc(A),B,tc_nat)=c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=8): 334 [] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.07 ---> New Demodulator: 335 [new_demod,334] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=15): 336 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(A,C,tc_nat).
% 38.95/39.07 ---> New Demodulator: 337 [new_demod,336] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(A,C,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=15): 338 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(B,C,tc_nat).
% 38.95/39.07 ---> New Demodulator: 339 [new_demod,338] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(B,C,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=24): 341 [copy,340,flip.1] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat),D,tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_nat),D,tc_nat),tc_nat).
% 38.95/39.07 ---> New Demodulator: 342 [new_demod,341] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat),D,tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_nat),D,tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=18): 343 [] c_HOL_Otimes__class_Otimes(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat).
% 38.95/39.07 ---> New Demodulator: 344 [new_demod,343] c_HOL_Otimes__class_Otimes(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=18): 345 [] c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat).
% 38.95/39.07 ---> New Demodulator: 346 [new_demod,345] c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=15): 347 [] 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).
% 38.95/39.07 ** KEPT (pick-wt=17): 348 [] 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).
% 38.95/39.07 ---> New Demodulator: 349 [new_demod,348] 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).
% 38.95/39.07 ** KEPT (pick-wt=7): 351 [copy,350,flip.1] c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 38.95/39.07 ---> New Demodulator: 352 [new_demod,351] c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 38.95/39.07 ** KEPT (pick-wt=7): 353 [] c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=A.
% 38.95/39.07 ---> New Demodulator: 354 [new_demod,353] c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=A.
% 38.95/39.07 Following clause subsumed by 305 during input processing: 0 [demod,352] A=A.
% 38.95/39.07 ** KEPT (pick-wt=9): 355 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),B,tc_nat)=A.
% 38.95/39.07 ---> New Demodulator: 356 [new_demod,355] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),B,tc_nat)=A.
% 38.95/39.07 ** KEPT (pick-wt=9): 357 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),A,tc_nat)=B.
% 38.95/39.07 ---> New Demodulator: 358 [new_demod,357] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),A,tc_nat)=B.
% 38.95/39.07 ** KEPT (pick-wt=13): 359 [] c_HOL_Otimes__class_Otimes(A,c_Suc(B),tc_nat)=c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat).
% 38.95/39.07 ---> New Demodulator: 360 [new_demod,359] c_HOL_Otimes__class_Otimes(A,c_Suc(B),tc_nat)=c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=13): 361 [] c_HOL_Otimes__class_Otimes(c_Suc(A),B,tc_nat)=c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat).
% 38.95/39.07 ---> New Demodulator: 362 [new_demod,361] c_HOL_Otimes__class_Otimes(c_Suc(A),B,tc_nat)=c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=11): 363 [] c_HOL_Ominus__class_Ominus(c_Suc(A),c_Suc(B),tc_nat)=c_HOL_Ominus__class_Ominus(A,B,tc_nat).
% 38.95/39.07 ---> New Demodulator: 364 [new_demod,363] c_HOL_Ominus__class_Ominus(c_Suc(A),c_Suc(B),tc_nat)=c_HOL_Ominus__class_Ominus(A,B,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=15): 366 [copy,365,demod,360,362,354] c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.07 ---> New Demodulator: 367 [new_demod,366] c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.07 ** KEPT (pick-wt=8): 368 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.07 ---> New Demodulator: 369 [new_demod,368] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=8): 370 [] c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.07 ---> New Demodulator: 371 [new_demod,370] c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.07 Following clause subsumed by 305 during input processing: 0 [demod,352] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.07 Following clause subsumed by 305 during input processing: 0 [demod,369,369] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.07 Following clause subsumed by 305 during input processing: 0 [demod,371,371] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.07 Following clause subsumed by 305 during input processing: 0 [demod,354] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.07 ** KEPT (pick-wt=13): 372 [] c_HOL_Oplus__class_Oplus(A,c_HOL_Ominus__class_Ominus(B,A,tc_nat),tc_nat)=B|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=15): 373 [] c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat)=c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat).
% 38.95/39.07 ---> New Demodulator: 374 [new_demod,373] c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat)=c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=18): 375 [] c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat).
% 38.95/39.07 ---> New Demodulator: 376 [new_demod,375] c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=18): 377 [] c_HOL_Otimes__class_Otimes(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat).
% 38.95/39.07 ---> New Demodulator: 378 [new_demod,377] c_HOL_Otimes__class_Otimes(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=7): 379 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 38.95/39.07 ---> New Demodulator: 380 [new_demod,379] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 38.95/39.07 ** KEPT (pick-wt=9): 381 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=5): 382 [] c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 38.95/39.07 Following clause subsumed by 382 during input processing: 0 [] c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=11): 383 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 38.95/39.07 Following clause subsumed by 383 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 38.95/39.07 ** KEPT (pick-wt=15): 384 [] c_Lambda_Oliftn(A,c_Lambda_OdB_OVar(B),C)=c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(B,A,tc_nat))|c_HOL_Oord__class_Oless(B,C,tc_nat).
% 38.95/39.07 Following clause subsumed by 382 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).
% 38.95/39.07 ** KEPT (pick-wt=6): 385 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat).
% 38.95/39.07 Following clause subsumed by 385 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat).
% 38.95/39.07 Following clause subsumed by 382 during input processing: 0 [unit_del,207] c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=9): 386 [] c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=11): 388 [copy,387,unit_del,207] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.07 ---> New Demodulator: 389 [new_demod,388] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.07 ** KEPT (pick-wt=7): 391 [copy,390,unit_del,207] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,A)=B.
% 38.95/39.07 ---> New Demodulator: 392 [new_demod,391] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,A)=B.
% 38.95/39.07 ** KEPT (pick-wt=13): 393 [] c_Lambda_Osubstn(A,B,C)=c_Lambda_Osubst(A,c_Lambda_Oliftn(C,B,c_HOL_Ozero__class_Ozero(tc_nat)),C).
% 38.95/39.07 ** KEPT (pick-wt=15): 394 [] 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).
% 38.95/39.07 ** KEPT (pick-wt=12): 395 [] c_Lambda_Oliftn(c_Suc(A),B,C)=c_Lambda_Olift(c_Lambda_Oliftn(A,B,C),C).
% 38.95/39.07 ** KEPT (pick-wt=15): 396 [] 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).
% 38.95/39.07 ** KEPT (pick-wt=10): 397 [] c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(A),B),c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat))).
% 38.95/39.07 ** KEPT (pick-wt=11): 398 [] c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.07 ---> New Demodulator: 399 [new_demod,398] c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.95/39.07 ** KEPT (pick-wt=16): 401 [copy,400,flip.1] c_Lambda_OdB_OApp(c_Lambda_Osubst(A,B,C),c_Lambda_Osubst(D,B,C))=c_Lambda_Osubst(c_Lambda_OdB_OApp(A,D),B,C).
% 38.95/39.07 ---> New Demodulator: 402 [new_demod,401] c_Lambda_OdB_OApp(c_Lambda_Osubst(A,B,C),c_Lambda_Osubst(D,B,C))=c_Lambda_Osubst(c_Lambda_OdB_OApp(A,D),B,C).
% 38.95/39.07 Following clause subsumed by 305 during input processing: 0 [demod,392] B=B.
% 38.95/39.07 ** KEPT (pick-wt=3): 403 [] v_n____=v_i____.
% 38.95/39.07 ---> New Demodulator: 404 [new_demod,403] v_n____=v_i____.
% 38.95/39.07 ** KEPT (pick-wt=3): 405 [] c_InductTermi_OIT(c_Lambda_OdB_OVar(A)).
% 38.95/39.07 ** KEPT (pick-wt=13): 406 [] c_Lambda_Olift(c_Lambda_OdB_OApp(A,B),C)=c_Lambda_OdB_OApp(c_Lambda_Olift(A,C),c_Lambda_Olift(B,C)).
% 38.95/39.07 ---> New Demodulator: 407 [new_demod,406] c_Lambda_Olift(c_Lambda_OdB_OApp(A,B),C)=c_Lambda_OdB_OApp(c_Lambda_Olift(A,C),c_Lambda_Olift(B,C)).
% 38.95/39.07 ** KEPT (pick-wt=2): 408 [] c_InductTermi_OIT(v_ua______).
% 38.95/39.07 ** KEPT (pick-wt=2): 409 [] c_InductTermi_OIT(v_u____).
% 38.95/39.07 ** KEPT (pick-wt=16): 411 [copy,410,flip.1] c_Lambda_OdB_OApp(c_Lambda_Oliftn(A,B,C),c_Lambda_Oliftn(A,D,C))=c_Lambda_Oliftn(A,c_Lambda_OdB_OApp(B,D),C).
% 38.95/39.07 ---> New Demodulator: 412 [new_demod,411] c_Lambda_OdB_OApp(c_Lambda_Oliftn(A,B,C),c_Lambda_Oliftn(A,D,C))=c_Lambda_Oliftn(A,c_Lambda_OdB_OApp(B,D),C).
% 38.95/39.07 ** KEPT (pick-wt=8): 413 [] c_Lambda_Osubst(c_Lambda_Olift(A,B),C,B)=A.
% 38.95/39.07 ---> New Demodulator: 414 [new_demod,413] c_Lambda_Osubst(c_Lambda_Olift(A,B),C,B)=A.
% 38.95/39.07 ** KEPT (pick-wt=6): 416 [copy,415,flip.1] c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB)=v_rs____.
% 38.95/39.07 ---> New Demodulator: 417 [new_demod,416] c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB)=v_rs____.
% 38.95/39.07 ** KEPT (pick-wt=16): 419 [copy,418,flip.1] c_Lambda_OdB_OApp(c_Lambda_Osubstn(A,B,C),c_Lambda_Osubstn(D,B,C))=c_Lambda_Osubstn(c_Lambda_OdB_OApp(A,D),B,C).
% 38.95/39.07 ---> New Demodulator: 420 [new_demod,419] c_Lambda_OdB_OApp(c_Lambda_Osubstn(A,B,C),c_Lambda_Osubstn(D,B,C))=c_Lambda_Osubstn(c_Lambda_OdB_OApp(A,D),B,C).
% 38.95/39.07 ** KEPT (pick-wt=16): 421 [] c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))).
% 38.95/39.07 ** KEPT (pick-wt=2): 422 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 423 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 424 [] class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 425 [] class_Ring__and__Field_Oordered__semiring__strict(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 426 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 427 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 428 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 429 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 430 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 431 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 432 [] class_OrderedGroup_Oab__semigroup__mult(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 433 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 434 [] class_Ring__and__Field_Ocomm__semiring(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 435 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 436 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 437 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 438 [] class_Ring__and__Field_Osemiring(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 439 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 440 [] class_Nat_Osemiring__char__0(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 441 [] class_Orderings_Opreorder(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 442 [] class_Orderings_Olinorder(tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=2): 443 [] class_Orderings_Oorder(tc_nat).
% 38.95/39.07 Following clause subsumed by 305 during input processing: 0 [copy,305,flip.1] A=A.
% 38.95/39.07 305 back subsumes 303.
% 38.95/39.07 305 back subsumes 302.
% 38.95/39.07 305 back subsumes 287.
% 38.95/39.07 >>>> Starting back demodulation with 307.
% 38.95/39.07 Following clause subsumed by 308 during input processing: 0 [copy,308,flip.1] c_HOL_Otimes__class_Otimes(A,B,tc_nat)=c_HOL_Otimes__class_Otimes(B,A,tc_nat).
% 38.95/39.07 Following clause subsumed by 321 during input processing: 0 [copy,309,flip.1] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat).
% 38.95/39.07 >>>> Starting back demodulation with 311.
% 38.95/39.07 >>>> Starting back demodulation with 314.
% 38.95/39.07 ** KEPT (pick-wt=11): 444 [copy,316,flip.1] c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat)=c_HOL_Oplus__class_Oplus(c_Suc(A),B,tc_nat).
% 38.95/39.07 Following clause subsumed by 321 during input processing: 0 [copy,321,flip.1] c_HOL_Oplus__class_Oplus(A,B,tc_nat)=c_HOL_Oplus__class_Oplus(B,A,tc_nat).
% 38.95/39.07 321 back subsumes 309.
% 38.95/39.07 ** KEPT (pick-wt=7): 445 [copy,322,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ominus__class_Ominus(A,A,tc_nat).
% 38.95/39.07 >>>> Starting back demodulation with 324.
% 38.95/39.07 Following clause subsumed by 326 during input processing: 0 [copy,326,flip.1] c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat).
% 38.95/39.07 >>>> Starting back demodulation with 328.
% 38.95/39.07 >>>> Starting back demodulation with 331.
% 38.95/39.07 ** KEPT (pick-wt=10): 446 [copy,332,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ominus__class_Ominus(A,c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat).
% 38.95/39.07 ** KEPT (pick-wt=15): 447 [copy,333,flip.1] c_HOL_Ominus__class_Ominus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat).
% 38.95/39.07 >>>> Starting back demodulation with 335.
% 38.95/39.07 >>>> Starting back demodulation with 337.
% 38.95/39.07 >>>> Starting back demodulation with 339.
% 38.95/39.07 >>>> Starting back demodulation with 342.
% 38.95/39.07 >>>> Starting back demodulation with 344.
% 38.95/39.07 >>>> Starting back demodulation with 346.
% 38.95/39.07 Following clause subsumed by 347 during input processing: 0 [copy,347,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).
% 38.95/39.07 >>>> Starting back demodulation with 349.
% 39.17/39.33 >>>> Starting back demodulation with 352.
% 39.17/39.33 >> back demodulating 310 with 352.
% 39.17/39.33 >> back demodulating 306 with 352.
% 39.17/39.33 >>>> Starting back demodulation with 354.
% 39.17/39.33 >> back demodulating 330 with 354.
% 39.17/39.33 >>>> Starting back demodulation with 356.
% 39.17/39.33 >>>> Starting back demodulation with 358.
% 39.17/39.33 >>>> Starting back demodulation with 360.
% 39.17/39.33 >>>> Starting back demodulation with 362.
% 39.17/39.33 >> back demodulating 173 with 362.
% 39.17/39.33 >> back demodulating 64 with 362.
% 39.17/39.33 >>>> Starting back demodulation with 364.
% 39.17/39.33 >>>> Starting back demodulation with 367.
% 39.17/39.33 >>>> Starting back demodulation with 369.
% 39.17/39.33 >> back demodulating 366 with 369.
% 39.17/39.33 >> back demodulating 269 with 369.
% 39.17/39.33 >> back demodulating 260 with 369.
% 39.17/39.33 >>>> Starting back demodulation with 371.
% 39.17/39.33 >> back demodulating 293 with 371.
% 39.17/39.33 >> back demodulating 270 with 371.
% 39.17/39.33 >> back demodulating 259 with 371.
% 39.17/39.33 >>>> Starting back demodulation with 374.
% 39.17/39.33 >>>> Starting back demodulation with 376.
% 39.17/39.33 >> back demodulating 341 with 376.
% 39.17/39.33 >>>> Starting back demodulation with 378.
% 39.17/39.33 >>>> Starting back demodulation with 380.
% 39.17/39.33 >>>> Starting back demodulation with 389.
% 39.17/39.33 >>>> Starting back demodulation with 392.
% 39.17/39.33 ** KEPT (pick-wt=13): 451 [copy,393,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).
% 39.17/39.33 ** KEPT (pick-wt=12): 452 [copy,395,flip.1] c_Lambda_Olift(c_Lambda_Oliftn(A,B,C),C)=c_Lambda_Oliftn(c_Suc(A),B,C).
% 39.17/39.33 >>>> Starting back demodulation with 399.
% 39.17/39.33 >>>> Starting back demodulation with 402.
% 39.17/39.33 >>>> Starting back demodulation with 404.
% 39.17/39.33 >>>> Starting back demodulation with 407.
% 39.17/39.33 >>>> Starting back demodulation with 412.
% 39.17/39.33 >>>> Starting back demodulation with 414.
% 39.17/39.33 >>>> Starting back demodulation with 417.
% 39.17/39.33 >>>> Starting back demodulation with 420.
% 39.17/39.33 Following clause subsumed by 316 during input processing: 0 [copy,444,flip.1] c_HOL_Oplus__class_Oplus(c_Suc(A),B,tc_nat)=c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat).
% 39.17/39.33 Following clause subsumed by 322 during input processing: 0 [copy,445,flip.1] c_HOL_Ominus__class_Ominus(A,A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.17/39.33 Following clause subsumed by 332 during input processing: 0 [copy,446,flip.1] c_HOL_Ominus__class_Ominus(A,c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.17/39.33 Following clause subsumed by 333 during input processing: 0 [copy,447,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,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat).
% 39.17/39.33 Following clause subsumed by 393 during input processing: 0 [copy,451,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).
% 39.17/39.33 Following clause subsumed by 395 during input processing: 0 [copy,452,flip.1] c_Lambda_Oliftn(c_Suc(A),B,C)=c_Lambda_Olift(c_Lambda_Oliftn(A,B,C),C).
% 39.17/39.33
% 39.17/39.33 ======= end of input processing =======
% 39.17/39.33
% 39.17/39.33 =========== start of search ===========
% 39.17/39.33
% 39.17/39.33
% 39.17/39.33 Resetting weight limit to 2.
% 39.17/39.33
% 39.17/39.33
% 39.17/39.33 Resetting weight limit to 2.
% 39.17/39.33
% 39.17/39.33 sos_size=90
% 39.17/39.33
% 39.17/39.33 Search stopped because sos empty.
% 39.17/39.33
% 39.17/39.33
% 39.17/39.33 Search stopped because sos empty.
% 39.17/39.33
% 39.17/39.33 ============ end of search ============
% 39.17/39.33
% 39.17/39.33 -------------- statistics -------------
% 39.17/39.33 clauses given 91
% 39.17/39.33 clauses generated 35660
% 39.17/39.33 clauses kept 389
% 39.17/39.33 clauses forward subsumed 92
% 39.17/39.33 clauses back subsumed 9
% 39.17/39.33 Kbytes malloced 4882
% 39.17/39.33
% 39.17/39.33 ----------- times (seconds) -----------
% 39.17/39.33 user CPU time 0.27 (0 hr, 0 min, 0 sec)
% 39.17/39.33 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 39.17/39.33 wall-clock time 39 (0 hr, 0 min, 39 sec)
% 39.17/39.33
% 39.17/39.33 Process 9906 finished Wed Jul 27 09:12:17 2022
% 39.17/39.33 Otter interrupted
% 39.17/39.33 PROOF NOT FOUND
%------------------------------------------------------------------------------