TSTP Solution File: LCL774-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL774-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 13:05:22 EDT 2022
% Result : Unsatisfiable 39.54s 39.68s
% Output : Refutation 39.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 1
% Number of leaves : 2
% Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 2 RR)
% Number of literals : 3 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 2 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 1 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(252,axiom,
~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)),
file('LCL774-1.p',unknown),
[] ).
cnf(400,axiom,
c_InductTermi_OIT(c_Lambda_OdB_OVar(A)),
file('LCL774-1.p',unknown),
[] ).
cnf(401,plain,
$false,
inference(binary,[status(thm)],[400,252]),
[iquote('binary,400.1,252.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : LCL774-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 09:22:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 39.46/39.66 ----- Otter 3.3f, August 2004 -----
% 39.46/39.66 The process was started by sandbox on n003.cluster.edu,
% 39.46/39.66 Wed Jul 27 09:22:41 2022
% 39.46/39.66 The command was "./otter". The process ID is 8232.
% 39.46/39.66
% 39.46/39.66 set(prolog_style_variables).
% 39.46/39.66 set(auto).
% 39.46/39.66 dependent: set(auto1).
% 39.46/39.66 dependent: set(process_input).
% 39.46/39.66 dependent: clear(print_kept).
% 39.46/39.66 dependent: clear(print_new_demod).
% 39.46/39.66 dependent: clear(print_back_demod).
% 39.46/39.66 dependent: clear(print_back_sub).
% 39.46/39.66 dependent: set(control_memory).
% 39.46/39.66 dependent: assign(max_mem, 12000).
% 39.46/39.66 dependent: assign(pick_given_ratio, 4).
% 39.46/39.66 dependent: assign(stats_level, 1).
% 39.46/39.66 dependent: assign(max_seconds, 10800).
% 39.46/39.66 clear(print_given).
% 39.46/39.66
% 39.46/39.66 list(usable).
% 39.46/39.66 0 [] A=A.
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)=c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat).
% 39.46/39.66 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).
% 39.46/39.66 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.
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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)).
% 39.46/39.66 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).
% 39.46/39.66 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)).
% 39.46/39.66 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)).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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.
% 39.46/39.66 0 [] c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_i,V_m,tc_nat)),tc_nat).
% 39.46/39.66 0 [] c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_i,tc_nat)),tc_nat).
% 39.46/39.66 0 [] c_HOL_Oord__class_Oless(V_m,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat)),tc_nat).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 0 [] c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)=c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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)).
% 39.46/39.66 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)).
% 39.46/39.66 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).
% 39.46/39.66 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.
% 39.46/39.66 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).
% 39.46/39.66 0 [] c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)!=V_m|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.46/39.66 0 [] V_x!=c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat)|V_a=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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.
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 0 [] c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.46/39.66 0 [] c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=V_m.
% 39.46/39.66 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).
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_Suc(V_m),tc_nat).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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.
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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).
% 39.46/39.66 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)).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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).
% 39.46/39.66 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)).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 0 [] V_x=c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 39.46/39.66 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=V_n.
% 39.46/39.66 0 [] c_HOL_Oplus__class_Oplus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=V_m.
% 39.46/39.66 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).
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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).
% 39.46/39.66 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_n,tc_nat)=V_m.
% 39.46/39.66 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_n,tc_nat)=V_m.
% 39.46/39.66 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.
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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)).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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).
% 39.46/39.66 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)).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.46/39.66 0 [] c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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.
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 0 [] -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_i,tc_nat).
% 39.46/39.66 0 [] -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_i,tc_nat).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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)).
% 39.46/39.66 0 [] -class_OrderedGroup_Oab__semigroup__idem__mult(T_a)|c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)=V_x.
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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.
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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)).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 0 [] V_n!=c_Suc(V_n).
% 39.46/39.66 0 [] c_Suc(V_n)!=V_n.
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 39.46/39.66 0 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k)=V_t.
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 0 [] c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat).
% 39.46/39.66 0 [] c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat).
% 39.46/39.66 0 [] c_Suc(V_m)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.46/39.66 0 [] c_Suc(V_nat_H)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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.
% 39.46/39.66 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).
% 39.46/39.66 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.
% 39.46/39.66 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).
% 39.46/39.66 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 39.46/39.66 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 39.46/39.66 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 39.46/39.66 0 [] -c_HOL_Oord__class_Oless(V_n,V_n,tc_nat).
% 39.46/39.66 0 [] -c_HOL_Oord__class_Oless(V_x,V_x,tc_nat).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 39.46/39.66 0 [] c_Suc(V_nat)!=c_Suc(V_nat_H)|V_nat=V_nat_H.
% 39.46/39.66 0 [] c_Suc(V_x)!=c_Suc(V_y)|V_x=V_y.
% 39.46/39.66 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_m).
% 39.46/39.66 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_nat_H).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 0 [] -c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 39.46/39.66 0 [] -c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 39.46/39.66 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).
% 39.46/39.66 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat).
% 39.46/39.66 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 0 [] c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t))| -c_Lambda_Obeta(V_s,V_t).
% 39.46/39.66 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).
% 39.46/39.66 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)).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 0 [] c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k)=V_t.
% 39.46/39.66 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).
% 39.46/39.66 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.
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.66 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).
% 39.46/39.67 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).
% 39.46/39.67 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).
% 39.46/39.67 0 [] c_Lambda_OdB_OAbs(V_dB)!=c_Lambda_OdB_OAbs(V_dB_H)|V_dB=V_dB_H.
% 39.46/39.67 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))).
% 39.46/39.67 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).
% 39.46/39.67 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)).
% 39.46/39.67 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).
% 39.46/39.67 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)).
% 39.46/39.67 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=c_Lambda_OdB_OVar(V_nat).
% 39.46/39.67 0 [] c_Lambda_OdB_OApp(V_dB1,V_dB2)!=c_Lambda_OdB_OAbs(V_dB_H).
% 39.46/39.67 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OVar(V_nat_H)|V_nat=V_nat_H.
% 39.46/39.67 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=c_Lambda_OdB_OApp(V_dB1,V_dB2).
% 39.46/39.67 0 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k)=V_u.
% 39.46/39.67 0 [] c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j))| -c_InductTermi_OIT(V_r).
% 39.46/39.67 0 [] -c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t).
% 39.46/39.67 0 [] c_Lambda_OdB_OApp(V_dB1,V_dB2)!=c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H)|V_dB1=V_dB1_H.
% 39.46/39.67 0 [] c_Lambda_OdB_OApp(V_dB1,V_dB2)!=c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H)|V_dB2=V_dB2_H.
% 39.46/39.67 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H).
% 39.46/39.67 0 [] c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))| -c_InductTermi_OIT(V_t).
% 39.46/39.67 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OAbs(V_dB_H).
% 39.46/39.67 0 [] c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)).
% 39.46/39.67 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)).
% 39.46/39.67 0 [] c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))| -c_InductTermi_OIT(V_r).
% 39.46/39.67 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).
% 39.46/39.67 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).
% 39.46/39.67 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)).
% 39.46/39.67 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)).
% 39.46/39.67 0 [] c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H)!=c_Lambda_OdB_OVar(V_nat).
% 39.46/39.67 0 [] c_InductTermi_OIT(v_r).
% 39.46/39.67 0 [] c_InductTermi_OIT(c_Lambda_OdB_OApp(v_r,c_Lambda_OdB_OVar(v_i))).
% 39.46/39.67 0 [] -c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)).
% 39.46/39.67 0 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 39.46/39.67 0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 39.46/39.67 0 [] class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat).
% 39.46/39.67 0 [] class_Ring__and__Field_Oordered__semiring__strict(tc_nat).
% 39.46/39.67 0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 39.46/39.67 0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 39.46/39.67 0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 39.46/39.67 0 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 39.46/39.67 0 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 39.46/39.67 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 39.46/39.67 0 [] class_OrderedGroup_Oab__semigroup__mult(tc_nat).
% 39.46/39.67 0 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 39.46/39.67 0 [] class_Ring__and__Field_Ocomm__semiring(tc_nat).
% 39.46/39.67 0 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 39.46/39.67 0 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 39.46/39.67 0 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 39.46/39.67 0 [] class_Ring__and__Field_Osemiring(tc_nat).
% 39.46/39.67 0 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 39.46/39.67 0 [] class_Nat_Osemiring__char__0(tc_nat).
% 39.46/39.67 0 [] class_Orderings_Opreorder(tc_nat).
% 39.46/39.67 0 [] class_Orderings_Olinorder(tc_nat).
% 39.46/39.67 0 [] class_Orderings_Oorder(tc_nat).
% 39.46/39.67 end_of_list.
% 39.46/39.67
% 39.46/39.67 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 39.46/39.67
% 39.46/39.67 This ia a non-Horn set with equality. The strategy will be
% 39.46/39.67 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 39.46/39.67 deletion, with positive clauses in sos and nonpositive
% 39.46/39.67 clauses in usable.
% 39.46/39.67
% 39.46/39.67 dependent: set(knuth_bendix).
% 39.46/39.67 dependent: set(anl_eq).
% 39.46/39.67 dependent: set(para_from).
% 39.46/39.67 dependent: set(para_into).
% 39.46/39.67 dependent: clear(para_from_right).
% 39.46/39.67 dependent: clear(para_into_right).
% 39.46/39.67 dependent: set(para_from_vars).
% 39.46/39.67 dependent: set(eq_units_both_ways).
% 39.46/39.67 dependent: set(dynamic_demod_all).
% 39.46/39.67 dependent: set(dynamic_demod).
% 39.46/39.67 dependent: set(order_eq).
% 39.46/39.67 dependent: set(back_demod).
% 39.46/39.67 dependent: set(lrpo).
% 39.46/39.67 dependent: set(hyper_res).
% 39.46/39.67 dependent: set(unit_deletion).
% 39.46/39.67 dependent: set(factor).
% 39.46/39.67
% 39.46/39.67 ------------> process usable:
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 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).
% 39.46/39.67 ** 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.
% 39.46/39.67 ** 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).
% 39.46/39.67 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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.
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 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).
% 39.46/39.67 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 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).
% 39.46/39.67 ** 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)).
% 39.46/39.67 ** 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)).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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.
% 39.46/39.67 ** 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).
% 39.46/39.67 ** KEPT (pick-wt=10): 21 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.46/39.67 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** KEPT (pick-wt=9): 23 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 39.46/39.67 ** KEPT (pick-wt=9): 24 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 39.46/39.67 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 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.
% 39.46/39.67 ** 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.
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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.
% 39.46/39.67 ** 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.
% 39.46/39.67 ** 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.
% 39.46/39.67 ** 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.
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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)).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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.
% 39.46/39.67 ** 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.
% 39.46/39.67 ** 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.
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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.
% 39.46/39.67 ** 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.
% 39.46/39.67 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.
% 39.46/39.67 ** 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.
% 39.46/39.67 ** 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.
% 39.46/39.67 ** 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.
% 39.46/39.67 ** 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.
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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)).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 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).
% 39.46/39.67 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 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).
% 39.46/39.67 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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).
% 39.46/39.67 ** 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.
% 39.46/39.67 ** 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.
% 39.46/39.67 ** 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.
% 39.46/39.67 ** 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.
% 39.46/39.67 ** KEPT (pick-wt=9): 101 [] -class_OrderedGroup_Omonoid__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A)=B.
% 39.46/39.67 ** KEPT (pick-wt=9): 102 [] -class_OrderedGroup_Omonoid__add(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 39.46/39.67 ** 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.
% 39.46/39.67 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.
% 39.46/39.67 ** 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).
% 39.54/39.67 ** 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.
% 39.54/39.67 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).
% 39.54/39.67 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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)).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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.
% 39.54/39.67 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.
% 39.54/39.67 ** 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.
% 39.54/39.67 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.
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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.
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** KEPT (pick-wt=7): 148 [] -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),A,tc_nat).
% 39.54/39.67 ** KEPT (pick-wt=7): 149 [] -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),B,tc_nat).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** KEPT (pick-wt=8): 165 [] -class_OrderedGroup_Oab__semigroup__idem__mult(A)|c_HOL_Otimes__class_Otimes(B,B,A)=B.
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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.
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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)).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 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).
% 39.54/39.67 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.67 ** 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).
% 39.54/39.68 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** KEPT (pick-wt=4): 194 [copy,193,flip.1] c_Suc(A)!=A.
% 39.54/39.68 Following clause subsumed by 194 during input processing: 0 [] c_Suc(A)!=A.
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** KEPT (pick-wt=5): 201 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.54/39.68 Following clause subsumed by 201 during input processing: 0 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.54/39.68 ** 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).
% 39.54/39.68 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).
% 39.54/39.68 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.
% 39.54/39.68 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).
% 39.54/39.68 ** 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.
% 39.54/39.68 ** KEPT (pick-wt=6): 204 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 39.54/39.68 ** KEPT (pick-wt=6): 205 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 39.54/39.68 ** KEPT (pick-wt=6): 206 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 39.54/39.68 ** KEPT (pick-wt=4): 207 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 39.54/39.68 Following clause subsumed by 207 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 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).
% 39.54/39.68 ** KEPT (pick-wt=8): 212 [] c_Suc(A)!=c_Suc(B)|A=B.
% 39.54/39.68 Following clause subsumed by 212 during input processing: 0 [] c_Suc(A)!=c_Suc(B)|A=B.
% 39.54/39.68 Following clause subsumed by 201 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.54/39.68 Following clause subsumed by 201 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** KEPT (pick-wt=5): 221 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 39.54/39.68 Following clause subsumed by 221 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** 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).
% 39.54/39.68 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).
% 39.54/39.68 ** KEPT (pick-wt=8): 227 [] c_Lambda_Obeta(c_Lambda_OdB_OAbs(A),c_Lambda_OdB_OAbs(B))| -c_Lambda_Obeta(A,B).
% 39.54/39.68 ** 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).
% 39.54/39.68 ** KEPT (pick-wt=10): 230 [] c_Lambda_Obeta(c_Lambda_Olift(A,B),c_Lambda_Olift(C,B))| -c_Lambda_Obeta(A,C).
% 39.54/39.68 ** KEPT (pick-wt=11): 231 [] c_Lambda_Olift(c_Lambda_OdB_OVar(A),B)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 39.54/39.68 ** KEPT (pick-wt=12): 232 [] c_Lambda_Oliftn(A,c_Lambda_OdB_OVar(B),C)=c_Lambda_OdB_OVar(B)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 39.54/39.68 ** KEPT (pick-wt=12): 233 [] c_Lambda_Obeta(c_Lambda_Osubst(A,B,C),c_Lambda_Osubst(D,B,C))| -c_Lambda_Obeta(A,D).
% 39.54/39.68 ** KEPT (pick-wt=8): 234 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OAbs(B)|A=B.
% 39.54/39.68 ** KEPT (pick-wt=9): 235 [] c_Lambda_Obeta(A,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(A,B))| -c_Lambda_Obeta(c_Lambda_OdB_OAbs(A),B).
% 39.54/39.68 ** KEPT (pick-wt=12): 236 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,C)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 39.54/39.68 ** KEPT (pick-wt=5): 237 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 39.54/39.68 ** KEPT (pick-wt=6): 238 [] c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OAbs(C).
% 39.54/39.68 ** KEPT (pick-wt=8): 239 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OVar(B)|A=B.
% 39.54/39.68 ** KEPT (pick-wt=6): 240 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OApp(B,C).
% 39.54/39.68 ** KEPT (pick-wt=8): 241 [] c_InductTermi_OIT(c_Lambda_Osubst(A,c_Lambda_OdB_OVar(B),C))| -c_InductTermi_OIT(A).
% 39.54/39.68 ** KEPT (pick-wt=4): 242 [] -c_Lambda_Obeta(c_Lambda_OdB_OVar(A),B).
% 39.54/39.68 ** KEPT (pick-wt=10): 243 [] c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OApp(C,D)|A=C.
% 39.54/39.68 ** KEPT (pick-wt=10): 244 [] c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OApp(C,D)|B=D.
% 39.54/39.68 ** KEPT (pick-wt=6): 245 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OApp(B,C).
% 39.54/39.68 ** KEPT (pick-wt=6): 246 [] c_InductTermi_OIT(c_Lambda_Olift(A,B))| -c_InductTermi_OIT(A).
% 39.54/39.68 ** KEPT (pick-wt=5): 247 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 39.54/39.68 ** KEPT (pick-wt=5): 248 [] c_InductTermi_OIT(c_Lambda_OdB_OAbs(A))| -c_InductTermi_OIT(A).
% 39.54/39.68 ** KEPT (pick-wt=10): 249 [] c_Lambda_Obeta(c_Lambda_OdB_OApp(A,B),c_Lambda_OdB_OApp(A,C))| -c_Lambda_Obeta(B,C).
% 39.54/39.68 ** KEPT (pick-wt=10): 250 [] c_Lambda_Obeta(c_Lambda_OdB_OApp(A,B),c_Lambda_OdB_OApp(C,B))| -c_Lambda_Obeta(A,C).
% 39.54/39.68 ** KEPT (pick-wt=6): 251 [] c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OVar(C).
% 39.54/39.68 ** KEPT (pick-wt=3): 252 [] -c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)).
% 39.54/39.68 142 back subsumes 84.
% 39.54/39.68 142 back subsumes 65.
% 39.54/39.68 182 back subsumes 125.
% 39.54/39.68 183 back subsumes 126.
% 39.54/39.68 207 back subsumes 197.
% 39.54/39.68 Following clause subsumed by 247 during input processing: 0 [copy,237,flip.1] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 39.54/39.68 Following clause subsumed by 240 during input processing: 0 [copy,238,flip.1] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OApp(B,C).
% 39.54/39.68 Following clause subsumed by 238 during input processing: 0 [copy,240,flip.1] c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OAbs(C).
% 39.54/39.68 Following clause subsumed by 251 during input processing: 0 [copy,245,flip.1] c_Lambda_OdB_OApp(A,B)!=c_Lambda_OdB_OVar(C).
% 39.54/39.68 Following clause subsumed by 237 during input processing: 0 [copy,247,flip.1] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 39.54/39.68 Following clause subsumed by 245 during input processing: 0 [copy,251,flip.1] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OApp(B,C).
% 39.54/39.68
% 39.54/39.68 ------------> process sos:
% 39.54/39.68 ** KEPT (pick-wt=3): 300 [] A=A.
% 39.54/39.68 ** KEPT (pick-wt=9): 301 [] 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).
% 39.54/39.68 ---> New Demodulator: 302 [new_demod,301] 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).
% 39.54/39.68 ** KEPT (pick-wt=9): 303 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)=c_HOL_Otimes__class_Otimes(B,A,tc_nat).
% 39.54/39.68 ** KEPT (pick-wt=21): 304 [] 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).
% 39.54/39.68 Following clause subsumed by 304 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).
% 39.54/39.68 ** KEPT (pick-wt=11): 305 [] 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)).
% 39.54/39.68 ---> New Demodulator: 306 [new_demod,305] 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)).
% 39.54/39.68 ** KEPT (pick-wt=11): 308 [copy,307,flip.1] c_Suc(c_HOL_Oplus__class_Oplus(A,B,tc_nat))=c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat).
% 39.54/39.68 ---> New Demodulator: 309 [new_demod,308] c_Suc(c_HOL_Oplus__class_Oplus(A,B,tc_nat))=c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat).
% 39.54/39.68 ** KEPT (pick-wt=11): 311 [copy,310,demod,309] c_HOL_Oplus__class_Oplus(c_Suc(A),B,tc_nat)=c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat).
% 39.54/39.68 ** KEPT (pick-wt=8): 313 [copy,312,demod,309] c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat),tc_nat).
% 39.54/39.68 ** KEPT (pick-wt=8): 315 [copy,314,demod,309] c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,c_Suc(A),tc_nat),tc_nat).
% 39.54/39.68 Following clause subsumed by 313 during input processing: 0 [demod,309] c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat),tc_nat).
% 39.54/39.68 ** KEPT (pick-wt=9): 316 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)=c_HOL_Oplus__class_Oplus(B,A,tc_nat).
% 39.54/39.68 ** KEPT (pick-wt=7): 317 [] c_HOL_Ominus__class_Ominus(A,A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.54/39.68 ** KEPT (pick-wt=7): 318 [] c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 39.54/39.68 ---> New Demodulator: 319 [new_demod,318] c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 39.54/39.68 ** KEPT (pick-wt=8): 320 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_Suc(A),tc_nat).
% 39.54/39.68 ** KEPT (pick-wt=15): 321 [] 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).
% 39.54/39.68 ** KEPT (pick-wt=15): 322 [] 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).
% 39.54/39.68 ---> New Demodulator: 323 [new_demod,322] 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).
% 39.54/39.68 ** KEPT (pick-wt=11): 325 [copy,324,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)).
% 39.54/39.68 ---> New Demodulator: 326 [new_demod,325] 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)).
% 39.54/39.68 ** KEPT (pick-wt=10): 327 [] c_HOL_Ominus__class_Ominus(A,c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.54/39.68 ** KEPT (pick-wt=15): 328 [] 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).
% 39.54/39.68 Following clause subsumed by 311 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).
% 39.54/39.68 ** KEPT (pick-wt=8): 329 [] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.54/39.68 ---> New Demodulator: 330 [new_demod,329] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.54/39.68 ** KEPT (pick-wt=15): 331 [] 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).
% 39.54/39.68 ---> New Demodulator: 332 [new_demod,331] 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).
% 39.54/39.68 ** KEPT (pick-wt=15): 333 [] 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).
% 39.54/39.68 ---> New Demodulator: 334 [new_demod,333] 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).
% 39.54/39.68 ** KEPT (pick-wt=24): 336 [copy,335,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).
% 39.54/39.68 ---> New Demodulator: 337 [new_demod,336] 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).
% 39.54/39.68 ** KEPT (pick-wt=18): 338 [] 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).
% 39.54/39.68 ---> New Demodulator: 339 [new_demod,338] 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).
% 39.54/39.68 ** KEPT (pick-wt=18): 340 [] 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).
% 39.54/39.68 ---> New Demodulator: 341 [new_demod,340] 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).
% 39.54/39.68 ** KEPT (pick-wt=15): 342 [] 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).
% 39.54/39.68 ** KEPT (pick-wt=17): 343 [] 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).
% 39.54/39.68 ---> New Demodulator: 344 [new_demod,343] 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).
% 39.54/39.68 ** KEPT (pick-wt=7): 346 [copy,345,flip.1] c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 39.54/39.68 ---> New Demodulator: 347 [new_demod,346] c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 39.54/39.68 ** KEPT (pick-wt=7): 348 [] c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=A.
% 39.54/39.68 ---> New Demodulator: 349 [new_demod,348] c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=A.
% 39.54/39.68 Following clause subsumed by 300 during input processing: 0 [demod,347] A=A.
% 39.54/39.68 ** KEPT (pick-wt=9): 350 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),B,tc_nat)=A.
% 39.54/39.68 ---> New Demodulator: 351 [new_demod,350] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),B,tc_nat)=A.
% 39.54/39.68 ** KEPT (pick-wt=9): 352 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),A,tc_nat)=B.
% 39.54/39.68 ---> New Demodulator: 353 [new_demod,352] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),A,tc_nat)=B.
% 39.54/39.68 ** KEPT (pick-wt=13): 354 [] 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).
% 39.54/39.68 ---> New Demodulator: 355 [new_demod,354] 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).
% 39.54/39.68 ** KEPT (pick-wt=13): 356 [] 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).
% 39.54/39.68 ---> New Demodulator: 357 [new_demod,356] 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).
% 39.54/39.68 ** KEPT (pick-wt=11): 358 [] c_HOL_Ominus__class_Ominus(c_Suc(A),c_Suc(B),tc_nat)=c_HOL_Ominus__class_Ominus(A,B,tc_nat).
% 39.54/39.68 ---> New Demodulator: 359 [new_demod,358] c_HOL_Ominus__class_Ominus(c_Suc(A),c_Suc(B),tc_nat)=c_HOL_Ominus__class_Ominus(A,B,tc_nat).
% 39.54/39.68 ** KEPT (pick-wt=15): 361 [copy,360,demod,355,357,349] 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)).
% 39.54/39.68 ---> New Demodulator: 362 [new_demod,361] 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)).
% 39.54/39.68 ** KEPT (pick-wt=8): 363 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.54/39.68 ---> New Demodulator: 364 [new_demod,363] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.54/39.68 ** KEPT (pick-wt=8): 365 [] c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.54/39.68 ---> New Demodulator: 366 [new_demod,365] c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.54/39.68 Following clause subsumed by 300 during input processing: 0 [demod,347] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 39.54/39.68 Following clause subsumed by 300 during input processing: 0 [demod,364,364] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.54/39.68 Following clause subsumed by 300 during input processing: 0 [demod,366,366] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.54/39.68 Following clause subsumed by 300 during input processing: 0 [demod,349] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 39.54/39.68 ** KEPT (pick-wt=13): 367 [] 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).
% 39.54/39.68 ** KEPT (pick-wt=15): 368 [] 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).
% 39.54/39.68 ---> New Demodulator: 369 [new_demod,368] 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).
% 39.54/39.68 ** KEPT (pick-wt=18): 370 [] 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).
% 39.54/39.68 ---> New Demodulator: 371 [new_demod,370] 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).
% 39.54/39.68 ** KEPT (pick-wt=18): 372 [] 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).
% 39.54/39.68 ---> New Demodulator: 373 [new_demod,372] 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).
% 39.54/39.68 ** KEPT (pick-wt=7): 374 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 39.54/39.68 ---> New Demodulator: 375 [new_demod,374] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 39.54/39.68 ** KEPT (pick-wt=9): 376 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 39.54/39.68 ** KEPT (pick-wt=5): 377 [] c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 39.54/39.68 Following clause subsumed by 377 during input processing: 0 [] c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 39.54/39.68 ** KEPT (pick-wt=11): 378 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 39.54/39.68 Following clause subsumed by 378 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 39.54/39.68 ** KEPT (pick-wt=15): 379 [] 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).
% 39.54/39.68 Following clause subsumed by 377 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).
% 39.54/39.68 ** KEPT (pick-wt=6): 380 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat).
% 39.54/39.68 Following clause subsumed by 380 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat).
% 39.54/39.68 Following clause subsumed by 377 during input processing: 0 [unit_del,207] c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 39.54/39.68 ** KEPT (pick-wt=9): 381 [] c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 39.54/39.68 ** KEPT (pick-wt=11): 383 [copy,382,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)).
% 39.54/39.68 ---> New Demodulator: 384 [new_demod,383] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 39.54/39.68 ** KEPT (pick-wt=8): 385 [] c_Lambda_Osubst(c_Lambda_Olift(A,B),C,B)=A.
% 39.54/39.68 ---> New Demodulator: 386 [new_demod,385] c_Lambda_Osubst(c_Lambda_Olift(A,B),C,B)=A.
% 39.54/39.68 ** KEPT (pick-wt=7): 388 [copy,387,unit_del,207] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,A)=B.
% 39.54/39.68 ---> New Demodulator: 389 [new_demod,388] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,A)=B.
% 39.54/39.68 ** KEPT (pick-wt=13): 390 [] c_Lambda_Osubstn(A,B,C)=c_Lambda_Osu
% 39.54/39.68 -------- PROOF --------
% 39.54/39.68 bst(A,c_Lambda_Oliftn(C,B,c_HOL_Ozero__class_Ozero(tc_nat)),C).
% 39.54/39.68 ** KEPT (pick-wt=15): 391 [] 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).
% 39.54/39.68 ** KEPT (pick-wt=12): 392 [] c_Lambda_Oliftn(c_Suc(A),B,C)=c_Lambda_Olift(c_Lambda_Oliftn(A,B,C),C).
% 39.54/39.68 ** KEPT (pick-wt=15): 393 [] 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).
% 39.54/39.68 ** KEPT (pick-wt=10): 394 [] 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))).
% 39.54/39.68 ** KEPT (pick-wt=11): 395 [] c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 39.54/39.68 ---> New Demodulator: 396 [new_demod,395] c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 39.54/39.68 ** KEPT (pick-wt=16): 398 [copy,397,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).
% 39.54/39.68 ---> New Demodulator: 399 [new_demod,398] 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).
% 39.54/39.68 Following clause subsumed by 300 during input processing: 0 [demod,389] B=B.
% 39.54/39.68 ** KEPT (pick-wt=3): 400 [] c_InductTermi_OIT(c_Lambda_OdB_OVar(A)).
% 39.54/39.68
% 39.54/39.68 ----> UNIT CONFLICT at 0.04 sec ----> 401 [binary,400.1,252.1] $F.
% 39.54/39.68
% 39.54/39.68 Length of proof is 0. Level of proof is 0.
% 39.54/39.68
% 39.54/39.68 ---------------- PROOF ----------------
% 39.54/39.68 % SZS status Unsatisfiable
% 39.54/39.68 % SZS output start Refutation
% See solution above
% 39.54/39.68 ------------ end of proof -------------
% 39.54/39.68
% 39.54/39.68
% 39.54/39.68 Search stopped by max_proofs option.
% 39.54/39.68
% 39.54/39.68
% 39.54/39.68 Search stopped by max_proofs option.
% 39.54/39.68
% 39.54/39.68 ============ end of search ============
% 39.54/39.68
% 39.54/39.68 -------------- statistics -------------
% 39.54/39.68 clauses given 0
% 39.54/39.68 clauses generated 55
% 39.54/39.68 clauses kept 346
% 39.54/39.68 clauses forward subsumed 69
% 39.54/39.68 clauses back subsumed 5
% 39.54/39.68 Kbytes malloced 3906
% 39.54/39.68
% 39.54/39.68 ----------- times (seconds) -----------
% 39.54/39.68 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 39.54/39.68 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 39.54/39.68 wall-clock time 40 (0 hr, 0 min, 40 sec)
% 39.54/39.68
% 39.54/39.68 That finishes the proof of the theorem.
% 39.54/39.68
% 39.54/39.68 Process 8232 finished Wed Jul 27 09:23:21 2022
% 39.54/39.68 Otter interrupted
% 39.54/39.68 PROOF FOUND
%------------------------------------------------------------------------------