TSTP Solution File: LCL837-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL837-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 13:05:35 EDT 2022
% Result : Unknown 249.58s 249.67s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : LCL837-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jul 27 09:12:05 EDT 2022
% 0.13/0.35 % CPUTime :
% 248.03/248.08 ----- Otter 3.3f, August 2004 -----
% 248.03/248.08 The process was started by sandbox on n022.cluster.edu,
% 248.03/248.08 Wed Jul 27 09:12:05 2022
% 248.03/248.08 The command was "./otter". The process ID is 5760.
% 248.03/248.08
% 248.03/248.08 set(prolog_style_variables).
% 248.03/248.08 set(auto).
% 248.03/248.08 dependent: set(auto1).
% 248.03/248.08 dependent: set(process_input).
% 248.03/248.08 dependent: clear(print_kept).
% 248.03/248.08 dependent: clear(print_new_demod).
% 248.03/248.08 dependent: clear(print_back_demod).
% 248.03/248.08 dependent: clear(print_back_sub).
% 248.03/248.08 dependent: set(control_memory).
% 248.03/248.08 dependent: assign(max_mem, 12000).
% 248.03/248.08 dependent: assign(pick_given_ratio, 4).
% 248.03/248.08 dependent: assign(stats_level, 1).
% 248.03/248.08 dependent: assign(max_seconds, 10800).
% 248.03/248.08 clear(print_given).
% 248.03/248.08
% 248.03/248.08 list(usable).
% 248.03/248.08 0 [] A=A.
% 248.03/248.08 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|V_m=c_HOL_Oone__class_Oone(tc_nat).
% 248.03/248.08 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),T_a)=c_HOL_Oone__class_Oone(T_a).
% 248.03/248.08 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.
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_Suc(V_m),T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),V_k))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_u,tc_nat)),V_k).
% 248.03/248.08 0 [] -class_Ring__and__Field_Osemiring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_e,T_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_b,V_e,T_a)),V_c))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_e,T_a)),V_c).
% 248.03/248.08 0 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_j)),V_i)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)))| -c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 248.03/248.08 0 [] c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_b,V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_b,V_a,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_c,T_a)=c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),V_a,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|V_n=c_HOL_Oone__class_Oone(tc_nat).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a)),V_c,T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(V_a,V_c,T_a)),V_b),V_c,T_a).
% 248.03/248.08 0 [] -c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)|hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_x)),V_s),V_x)=V_s.
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 248.03/248.08 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a)=c_HOL_Oone__class_Oone(T_a).
% 248.03/248.08 0 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(V_i)),V_k)=c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)))|c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 248.03/248.08 0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_u)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)=V_u.
% 248.03/248.08 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),T_a)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a).
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_d)).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_b).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_d).
% 248.03/248.08 0 [] -class_OrderedGroup_Oab__semigroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)).
% 248.03/248.08 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)).
% 248.03/248.08 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)).
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),V_k)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)).
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)).
% 248.03/248.08 0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)),V_z).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),c_HOL_Oone__class_Oone(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(V_a,V_c,T_a)),c_Divides_Odiv__class_Omod(V_b,V_c,T_a)),V_c,T_a).
% 248.03/248.08 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).
% 248.03/248.08 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)=c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat).
% 248.03/248.08 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).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a)=c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(V_x,c_Suc(V_n),T_a)=c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a).
% 248.03/248.08 0 [] -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a)=c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a).
% 248.03/248.08 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_a,T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_x,V_p,T_a),V_q,T_a)=c_Power_Opower__class_Opower(V_x,c_HOL_Otimes__class_Otimes(V_p,V_q,tc_nat),T_a).
% 248.03/248.08 0 [] hAPP(hAPP(hAPP(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).
% 248.03/248.08 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_m,tc_nat).
% 248.03/248.08 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),V_m,tc_nat),V_m,tc_nat).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a)).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_c,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_d,T_a))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_d,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_c,T_a)).
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat)).
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat)).
% 248.03/248.08 0 [] c_Suc(V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Oone__class_Oone(tc_nat)).
% 248.03/248.08 0 [] c_Suc(V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),V_n).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(V_m,V_n,tc_nat),T_a)=c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),V_n,T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(V_a,V_a,T_a)=c_HOL_Oone__class_Oone(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Odvd(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_b,c_HOL_Otimes__class_Otimes(V_b,V_k,T_a),T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a)=V_a.
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a)=V_a.
% 248.03/248.08 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a)=V_a.
% 248.03/248.08 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a)=V_a.
% 248.03/248.08 0 [] -class_OrderedGroup_Ocomm__monoid__mult(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a)=V_a.
% 248.03/248.08 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat)=V_n.
% 248.03/248.08 0 [] c_HOL_Otimes__class_Otimes(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=V_n.
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_x,T_a)=V_x.
% 248.03/248.08 0 [] c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a).
% 248.03/248.08 0 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_n,tc_nat)=V_m| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 248.03/248.08 0 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),V_n,tc_nat)=V_m| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oidom(T_a)|c_Ring__and__Field_Odvd__class_Odvd(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_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oidom(T_a)|c_Ring__and__Field_Odvd__class_Odvd(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_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 248.03/248.08 0 [] c_Ring__and__Field_Odvd__class_Odvd(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_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y),V_z,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(V_x,V_z,T_a)),c_Divides_Odiv__class_Odiv(V_y,V_z,T_a))| -c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a)),c_Divides_Odiv__class_Omod(V_a,V_b,T_a))),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a)),c_Divides_Odiv__class_Omod(V_a,V_b,T_a))),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c).
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(V_i,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_m)),tc_nat).
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(V_i,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_i)),tc_nat).
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(V_m,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_x)),tc_nat).
% 248.03/248.08 0 [] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(V_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_N,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(V_n,V_N,tc_nat).
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_y,tc_nat).
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_z,tc_nat).
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(V_i,V_k,tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_k,tc_nat).
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_m),tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_j),tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a).
% 248.03/248.08 0 [] c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)),V_k,tc_nat)=c_HOL_Oone__class_Oone(tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),V_k,tc_nat).
% 248.03/248.08 0 [] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 248.03/248.08 0 [] c_Lambda_Osubstn(c_Lambda_OdB_OAbs(V_t),V_s,V_k)=c_Lambda_OdB_OAbs(c_Lambda_Osubstn(V_t,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a).
% 248.03/248.08 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a).
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m).
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_l)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n)| -c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_x).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a),T_a).
% 248.03/248.08 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.
% 248.03/248.08 0 [] hAPP(V_e,V_i)=V_T| -c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)=c_HOL_Ozero__class_Ozero(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_n,tc_nat).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a).
% 248.03/248.08 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_a,T_a)=c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a)=c_Power_Opower__class_Opower(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_p),V_q),T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a)),V_b,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a))|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a)),V_b,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a))|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_m),V_m)=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a)),V_m,T_a).
% 248.03/248.08 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).
% 248.03/248.08 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_y)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)|V_y=V_z.
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)|V_m=V_n.
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n)|V_m=V_n.
% 248.03/248.08 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)|V_y=V_z.
% 248.03/248.08 0 [] -class_OrderedGroup_Ocancel__ab__semigroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)|V_b=V_c.
% 248.03/248.08 0 [] -class_OrderedGroup_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)|V_b=V_c.
% 248.03/248.08 0 [] -class_OrderedGroup_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a)|V_b=V_c.
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 248.03/248.08 0 [] c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a)),T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a)),T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d)).
% 248.03/248.08 0 [] c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(V_dB),tc_Lambda_OdB)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_a,T_a)=V_b| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),T_a)=V_b| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 248.03/248.08 0 [] hAPP(hAPP(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).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 248.03/248.08 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)).
% 248.03/248.08 0 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_j)),V_i)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)),V_j)| -c_HOL_Oord__class_Oless(V_j,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 248.03/248.08 0 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)),c_Suc(V_k))=hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_i)| -c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 248.03/248.08 0 [] c_HOL_Otimes__class_Otimes(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat).
% 248.03/248.08 0 [] c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_k,tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 0 [] c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_a),V_b),V_c,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(V_a,V_c,tc_nat)),c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(V_a,V_c,tc_nat)),c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat)),V_c,tc_nat)).
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_i,V_m,tc_nat),c_Power_Opower__class_Opower(V_i,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_i,tc_nat).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(V_a,V_b,T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(V_a,V_b,T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)|V_k=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.08 0 [] -c_Type_Otyping(V_e_H,V_u,V_U)| -c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)|c_Type_Otyping(V_e_H,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),V_T).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a)),T_a).
% 248.03/248.08 0 [] c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)),V_m),V_n,tc_nat)=c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a)),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a)),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_m,T_a)),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a))=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_m,T_a).
% 248.03/248.08 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)|c_HOL_Oord__class_Oless(V_m,c_HOL_Otimes__class_Otimes(V_n,c_Suc(c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)),tc_nat),tc_nat).
% 248.03/248.08 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat)|V_k=c_HOL_Ozero__class_Ozero(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oidom(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oidom(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a),V_b,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)),c_HOL_Oone__class_Oone(T_a))|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_b,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)),c_HOL_Oone__class_Oone(T_a))|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),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).
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat).
% 248.03/248.08 0 [] c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t))| -c_Lambda_Obeta(V_s,V_t).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Otimes__class_Otimes(V_m,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_n,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_m,T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(V_a,c_HOL_Oone__class_Oone(T_a),T_a)=V_a.
% 248.03/248.08 0 [] -c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)|V_k=c_HOL_Ozero__class_Ozero(tc_nat)| -hBOOL(hAPP(V_P,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat)),V_j),V_k,tc_nat)))|hBOOL(hAPP(V_P,V_j)).
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat).
% 248.03/248.08 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a).
% 248.03/248.08 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 248.03/248.08 0 [] -c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 248.03/248.08 0 [] -c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)| -class_Ring__and__Field_Ono__zero__divisors(T_a)| -class_Ring__and__Field_Omult__zero(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(V_a,V_n,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oring__1__no__zero__divisors(T_a)|c_Power_Opower__class_Opower(V_a,V_n,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)|c_HOL_Oone__class_Oone(T_a)!=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OAbs(V_dB_H).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(V_x,c_HOL_Oone__class_Oone(tc_nat),T_a)=V_x.
% 248.03/248.08 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a)=V_a.
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_b,V_c,T_a)!=c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)|c_Divides_Odiv__class_Omod(V_a,V_c,T_a)!=c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c,T_a).
% 248.03/248.08 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 248.03/248.08 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(V_x,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_x,tc_nat).
% 248.03/248.08 0 [] c_HOL_Otimes__class_Otimes(V_m,c_Suc(V_n),tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)).
% 248.03/248.08 0 [] c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)).
% 248.03/248.08 0 [] -c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)|V_k=c_HOL_Ozero__class_Ozero(tc_nat)| -hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat)),V_j),V_k,tc_nat)))|hBOOL(hAPP(V_P,V_i)).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),V_n,T_a)=c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a).
% 248.03/248.08 0 [] hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x)=V_T.
% 248.03/248.08 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).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 248.03/248.08 0 [] c_Lambda_OdB_OAbs(V_dB)!=c_Lambda_OdB_OAbs(V_dB_H)|V_dB=V_dB_H.
% 248.03/248.08 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a)),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 248.03/248.08 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).
% 248.03/248.08 0 [] c_Divides_Odiv__class_Omod(c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)),V_m)),V_n,tc_nat)=c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_w,V_y,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_w,V_z,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a))|V_y=V_z|V_w=V_x.
% 248.03/248.08 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_c,T_a)),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_d,T_a)),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a))|V_c=V_d|V_a=V_b.
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_a,V_c,tc_nat)),c_HOL_Otimes__class_Otimes(V_b,V_d,tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_a,V_d,tc_nat)),c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat))|V_c=V_d|V_a=V_b.
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_w,V_y,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_w,V_z,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat))|V_y=V_z|V_w=V_x.
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a)=V_a|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a)=V_a|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] V_m!=c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Oone__class_Oone(tc_nat).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_b,V_c,T_a)!=c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)|c_Divides_Odiv__class_Omod(V_a,V_c,T_a)!=c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a_H,V_b_H,T_a),V_c,T_a).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_m,T_a)),V_m)=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a)),V_m,T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_m),c_HOL_Otimes__class_Otimes(V_a,V_m,T_a))=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a)),V_m,T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_a,c_HOL_Oone__class_Oone(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k),tc_nat).
% 248.03/248.08 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_k,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat).
% 248.03/248.08 0 [] c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)=V_m| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 248.03/248.08 0 [] -c_HOL_Oord__class_Oless(V_x,V_x,tc_nat).
% 248.03/248.08 0 [] -c_HOL_Oord__class_Oless(V_n,V_n,tc_nat).
% 248.03/248.08 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 248.03/248.08 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 248.03/248.08 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 248.03/248.08 0 [] c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k)=c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_n))|c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 248.03/248.08 0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 248.03/248.08 0 [] c_Lambda_Oliftn(V_n,c_Lambda_OdB_OAbs(V_s),V_k)=c_Lambda_OdB_OAbs(c_Lambda_Oliftn(V_n,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))).
% 248.03/248.08 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.
% 248.03/248.08 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).
% 248.03/248.08 0 [] V_x=V_y| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 248.03/248.08 0 [] V_x=V_y| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 248.03/248.08 0 [] -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)|V_x=V_y| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 248.03/248.08 0 [] V_m=V_n| -c_Ring__and__Field_Odvd__class_Odvd(V_n,V_m,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat).
% 248.03/248.08 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.
% 248.03/248.08 0 [] hBOOL(hAPP(hAPP(V_P,V_n),V_m))|c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)|V_m=V_n|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 248.03/248.08 0 [] V_x=V_y| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat).
% 248.03/248.08 0 [] -c_Ring__and__Field_Odvd__class_Odvd(V_b,V_a,tc_nat)|V_a=V_b| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,tc_nat).
% 248.03/248.08 0 [] -c_Ring__and__Field_Odvd__class_Odvd(V_b,V_a,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,tc_nat)|V_a=V_b.
% 248.03/248.08 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.
% 248.03/248.08 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.
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 0 [] -c_Ring__and__Field_Odvd__class_Odvd(V_n,V_m,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_m,tc_nat).
% 248.03/248.08 0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)| -c_HOL_Oord__class_Oless(V_c,V_d,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_l),tc_nat)| -c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,V_a,T_a).
% 248.03/248.08 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,V_x,tc_nat).
% 248.03/248.08 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 248.03/248.08 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 248.03/248.08 0 [] -c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oidom(T_a)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a),T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oidom(T_a)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a).
% 248.03/248.08 0 [] c_Ring__and__Field_Odvd__class_Odvd(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),tc_nat).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a).
% 248.03/248.08 0 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,tc_nat),V_c,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat),tc_nat)),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat),tc_nat),V_c,tc_nat)).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 0 [] c_Ring__and__Field_Odvd__class_Odvd(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_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat).
% 248.03/248.08 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(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).
% 248.03/248.08 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a)),T_a).
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(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_Oone__class_Oone(tc_nat),V_n,tc_nat).
% 248.03/248.08 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).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),c_Divides_Odiv__class_Odiv(V_w,V_z,T_a),T_a)=c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_x,V_w,T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_z,V_w,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a).
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Otimes__class_Otimes(V_n,V_xa,tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),c_HOL_Otimes__class_Otimes(V_n,V_xb,tc_nat))|c_Divides_Odiv__class_Omod(V_x,V_n,tc_nat)=c_Divides_Odiv__class_Omod(V_y,V_n,tc_nat).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_Power_Opower__class_Opower(V_a,V_m,T_a)!=c_Power_Opower__class_Opower(V_a,V_n,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)|V_m=V_n.
% 248.03/248.08 0 [] c_Power_Opower__class_Opower(V_p,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 248.03/248.08 0 [] -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Oone__class_Oone(T_a).
% 248.03/248.08 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|V_x!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_a,V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=V_a.
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a))=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)|c_HOL_Ozero__class_Ozero(T_a)!=c_HOL_Oone__class_Oone(T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_x)=V_x.
% 248.03/248.08 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 248.03/248.08 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|V_x=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Ozero__class_Ozero(T_a)).
% 248.03/248.08 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))=V_a.
% 248.03/248.08 0 [] -class_OrderedGroup_Omonoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 248.03/248.08 0 [] -class_OrderedGroup_Omonoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))=V_a.
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))=V_a.
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 248.03/248.08 0 [] -class_Ring__and__Field_Osemiring__0(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Oone__class_Oone(T_a).
% 248.03/248.08 0 [] -hBOOL(hAPP(V_P,V_n))|hBOOL(hAPP(V_P,c_Divides_Odiv__class_Omod(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))).
% 248.03/248.08 0 [] -hBOOL(hAPP(V_P,c_Divides_Odiv__class_Omod(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))|hBOOL(hAPP(V_P,V_n)).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 0 [] hBOOL(hAPP(V_P,V_nat))|hBOOL(hAPP(V_P,v_sko__List__Xlexn__Xinduct__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.08 0 [] hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat)))| -hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(V_P)))| -hBOOL(hAPP(V_P,V_k)).
% 248.03/248.08 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 248.03/248.08 0 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k)=V_t.
% 248.03/248.08 0 [] hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.08 0 [] -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat)))|hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))).
% 248.03/248.08 0 [] -hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))|hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.08 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).
% 248.03/248.08 0 [] hBOOL(hAPP(V_P,V_n))|hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.08 0 [] c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.08 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.08 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).
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.08 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.
% 248.03/248.08 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.
% 248.03/248.08 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).
% 248.03/248.08 0 [] V_x!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_a)|V_a=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=V_m|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.08 0 [] hBOOL(hAPP(V_P,V_nat))|hBOOL(hAPP(V_P,v_sko__List__Xreplicate__Xinduct__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.08 0 [] hBOOL(hAPP(V_P,V_nat))|hBOOL(hAPP(V_P,v_sko__Nat__Xnat__Xinducts__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.08 0 [] hBOOL(hAPP(V_P,V_nat))|hBOOL(hAPP(V_P,v_sko__Nat__Xnat__Xinduct__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.08 0 [] -c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 248.03/248.08 0 [] -c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 248.03/248.08 0 [] hBOOL(hAPP(V_P,V_nat))|hBOOL(hAPP(V_P,v_sko__List__Xupt__Xinduct__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.08 0 [] V_x=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)=V_n.
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat))=V_m.
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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.
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 0 [] c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat)=c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)),V_n,tc_nat).
% 248.03/248.08 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).
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat).
% 248.03/248.08 0 [] c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n)=c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)).
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n))=c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)).
% 248.03/248.08 0 [] c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat)=c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat))|c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat))=V_n.
% 248.03/248.08 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 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).
% 248.03/248.08 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=c_Lambda_OdB_OAbs(V_dB_H).
% 248.03/248.08 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2).
% 248.03/248.08 0 [] c_Lambda_OdB_OVar(V_nat)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H).
% 248.03/248.08 0 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_s),hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_t))| -c_Lambda_Obeta(V_s,V_t).
% 248.03/248.08 0 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_u),hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u))| -c_Lambda_Obeta(V_s,V_t).
% 248.03/248.08 0 [] c_Lambda_Oliftn(V_n,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(V_n,V_s,V_k)),c_Lambda_Oliftn(V_n,V_t,V_k)).
% 248.03/248.08 0 [] c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(V_t,V_s,V_k)),c_Lambda_Osubstn(V_u,V_s,V_k)).
% 248.03/248.08 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)!=c_Lambda_OdB_OVar(V_nat).
% 248.03/248.08 0 [] c_Lambda_Osubstn(V_t,V_s,V_n)=hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),c_Lambda_Oliftn(V_n,V_s,c_HOL_Ozero__class_Ozero(tc_nat))),V_n).
% 248.03/248.08 0 [] c_List_Omap(V_f,V_xs,T_b,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_b).
% 248.03/248.08 0 [] c_List_Olist_ONil(T_a)!=c_List_Omap(V_f,V_xs,T_b,T_a)|V_xs=c_List_Olist_ONil(T_b).
% 248.03/248.08 0 [] c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a)=c_List_Olist_ONil(T_a).
% 248.03/248.08 0 [] c_List_Olist_ONil(T_a)=c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a).
% 248.03/248.08 0 [] V_T=V_U| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_U)| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 248.03/248.08 0 [] c_Lambda_OdB_OAbs(V_r)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_ss=c_List_Olist_ONil(tc_Lambda_OdB).
% 248.03/248.08 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB).
% 248.03/248.08 0 [] c_Lambda_OdB_OVar(V_m)=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 248.03/248.08 0 [] c_Lambda_OdB_OAbs(V_r)=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 248.03/248.08 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)!=c_Lambda_OdB_OAbs(V_r)|V_ss=c_List_Olist_ONil(tc_Lambda_OdB).
% 248.03/248.08 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OAbs(V_r).
% 248.03/248.08 0 [] c_Lambda_OdB_OVar(V_m)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_ss=c_List_Olist_ONil(tc_Lambda_OdB).
% 248.03/248.08 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB).
% 248.03/248.08 0 [] c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b)=V_a.
% 248.03/248.08 0 [] -class_OrderedGroup_Osemigroup__add(T_a)|c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y),V_zs,T_a,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_y,V_zs,T_a,T_a)).
% 248.03/248.08 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k)=V_u.
% 248.03/248.08 0 [] c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_t),V_i),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),V_i))| -c_Lambda_Obeta(V_r,V_s).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Oone__class_Oone(T_a).
% 248.03/248.08 0 [] c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat).
% 248.03/248.08 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.08 0 [] c_Divides_Odiv__class_Odiv(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),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.08 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a)=c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a).
% 248.03/248.09 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_q,T_a),V_x,T_a)=c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a).
% 248.03/248.09 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a).
% 248.03/248.09 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a).
% 248.03/248.09 0 [] hAPP(c_Type_Oshift(V_e,V_i,V_T,T_a),V_j)=hAPP(V_e,V_j)| -c_HOL_Oord__class_Oless(V_j,V_i,tc_nat).
% 248.03/248.09 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).
% 248.03/248.09 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).
% 248.03/248.09 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).
% 248.03/248.09 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a).
% 248.03/248.09 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a).
% 248.03/248.09 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 248.03/248.09 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a).
% 248.03/248.09 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,c_Suc(V_n),tc_nat),tc_nat,T_a)=c_HOL_Ozero__class_Ozero(T_a)| -c_HOL_Oord__class_Oless(V_n,V_m,tc_nat).
% 248.03/248.09 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)| -c_HOL_Oord__class_Oless(V_b,V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 248.03/248.09 0 [] c_Divides_Odiv__class_Omod(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat),tc_nat)),c_Divides_Odiv__class_Omod(V_a,V_b,tc_nat)).
% 248.03/248.09 0 [] hAPP(hAPP(hAPP(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).
% 248.03/248.09 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(V_a,V_c,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_c,V_b,T_a).
% 248.03/248.09 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a).
% 248.03/248.09 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a).
% 248.03/248.09 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_a,V_N,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(V_n,V_N,tc_nat).
% 248.03/248.09 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_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 248.03/248.09 0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat).
% 248.03/248.09 0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat).
% 248.03/248.09 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 248.03/248.09 0 [] c_Divides_Odiv__class_Odiv(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat).
% 248.03/248.09 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(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_Ring__and__Field_Odvd__class_Odvd(V_c,V_d,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 248.03/248.09 0 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Omod(V_q,V_c,tc_nat),tc_nat)),V_r),c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_r,V_b,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_c,tc_nat).
% 248.03/248.09 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Otimes__class_Otimes(V_r,V_c,T_a))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Otimes__class_Otimes(V_r,V_d,T_a))|V_c=V_d|V_r=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.09 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Otimes__class_Otimes(V_r,V_c,tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Otimes__class_Otimes(V_r,V_d,tc_nat))|V_c=V_d|V_r=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.09 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a))!=c_HOL_Ozero__class_Ozero(T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.09 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a))!=c_HOL_Ozero__class_Ozero(T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.09 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_x,c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 248.03/248.09 0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 248.03/248.09 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 248.03/248.09 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a).
% 248.03/248.09 0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 248.03/248.09 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 248.03/248.09 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a).
% 248.03/248.09 0 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k),tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 248.03/248.09 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat).
% 248.03/248.09 0 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 248.03/248.09 0 [] c_Type_Otyping(V_e,V_t_H,V_T)| -c_Lambda_Obeta(V_t,V_t_H)| -c_Type_Otyping(V_e,V_t,V_T).
% 248.03/248.09 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,c_Suc(V_n),tc_nat),tc_nat,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a)),hAPP(V_f,V_n))|c_HOL_Oord__class_Oless(V_n,V_m,tc_nat).
% 248.03/248.09 0 [] V_n=c_HOL_Oone__class_Oone(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(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).
% 248.03/248.09 0 [] V_n=c_HOL_Oone__class_Oone(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat).
% 248.03/248.09 0 [] -class_OrderedGroup_Oab__semigroup__idem__mult(T_a)|c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)=V_x.
% 248.03/248.09 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.09 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.09 0 [] c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_d,V_x,tc_nat),V_d,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.09 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OVar(V_nat_H)|V_nat=V_nat_H.
% 248.03/248.09 0 [] V_m=c_HOL_Oone__class_Oone(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 248.03/248.09 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=c_Lambda_OdB_OVar(V_nat).
% 248.03/248.09 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a))=V_a.
% 248.03/248.09 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),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))=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.09 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).
% 248.03/248.09 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).
% 248.03/248.09 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).
% 248.03/248.09 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).
% 248.03/248.09 0 [] V_n=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_x,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(V_x,V_n,tc_nat),tc_nat).
% 248.03/248.09 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)).
% 248.03/248.09 0 [] c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(V_nat),tc_Lambda_OdB)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.09 0 [] -class_OrderedGroup_Ocomm__monoid__mult(T_a)|c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_n,T_a)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a).
% 248.03/248.09 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_q,T_a)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_q,T_a),c_Power_Opower__class_Opower(V_y,V_q,T_a),T_a).
% 248.03/248.09 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(V_a,V_c,T_a)),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a).
% 248.03/248.09 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a)),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a).
% 248.03/248.09 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(V_m),V_n,tc_nat),tc_nat,T_a))| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 248.03/248.09 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a)=c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a).
% 248.03/248.09 0 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 248.03/248.09 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a)),c_Divides_Odiv__class_Omod(V_a,V_b,T_a))=V_a.
% 248.03/248.09 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a)),c_Divides_Odiv__class_Omod(V_a,V_b,T_a))=V_a.
% 248.03/248.09 0 [] -class_Divides_Osemiring__div(T_a)|V_a=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a)),c_Divides_Odiv__class_Omod(V_a,V_b,T_a)).
% 248.03/248.09 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(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_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a).
% 248.03/248.09 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(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_Otimes__class_Otimes(V_c,c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a).
% 248.03/248.09 0 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(V_s)),V_k)=c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,V_s),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))).
% 248.03/248.09 0 [] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(V_dB))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.09 0 [] c_HOL_Oone__class_Oone(tc_nat)!=c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)|V_m=c_HOL_Oone__class_Oone(tc_nat).
% 248.03/248.09 0 [] c_HOL_Oone__class_Oone(tc_nat)!=c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)|V_n=c_HOL_Oone__class_Oone(tc_nat).
% 248.03/248.09 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).
% 248.03/248.09 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).
% 248.03/248.09 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).
% 248.03/248.09 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).
% 248.03/248.09 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).
% 248.03/248.09 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).
% 248.03/248.09 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).
% 248.03/248.09 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_c,T_a)),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a)).
% 248.03/248.09 0 [] -class_Ring__and__Field_Ocomm__semiring(T_a)|c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_c,T_a)),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a)).
% 248.03/248.09 0 [] c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),V_k,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat)),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat)).
% 248.03/248.09 0 [] c_HOL_Otimes__class_Otimes(V_k,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)).
% 248.03/248.09 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z),T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a)).
% 248.03/248.09 0 [] c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,V_t),V_i),V_T)| -c_Type_Otyping(V_e,V_t,V_T).
% 248.03/248.09 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).
% 248.03/248.09 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).
% 248.03/248.09 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 248.03/248.09 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 248.03/248.09 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).
% 248.03/248.09 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).
% 248.03/248.09 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(V_t)),V_s),V_k)=c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_s),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))).
% 248.03/248.09 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_v),V_i)),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_v),V_j)),V_i)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i)),V_v),V_j)| -c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 248.03/248.09 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))).
% 248.03/248.09 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_ua______)).
% 248.03/248.09 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r)))| -hBOOL(hAPP(c_InductTermi_OIT,V_r)).
% 248.03/248.09 0 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,V_r),V_i),hAPP(hAPP(c_Lambda_Olift,V_s),V_i))| -c_Lambda_Obeta(V_r,V_s).
% 248.03/248.09 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),V_u),V_i)))| -c_Type_Otyping(V_e,V_u,v_T____)| -hBOOL(hAPP(c_InductTermi_OIT,V_u))| -c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),v_a____,V_T_H).
% 248.03/248.09 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(V_f,c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Ozero__class_Ozero(T_a)|c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_k,tc_nat),tc_nat,T_a)=c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat),tc_nat,T_a).
% 248.03/248.09 0 [] c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB1)),c_Lambda_OdB_OdB__size(V_dB2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.09 0 [] c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),tc_Lambda_OdB)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(V_dB2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.09 0 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.09 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)))| -c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB).
% 248.03/248.09 0 [] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____).
% 248.03/248.09 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)| -class_Ring__and__Field_Ono__zero__divisors(T_a)| -class_Ring__and__Field_Omult__zero(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a)=c_HOL_Ozero__class_Ozero(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.09 0 [] -class_Ring__and__Field_Osemiring__0(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a)=c_HOL_Ozero__class_Ozero(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.09 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)| -class_Ring__and__Field_Ono__zero__divisors(T_a)| -class_Ring__and__Field_Omult__zero(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a)!=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.09 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).
% 248.03/248.09 0 [] -class_Ring__and__Field_Osemiring__0(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Suc(V_n),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 248.03/248.09 0 [] V_y=c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(V_y))|V_y=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.09 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.09 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.03/248.09 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.03/248.09 0 [] hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat)))|hBOOL(hAPP(V_P,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(V_P))))| -hBOOL(hAPP(V_P,V_k)).
% 248.03/248.09 0 [] c_Power_Opower__class_Opower(V_x,V_m,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_x=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.09 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.03/248.09 0 [] hBOOL(hAPP(V_P,V_nat))| -hBOOL(hAPP(V_P,c_Suc(v_sko__List__Xlexn__Xinduct__1(V_P))))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.09 0 [] c_Divides_Odiv__class_Omod(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.09 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)).
% 248.03/248.09 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 248.03/248.09 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.09 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.03/248.09 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 248.03/248.09 0 [] c_HOL_Oone__class_Oone(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.03/248.09 0 [] c_Type_Oshift(c_Type_Oshift(V_e,V_i,V_U,T_a),c_HOL_Ozero__class_Ozero(tc_nat),V_T,T_a)=c_Type_Oshift(c_Type_Oshift(V_e,c_HOL_Ozero__class_Ozero(tc_nat),V_T,T_a),c_Suc(V_i),V_U,T_a).
% 248.03/248.09 0 [] hBOOL(hAPP(V_P,V_n))| -hBOOL(hAPP(V_P,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(V_P))))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.09 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)).
% 248.03/248.09 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)).
% 248.03/248.09 0 [] hBOOL(hAPP(V_P,V_nat))| -hBOOL(hAPP(V_P,c_Suc(v_sko__List__Xreplicate__Xinduct__1(V_P))))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.09 0 [] hBOOL(hAPP(V_P,V_nat))| -hBOOL(hAPP(V_P,c_Suc(v_sko__List__Xupt__Xinduct__1(V_P))))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.09 0 [] V_v=c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(V_v))|V_v=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.09 0 [] c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.03/248.09 0 [] hBOOL(hAPP(V_P,V_nat))| -hBOOL(hAPP(V_P,c_Suc(v_sko__Nat__Xnat__Xinduct__1(V_P))))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.09 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.03/248.09 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).
% 248.03/248.09 0 [] hBOOL(hAPP(V_P,V_nat))| -hBOOL(hAPP(V_P,c_Suc(v_sko__Nat__Xnat__Xinducts__1(V_P))))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.09 0 [] V_n=c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(V_n))|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.09 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_k,tc_nat).
% 248.03/248.09 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.09 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.09 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.03/248.09 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat).
% 248.03/248.09 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat).
% 248.03/248.09 0 [] c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat))!=V_n|c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.09 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.09 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.03/248.09 0 [] c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.03/248.09 0 [] c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.03/248.09 0 [] V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))| -c_Ring__and__Field_Odvd__class_Odvd(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 248.03/248.09 0 [] c_Divides_Odiv__class_Odiv(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=V_m.
% 248.03/248.09 0 [] -class_OrderedGroup_Omonoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_zs,T_a,T_a))=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_x,V_zs,T_a,T_a).
% 248.03/248.09 0 [] c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.03/248.09 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 248.03/248.09 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_m=V_n.
% 248.03/248.09 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_rs=V_ss.
% 248.03/248.09 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)|hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s)=V_t.
% 248.03/248.09 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)!=c_Lambda_OdB_OAbs(V_r)|V_s=c_Lambda_OdB_OAbs(V_r).
% 248.03/248.09 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_r=V_s.
% 248.03/248.09 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_rs=V_ss.
% 248.03/248.09 0 [] c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB))| -c_Lambda_Obeta(V_r,V_s).
% 248.03/248.09 0 [] c_Lambda_OdB_OVar(V_m)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|c_Lambda_OdB_OVar(V_m)=V_s.
% 248.03/248.09 0 [] c_Lambda_OdB_OAbs(V_r)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|c_Lambda_OdB_OAbs(V_r)=V_s.
% 248.03/248.09 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),c_Lambda_OdB_OVar(V_i))))| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 248.03/248.09 0 [] c_Type_Otypings(V_e,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts)| -c_Type_Otypings(c_Type_Oshift(V_e,V_i,V_T,tc_Type_Otype),V_ts,V_Ts)| -c_Type_Otyping(V_e,V_u,V_T).
% 248.03/248.09 0 [] c_Lambda_Oliftn(c_Suc(V_n),V_t,V_k)=hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(V_n,V_t,V_k)),V_k).
% 248.03/248.09 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),c_Lambda_OdB_OVar(V_i)),V_j)))| -hBOOL(hAPP(c_InductTermi_OIT,V_r)).
% 248.03/248.09 0 [] c_Type_Otypings(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts)| -c_Type_Otypings(V_e,V_ts,V_Ts).
% 248.03/248.09 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i)))| -c_Type_Otyping(V_e,V_u,v_T____)| -hBOOL(hAPP(c_InductTermi_OIT,V_u))| -c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),V_T_H).
% 248.03/248.09 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r)),V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(c_InductTermi_OIT,V_s))| -hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_s),c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))).
% 248.03/248.09 0 [] c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)| -c_List_Olistsp(c_InductTermi_OIT,V_ts,tc_Lambda_OdB).
% 248.03/248.09 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_a____)).
% 248.03/248.09 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_s),V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_k)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_s),V_k)).
% 248.03/248.09 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))).
% 248.03/248.09 0 [] V_n!=c_Suc(V_n).
% 248.03/248.09 0 [] c_Suc(V_n)!=V_n.
% 248.03/248.09 0 [] hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_i)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_t),V_i),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 248.03/248.09 0 [] c_Suc(V_m)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.09 0 [] c_Suc(V_nat_H)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.09 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)|V_dB1=V_dB1_H.
% 248.03/248.09 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)|V_dB2=V_dB2_H.
% 248.03/248.09 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)))| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 248.03/248.09 0 [] c_Suc(V_nat)!=c_Suc(V_nat_H)|V_nat=V_nat_H.
% 248.03/248.09 0 [] c_Suc(V_x)!=c_Suc(V_y)|V_x=V_y.
% 248.03/248.09 0 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_s),V_k)),hAPP(hAPP(c_Lambda_Olift,V_t),V_k)).
% 248.03/248.09 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 248.03/248.09 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_m).
% 248.03/248.09 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_nat_H).
% 248.03/248.09 0 [] hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R)=hAPP(hAPP(V_P,V_R),V_Q).
% 248.03/248.09 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)|V_r=V_s.
% 248.03/248.09 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_u____)).
% 248.03/248.09 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k)=V_t.
% 248.03/248.09 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))).
% 248.03/248.09 0 [] -hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),hAPP(hAPP(c_Lambda_Olift,v_u____),c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(v_i____))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))).
% 248.03/248.09 0 [] class_Orderings_Opreorder(tc_fun(T_2,T_1))| -class_Orderings_Opreorder(T_1).
% 248.03/248.09 0 [] class_Orderings_Oorder(tc_fun(T_2,T_1))| -class_Orderings_Oorder(T_1).
% 248.03/248.09 0 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 248.03/248.09 0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 248.03/248.09 0 [] class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat).
% 248.03/248.09 0 [] class_Ring__and__Field_Oordered__semiring__strict(tc_nat).
% 248.03/248.09 0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 248.03/248.09 0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 248.03/248.09 0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 248.03/248.09 0 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 248.03/248.09 0 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 248.03/248.09 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 248.03/248.09 0 [] class_OrderedGroup_Oab__semigroup__mult(tc_nat).
% 248.03/248.09 0 [] class_OrderedGroup_Ocomm__monoid__mult(tc_nat).
% 248.03/248.09 0 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 248.03/248.09 0 [] class_Ring__and__Field_Ocomm__semiring(tc_nat).
% 248.03/248.09 0 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 248.03/248.09 0 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 248.03/248.09 0 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 248.03/248.09 0 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 248.03/248.09 0 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 248.03/248.09 0 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 248.03/248.09 0 [] class_OrderedGroup_Omonoid__mult(tc_nat).
% 248.03/248.09 0 [] class_Ring__and__Field_Osemiring(tc_nat).
% 248.03/248.09 0 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 248.03/248.09 0 [] class_Divides_Osemiring__div(tc_nat).
% 248.03/248.09 0 [] class_Nat_Osemiring__char__0(tc_nat).
% 248.03/248.09 0 [] class_Ring__and__Field_Odvd(tc_nat).
% 248.03/248.09 0 [] class_Orderings_Opreorder(tc_nat).
% 248.03/248.09 0 [] class_Orderings_Olinorder(tc_nat).
% 248.03/248.09 0 [] class_Orderings_Oorder(tc_nat).
% 248.03/248.09 0 [] class_Power_Opower(tc_nat).
% 248.03/248.09 0 [] hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R)=hAPP(hAPP(V_P,V_R),V_Q).
% 248.03/248.09 0 [] c_COMBB(V_P,V_Q,V_R,T_b,T_a,T_c)=hAPP(V_P,hAPP(V_Q,V_R)).
% 248.03/248.09 0 [] c_fe_qual(V_x,V_x,T_a).
% 248.03/248.09 0 [] V_X=V_Y| -c_fe_qual(V_X,V_Y,T_a).
% 248.03/248.09 end_of_list.
% 248.03/248.09
% 248.03/248.09 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 248.03/248.09
% 248.03/248.09 This ia a non-Horn set with equality. The strategy will be
% 248.03/248.09 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 248.03/248.09 deletion, with positive clauses in sos and nonpositive
% 248.03/248.09 clauses in usable.
% 248.03/248.09
% 248.03/248.09 dependent: set(knuth_bendix).
% 248.03/248.09 dependent: set(anl_eq).
% 248.03/248.09 dependent: set(para_from).
% 248.03/248.09 dependent: set(para_into).
% 248.03/248.09 dependent: clear(para_from_right).
% 248.03/248.09 dependent: clear(para_into_right).
% 248.03/248.09 dependent: set(para_from_vars).
% 248.03/248.09 dependent: set(eq_units_both_ways).
% 248.03/248.09 dependent: set(dynamic_demod_all).
% 248.03/248.09 dependent: set(dynamic_demod).
% 248.03/248.09 dependent: set(order_eq).
% 248.03/248.09 dependent: set(back_demod).
% 248.03/248.09 dependent: set(lrpo).
% 248.03/248.09 dependent: set(hyper_res).
% 248.03/248.09 dependent: set(unit_deletion).
% 248.03/248.09 dependent: set(factor).
% 248.03/248.09
% 248.03/248.09 ------------> process usable:
% 248.03/248.09 ** KEPT (pick-wt=11): 1 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|A=c_HOL_Oone__class_Oone(tc_nat).
% 248.03/248.09 ** KEPT (pick-wt=9): 2 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 248.03/248.09 ** KEPT (pick-wt=17): 3 [] 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.
% 248.03/248.09 ** KEPT (pick-wt=15): 4 [] 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).
% 248.03/248.09 ** KEPT (pick-wt=15): 5 [] 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).
% 248.03/248.09 ** KEPT (pick-wt=16): 6 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A)).
% 248.03/248.09 ** KEPT (pick-wt=20): 7 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A).
% 248.03/248.09 ** KEPT (pick-wt=34): 9 [copy,8,flip.2] -class_Ring__and__Field_Osemiring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A)),E)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,D,A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(C,D,A)),E)).
% 248.03/248.09 ** KEPT (pick-wt=43): 10 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),D)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),D)),hAPP(hAPP(c_Lambda_Olift,B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)))| -c_HOL_Oord__class_Oless(D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 248.03/248.09 ** KEPT (pick-wt=13): 11 [] 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).
% 248.03/248.09 ** KEPT (pick-wt=13): 12 [] 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).
% 248.03/248.09 ** KEPT (pick-wt=22): 13 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 248.03/248.09 ** KEPT (pick-wt=13): 14 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,C,A)=c_HOL_Ozero__class_Ozero(A)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,A).
% 248.03/248.09 ** KEPT (pick-wt=13): 15 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|c_Ring__and__Field_Odvd__class_Odvd(C,B,A).
% 248.03/248.09 ** KEPT (pick-wt=21): 16 [] -class_Divides_Osemiring__div(A)|c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),D,A)=c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,D,A),C,A)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,A).
% 248.03/248.09 ** KEPT (pick-wt=10): 17 [] -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).
% 248.03/248.09 ** KEPT (pick-wt=16): 18 [] 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).
% 248.03/248.09 ** KEPT (pick-wt=11): 19 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|B=c_HOL_Oone__class_Oone(tc_nat).
% 248.03/248.09 ** KEPT (pick-wt=24): 21 [copy,20,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A).
% 248.03/248.09 ** KEPT (pick-wt=24): 23 [copy,22,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),D),C,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A).
% 248.03/248.09 ** KEPT (pick-wt=20): 24 [] -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat).
% 248.03/248.09 ** KEPT (pick-wt=12): 25 [] c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(A,B,tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 248.03/248.09 ** KEPT (pick-wt=10): 26 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A)=c_HOL_Oone__class_Oone(A).
% 248.03/248.09 ** KEPT (pick-wt=28): 27 [] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)=E.
% 248.03/248.09 ** KEPT (pick-wt=22): 28 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),A)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A).
% 248.03/248.09 ** KEPT (pick-wt=20): 29 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),tc_nat).
% 248.03/248.09 ** KEPT (pick-wt=25): 30 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 248.03/248.09 ** KEPT (pick-wt=25): 31 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)).
% 248.03/248.09 ** KEPT (pick-wt=25): 32 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C).
% 248.03/248.09 Following clause subsumed by 30 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 248.03/248.09 ** KEPT (pick-wt=25): 33 [] -class_OrderedGroup_Oab__semigroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 248.03/248.09 ** KEPT (pick-wt=25): 34 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)).
% 248.03/248.09 ** KEPT (pick-wt=25): 35 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 248.03/248.09 ** KEPT (pick-wt=25): 36 [] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)).
% 248.03/248.09 Following clause subsumed by 30 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 248.03/248.09 ** KEPT (pick-wt=14): 37 [] -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).
% 248.03/248.09 ** KEPT (pick-wt=14): 38 [] -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).
% 248.03/248.09 ** KEPT (pick-wt=21): 39 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,c_Suc(C),A),c_HOL_Oone__class_Oone(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 248.03/248.09 ** KEPT (pick-wt=27): 41 [copy,40,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),c_Divides_Odiv__class_Omod(D,C,A)),C,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A).
% 248.03/248.09 ** KEPT (pick-wt=11): 42 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,C,A)=c_HOL_Otimes__class_Otimes(C,B,A).
% 248.03/248.09 Following clause subsumed by 42 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).
% 248.03/248.09 ** KEPT (pick-wt=15): 43 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A).
% 248.03/248.09 Following clause subsumed by 43 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A).
% 248.03/248.09 ** KEPT (pick-wt=15): 44 [] -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A).
% 248.03/248.09 ** KEPT (pick-wt=15): 45 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),B,A).
% 248.03/248.09 ** KEPT (pick-wt=17): 46 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(B,C,A),D,A)=c_Power_Opower__class_Opower(B,c_HOL_Otimes__class_Otimes(C,D,tc_nat),A).
% 248.03/248.09 ** KEPT (pick-wt=13): 47 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),A,tc_nat).
% 248.03/248.09 ** KEPT (pick-wt=13): 48 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat),A,tc_nat).
% 248.03/248.09 ** KEPT (pick-wt=29): 49 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,C,A)),c_HOL_Otimes__class_Otimes(B,D,A))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,D,A)),c_HOL_Otimes__class_Otimes(B,C,A)).
% 248.03/248.09 Following clause subsumed by 49 during input processing: 0 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,C,A)),c_HOL_Otimes__class_Otimes(B,D,A))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,D,A)),c_HOL_Otimes__class_Otimes(B,C,A)).
% 248.03/248.09 ** KEPT (pick-wt=14): 50 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,A),C,A)=c_Divides_Odiv__class_Omod(B,C,A).
% 248.03/248.09 ** KEPT (pick-wt=15): 51 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(B,C,tc_nat),A)=c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(B,A),C,A).
% 248.03/248.09 ** KEPT (pick-wt=13): 52 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(B,B,A)=c_HOL_Oone__class_Oone(A)|B=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.09 ** KEPT (pick-wt=9): 53 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(C,B,A),A).
% 248.03/248.09 ** KEPT (pick-wt=9): 54 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(B,C,A),A).
% 248.03/248.09 ** KEPT (pick-wt=9): 55 [] -class_Ring__and__Field_Odvd(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(B,C,A),A).
% 248.03/248.09 ** KEPT (pick-wt=9): 56 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A)=B.
% 248.03/248.09 ** KEPT (pick-wt=9): 57 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oone__class_Oone(A),A)=B.
% 248.03/248.09 ** KEPT (pick-wt=9): 58 [] -class_OrderedGroup_Omonoid__mult(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oone__class_Oone(A),A)=B.
% 248.03/248.09 ** KEPT (pick-wt=9): 59 [] -class_OrderedGroup_Omonoid__mult(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A)=B.
% 248.03/248.09 ** KEPT (pick-wt=9): 60 [] -class_OrderedGroup_Ocomm__monoid__mult(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A)=B.
% 248.03/248.09 Following clause subsumed by 56 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A)=B.
% 248.03/248.09 ** KEPT (pick-wt=14): 61 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),B,tc_nat)=A| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 248.03/248.09 ** KEPT (pick-wt=14): 62 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),A,tc_nat)=B| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 248.03/248.09 ** KEPT (pick-wt=16): 63 [] -class_Ring__and__Field_Oidom(A)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A).
% 248.03/248.09 ** KEPT (pick-wt=16): 64 [] -class_Ring__and__Field_Oidom(A)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(C,D,A).
% 248.03/248.09 ** KEPT (pick-wt=14): 65 [] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat).
% 248.03/248.09 ** KEPT (pick-wt=20): 66 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,C,A),D,A),C,A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,D,A),C,A).
% 248.03/248.09 ** KEPT (pick-wt=32): 68 [copy,67,flip.2] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(B,C,A)),c_Divides_Odiv__class_Odiv(D,C,A))=c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A)| -c_Ring__and__Field_Odvd__class_Odvd(C,D,A)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,A).
% 248.03/248.09 ** KEPT (pick-wt=29): 69 [] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,A),A)),c_Divides_Odiv__class_Omod(C,B,A))),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D).
% 248.03/248.09 ** KEPT (pick-wt=29): 70 [] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A)),c_Divides_Odiv__class_Omod(B,C,A))),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D).
% 248.03/248.09 ** KEPT (pick-wt=26): 71 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(D,C,tc_nat).
% 248.03/248.09 ** KEPT (pick-wt=13): 72 [] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 248.03/248.09 ** KEPT (pick-wt=13): 73 [] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 248.03/248.09 ** KEPT (pick-wt=13): 74 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 248.03/248.09 Following clause subsumed by 72 during input processing: 0 [] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 248.03/248.09 Following clause subsumed by 73 during input processing: 0 [] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 248.03/248.09 ** KEPT (pick-wt=17): 75 [] -class_Divides_Osemiring__div(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A).
% 248.03/248.09 ** KEPT (pick-wt=17): 76 [] -class_Divides_Osemiring__div(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A).
% 248.03/248.09 Following clause subsumed by 75 during input processing: 0 [] -class_Divides_Osemiring__div(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A).
% 248.03/248.09 Following clause subsumed by 76 during input processing: 0 [] -class_Divides_Osemiring__div(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,A).
% 248.03/248.09 ** KEPT (pick-wt=16): 77 [] c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(A,B,tc_nat)),A,tc_nat)=c_HOL_Oone__class_Oone(tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat).
% 248.03/248.09 ** KEPT (pick-wt=15): 78 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B).
% 248.03/248.09 ** KEPT (pick-wt=15): 79 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B).
% 248.03/248.09 ** KEPT (pick-wt=21): 80 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)| -c_HOL_Oord__class_Oless(C,B,tc_nat)|c_HOL_Oord__class_Oless(A,D,tc_nat).
% 248.03/248.10 Following clause subsumed by 78 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B).
% 248.03/248.10 ** KEPT (pick-wt=11): 81 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A),A).
% 248.03/248.10 ** KEPT (pick-wt=12): 82 [] -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.
% 248.03/248.10 ** KEPT (pick-wt=10): 83 [] hAPP(A,B)=C| -c_Type_Otyping(A,c_Lambda_OdB_OVar(B),C).
% 248.03/248.10 ** KEPT (pick-wt=12): 84 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(B,C,A),C,A)=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.10 ** KEPT (pick-wt=16): 85 [] c_Divides_Odiv__class_Odiv(A,B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=23): 87 [copy,86,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,C,A),c_Divides_Odiv__class_Omod(D,C,A),A),C,A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,D,A),C,A).
% 248.03/248.10 ** KEPT (pick-wt=17): 88 [] -class_OrderedGroup_Omonoid__mult(A)|c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),B,A)=c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A).
% 248.03/248.10 ** KEPT (pick-wt=22): 90 [copy,89,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),A)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A).
% 248.03/248.10 ** KEPT (pick-wt=28): 91 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Otimes__class_Otimes(C,D,A)),C,A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),c_Divides_Odiv__class_Odiv(B,C,A))|C=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.10 ** KEPT (pick-wt=28): 92 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Otimes__class_Otimes(C,D,A)),D,A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),c_Divides_Odiv__class_Odiv(B,D,A))|D=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.10 ** KEPT (pick-wt=20): 93 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B)=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)),B,A).
% 248.03/248.10 ** KEPT (pick-wt=16): 94 [] 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).
% 248.03/248.10 ** KEPT (pick-wt=16): 95 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)|B=C.
% 248.03/248.10 ** KEPT (pick-wt=16): 96 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B)|A=C.
% 248.03/248.10 Following clause subsumed by 95 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)|B=C.
% 248.03/248.10 ** KEPT (pick-wt=20): 97 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)|C=D.
% 248.03/248.10 ** KEPT (pick-wt=18): 98 [] -class_OrderedGroup_Ocancel__ab__semigroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)|C=D.
% 248.03/248.10 ** KEPT (pick-wt=18): 99 [] -class_OrderedGroup_Ocancel__semigroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)|C=D.
% 248.03/248.10 ** KEPT (pick-wt=18): 100 [] -class_OrderedGroup_Ocancel__semigroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C)|B=D.
% 248.03/248.10 ** KEPT (pick-wt=16): 101 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A).
% 248.03/248.10 Following clause subsumed by 66 during input processing: 0 [flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,A),C,A),D,A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),D,A).
% 248.03/248.10 ** KEPT (pick-wt=20): 103 [copy,102,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Omod(C,D,A),A),D,A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),D,A).
% 248.03/248.10 ** KEPT (pick-wt=24): 104 [] -class_Divides_Osemiring__div(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(B,D,A),c_Divides_Odiv__class_Odiv(C,D,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(D,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(D,B,A).
% 248.03/248.10 ** KEPT (pick-wt=24): 105 [] -class_Divides_Osemiring__div(A)|c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(B,C,A),c_Divides_Odiv__class_Odiv(D,C,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A)| -c_Ring__and__Field_Odvd__class_Odvd(C,D,A)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,A).
% 248.03/248.10 ** KEPT (pick-wt=11): 106 [] c_Divides_Odiv__class_Odiv(A,B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=22): 107 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,B,A)),c_HOL_Otimes__class_Otimes(C,C,A)),A)|B=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.10 ** KEPT (pick-wt=22): 108 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,B,A)),c_HOL_Otimes__class_Otimes(C,C,A)),A)|C=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.10 ** KEPT (pick-wt=35): 109 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)).
% 248.03/248.10 ** KEPT (pick-wt=9): 110 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=12): 111 [] c_Lambda_Oliftn(A,c_Lambda_OdB_OVar(B),C)=c_Lambda_OdB_OVar(B)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=19): 112 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,A).
% 248.03/248.10 ** KEPT (pick-wt=22): 113 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=20): 114 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=22): 115 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=20): 116 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=15): 117 [] -class_Divides_Osemiring__div(A)|c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A)=B| -c_Ring__and__Field_Odvd__class_Odvd(C,B,A).
% 248.03/248.10 ** KEPT (pick-wt=15): 118 [] -class_Divides_Osemiring__div(A)|c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,A),A)=C| -c_Ring__and__Field_Odvd__class_Odvd(B,C,A).
% 248.03/248.10 ** KEPT (pick-wt=13): 119 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(A)),B)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=25): 120 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A),c_Power_Opower__class_Opower(B,C,A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 248.03/248.10 ** KEPT (pick-wt=43): 121 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),D)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,B),D)),C)| -c_HOL_Oord__class_Oless(C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=30): 122 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,A),B)),c_Suc(C))=hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,A),C)),B)| -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=19): 123 [] 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).
% 248.03/248.10 ** KEPT (pick-wt=19): 124 [] 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).
% 248.03/248.10 Following clause subsumed by 124 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).
% 248.03/248.10 Following clause subsumed by 123 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).
% 248.03/248.10 ** KEPT (pick-wt=19): 125 [] 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).
% 248.03/248.10 Following clause subsumed by 124 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).
% 248.03/248.10 ** KEPT (pick-wt=21): 126 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=21): 127 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=21): 128 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=21): 129 [] -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).
% 248.03/248.10 Following clause subsumed by 127 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).
% 248.03/248.10 ** KEPT (pick-wt=21): 130 [] -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).
% 248.03/248.10 Following clause subsumed by 129 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).
% 248.03/248.10 Following clause subsumed by 127 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).
% 248.03/248.10 ** KEPT (pick-wt=21): 131 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=21): 132 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=21): 133 [] -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).
% 248.03/248.10 Following clause subsumed by 131 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).
% 248.03/248.10 ** KEPT (pick-wt=21): 134 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=19): 135 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(C,A,tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=21): 136 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)=c_Divides_Odiv__class_Odiv(C,D,A)|B=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.10 ** KEPT (pick-wt=21): 137 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)=c_Divides_Odiv__class_Odiv(B,D,A)|C=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.10 ** KEPT (pick-wt=22): 138 [] -c_Type_Otyping(A,B,C)| -c_Type_Otyping(c_Type_Oshift(A,D,C,tc_Type_Otype),E,F)|c_Type_Otyping(A,hAPP(hAPP(hAPP(c_Lambda_Osubst,E),B),D),F).
% 248.03/248.10 ** KEPT (pick-wt=14): 139 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)),A).
% 248.03/248.10 ** KEPT (pick-wt=19): 140 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Otimes__class_Otimes(C,D,A)),D,A)=c_Divides_Odiv__class_Omod(B,D,A).
% 248.03/248.10 ** KEPT (pick-wt=19): 141 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Otimes__class_Otimes(C,D,A)),C,A)=c_Divides_Odiv__class_Omod(B,C,A).
% 248.03/248.10 ** KEPT (pick-wt=24): 142 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,C,A)),c_HOL_Otimes__class_Otimes(D,C,A))=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A).
% 248.03/248.10 ** KEPT (pick-wt=16): 143 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|c_HOL_Oord__class_Oless(B,c_HOL_Otimes__class_Otimes(A,c_Suc(c_Divides_Odiv__class_Odiv(B,A,tc_nat)),tc_nat),tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=18): 144 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)|C=c_HOL_Ozero__class_Ozero(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(C,A,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=20): 145 [] -class_Ring__and__Field_Oidom(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A)|D=c_HOL_Ozero__class_Ozero(A)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A).
% 248.03/248.10 ** KEPT (pick-wt=20): 146 [] -class_Ring__and__Field_Oidom(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A)|D=c_HOL_Ozero__class_Ozero(A)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 248.03/248.10 ** KEPT (pick-wt=26): 148 [copy,147,flip.2] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(B,C,A)),c_HOL_Oone__class_Oone(A))=c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B),C,A)|C=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.10 ** KEPT (pick-wt=26): 150 [copy,149,flip.2] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(B,C,A)),c_HOL_Oone__class_Oone(A))=c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A)|C=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.10 ** KEPT (pick-wt=22): 151 [] -class_Ring__and__Field_Oordered__ring__strict(A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),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).
% 248.03/248.10 ** KEPT (pick-wt=8): 152 [] c_Lambda_Obeta(c_Lambda_OdB_OAbs(A),c_Lambda_OdB_OAbs(B))| -c_Lambda_Obeta(A,B).
% 248.03/248.10 ** KEPT (pick-wt=20): 153 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Otimes__class_Otimes(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A).
% 248.03/248.10 ** KEPT (pick-wt=9): 154 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(B,c_HOL_Oone__class_Oone(A),A)=B.
% 248.03/248.10 ** KEPT (pick-wt=27): 155 [] -c_HOL_Oord__class_Oless(A,B,tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat)| -hBOOL(hAPP(C,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(B,D,tc_nat)),A),B,tc_nat)))|hBOOL(hAPP(C,A)).
% 248.03/248.10 Following clause subsumed by 73 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 248.03/248.10 Following clause subsumed by 72 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=17): 156 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A).
% 248.03/248.10 ** KEPT (pick-wt=17): 157 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 248.03/248.10 ** KEPT (pick-wt=16): 158 [] -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat).
% 248.03/248.10 Following clause subsumed by 158 during input processing: 0 [] -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=19): 159 [] -class_Ring__and__Field_Ozero__ne_q__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.10 ** KEPT (pick-wt=13): 160 [] -class_Ring__and__Field_Oring__1__no__zero__divisors(A)|c_Power_Opower__class_Opower(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.10 ** KEPT (pick-wt=10): 161 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=10): 162 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=10): 163 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=10): 164 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=10): 165 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=10): 166 [] -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).
% 248.03/248.10 Following clause subsumed by 161 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).
% 248.03/248.10 ** KEPT (pick-wt=7): 167 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ozero__class_Ozero(A),A).
% 248.03/248.10 ** KEPT (pick-wt=7): 169 [copy,168,flip.2] -class_Ring__and__Field_Ozero__ne_q__one(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Oone__class_Oone(A).
% 248.03/248.10 ** KEPT (pick-wt=17): 170 [] -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).
% 248.03/248.10 Following clause subsumed by 170 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)|C=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.10 ** KEPT (pick-wt=17): 171 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=10): 172 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.10 ** KEPT (pick-wt=10): 173 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.10 ** KEPT (pick-wt=5): 174 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 248.03/248.10 ** KEPT (pick-wt=9): 175 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A)=B.
% 248.03/248.10 ** KEPT (pick-wt=9): 176 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A)=B.
% 248.03/248.10 ** KEPT (pick-wt=39): 177 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,C,A)!=c_Divides_Odiv__class_Omod(D,C,A)|c_Divides_Odiv__class_Omod(E,C,A)!=c_Divides_Odiv__class_Omod(F,C,A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),E),B),C,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),F),D),C,A).
% 248.03/248.10 ** KEPT (pick-wt=17): 178 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 248.03/248.10 ** KEPT (pick-wt=17): 179 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A).
% 248.03/248.10 ** KEPT (pick-wt=17): 180 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A).
% 248.03/248.10 ** KEPT (pick-wt=17): 181 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 248.03/248.10 ** KEPT (pick-wt=20): 182 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=20): 183 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=20): 184 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=20): 185 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=18): 186 [] 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).
% 248.03/248.10 ** KEPT (pick-wt=15): 187 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 248.03/248.10 ** KEPT (pick-wt=13): 188 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=27): 189 [] -c_HOL_Oord__class_Oless(A,B,tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat)| -hBOOL(hAPP(C,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(B,D,tc_nat)),A),B,tc_nat)))|hBOOL(hAPP(C,D)).
% 248.03/248.10 ** KEPT (pick-wt=24): 190 [] -class_Divides_Osemiring__div(A)|c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(B,C,A),D,A)=c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,A).
% 248.03/248.10 ** KEPT (pick-wt=8): 191 [] -class_Ring__and__Field_Oordered__semidom(A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A).
% 248.03/248.10 ** KEPT (pick-wt=8): 192 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OAbs(B)|A=B.
% 248.03/248.10 ** KEPT (pick-wt=18): 193 [] -class_Ring__and__Field_Oordered__ring__strict(A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,B,A)),c_HOL_Otimes__class_Otimes(C,C,A)),c_HOL_Ozero__class_Ozero(A),A).
% 248.03/248.10 ** KEPT (pick-wt=17): 194 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=35): 195 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,C,A)),c_HOL_Otimes__class_Otimes(D,E,A))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,E,A)),c_HOL_Otimes__class_Otimes(D,C,A))|C=E|B=D.
% 248.03/248.10 Following clause subsumed by 195 during input processing: 0 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,C,A)),c_HOL_Otimes__class_Otimes(D,E,A))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,E,A)),c_HOL_Otimes__class_Otimes(D,C,A))|C=E|B=D.
% 248.03/248.10 ** KEPT (pick-wt=31): 196 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),c_HOL_Otimes__class_Otimes(C,D,tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,D,tc_nat)),c_HOL_Otimes__class_Otimes(C,B,tc_nat))|B=D|A=C.
% 248.03/248.10 Following clause subsumed by 196 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),c_HOL_Otimes__class_Otimes(C,D,tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,D,tc_nat)),c_HOL_Otimes__class_Otimes(C,B,tc_nat))|B=D|A=C.
% 248.03/248.10 ** KEPT (pick-wt=15): 197 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),C,A)=B|C=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.10 ** KEPT (pick-wt=15): 198 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),B,A)=C|B=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.10 ** KEPT (pick-wt=14): 200 [copy,199,flip.1] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=A|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Oone__class_Oone(tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=35): 201 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,C,A)!=c_Divides_Odiv__class_Omod(D,C,A)|c_Divides_Odiv__class_Omod(E,C,A)!=c_Divides_Odiv__class_Omod(F,C,A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(E,B,A),C,A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(F,D,A),C,A).
% 248.03/248.10 ** KEPT (pick-wt=23): 202 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=23): 203 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=23): 204 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=22): 205 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,C,A)),C)=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)),C,A).
% 248.03/248.10 ** KEPT (pick-wt=22): 206 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Otimes__class_Otimes(C,B,A))=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),c_HOL_Oone__class_Oone(A)),B,A).
% 248.03/248.10 ** KEPT (pick-wt=10): 207 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,c_HOL_Oone__class_Oone(A),A)=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.10 ** KEPT (pick-wt=13): 208 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=13): 209 [] c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=10): 210 [] c_Divides_Odiv__class_Omod(A,B,tc_nat)=A| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=4): 211 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 248.03/248.10 Following clause subsumed by 211 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=6): 212 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 248.03/248.10 ** KEPT (pick-wt=6): 213 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 248.03/248.10 ** KEPT (pick-wt=6): 214 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 248.03/248.10 ** KEPT (pick-wt=22): 215 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 248.03/248.10 ** KEPT (pick-wt=18): 216 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A).
% 248.03/248.10 ** KEPT (pick-wt=13): 217 [] -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.
% 248.03/248.10 ** KEPT (pick-wt=13): 218 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(C,B,A)|c_HOL_Oord__class_Oless(B,C,A).
% 248.03/248.10 ** KEPT (pick-wt=11): 219 [] A=B| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 248.03/248.10 Following clause subsumed by 219 during input processing: 0 [] A=B| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 248.03/248.10 Following clause subsumed by 219 during input processing: 0 [] -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)|B=A| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat).
% 248.03/248.10 Following clause subsumed by 219 during input processing: 0 [] A=B| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 248.03/248.10 Following clause subsumed by 219 during input processing: 0 [] A=B| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat).
% 248.03/248.10 Following clause subsumed by 219 during input processing: 0 [] -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)|B=A| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat).
% 248.03/248.10 Following clause subsumed by 219 during input processing: 0 [] -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat)|B=A.
% 248.03/248.10 Following clause subsumed by 218 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.
% 248.03/248.10 Following clause subsumed by 218 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).
% 248.03/248.10 Following clause subsumed by 218 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A).
% 248.03/248.10 ** KEPT (pick-wt=13): 220 [] -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_HOL_Oord__class_Oless(B,A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=24): 221 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A)| -c_HOL_Oord__class_Oless(C,E,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 248.03/248.10 ** KEPT (pick-wt=22): 222 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat)| -c_HOL_Oord__class_Oless(B,D,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=14): 223 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(D,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A).
% 248.03/248.10 ** KEPT (pick-wt=6): 224 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,B,A).
% 248.03/248.10 ** KEPT (pick-wt=20): 225 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=12): 226 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=16): 227 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,c_Suc(C),A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A).
% 248.03/248.10 ** KEPT (pick-wt=4): 228 [] -c_Lambda_Obeta(c_Lambda_OdB_OVar(A),B).
% 248.03/248.10 ** KEPT (pick-wt=14): 229 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=14): 230 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=14): 231 [] -class_Ring__and__Field_Oidom(A)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(C,c_HOL_Ozero__class_Ozero(A),A),A).
% 248.03/248.10 ** KEPT (pick-wt=14): 232 [] -class_Ring__and__Field_Oidom(A)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),C,A),A).
% 248.03/248.10 ** KEPT (pick-wt=8): 233 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A).
% 248.03/248.10 ** KEPT (pick-wt=14): 234 [] 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).
% 248.03/248.10 ** KEPT (pick-wt=14): 235 [] 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).
% 248.03/248.10 Following clause subsumed by 65 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=19): 236 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(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).
% 248.03/248.10 Following clause subsumed by 236 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(C,A,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=12): 237 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)),A).
% 248.03/248.10 ** KEPT (pick-wt=17): 238 [] c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(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_Oone__class_Oone(tc_nat),B,tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=14): 239 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=31): 240 [] -class_Divides_Osemiring__div(A)|c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),c_Divides_Odiv__class_Odiv(D,E,A),A)=c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,E,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(E,D,A)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,A).
% 248.03/248.10 ** KEPT (pick-wt=28): 241 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Otimes__class_Otimes(B,C,tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Otimes__class_Otimes(B,E,tc_nat))|c_Divides_Odiv__class_Omod(A,B,tc_nat)=c_Divides_Odiv__class_Omod(D,B,tc_nat).
% 248.03/248.10 ** KEPT (pick-wt=14): 242 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=14): 243 [] -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).
% 248.03/248.10 ** KEPT (pick-wt=7): 244 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(A),B,A).
% 248.03/248.10 ** KEPT (pick-wt=19): 245 [] -class_Ring__and__Field_Oordered__semidom(A)|c_Power_Opower__class_Opower(B,C,A)!=c_Power_Opower__class_Opower(B,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A)|C=D.
% 248.03/248.11 ** KEPT (pick-wt=10): 246 [] -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 248.03/248.11 ** KEPT (pick-wt=15): 247 [] -class_OrderedGroup_Olordered__ab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.11 ** KEPT (pick-wt=16): 249 [copy,248,flip.3] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=B|C=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.11 ** KEPT (pick-wt=9): 250 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.11 ** KEPT (pick-wt=9): 251 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 248.03/248.11 ** KEPT (pick-wt=10): 252 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.11 ** KEPT (pick-wt=13): 253 [] -class_OrderedGroup_Olordered__ab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.11 Following clause subsumed by 169 during input processing: 0 [] -class_Ring__and__Field_Ozero__ne_q__one(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Oone__class_Oone(A).
% 248.03/248.11 ** KEPT (pick-wt=11): 254 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|B=c_HOL_Ozero__class_Ozero(A)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(A),B,A).
% 248.03/248.11 ** KEPT (pick-wt=11): 255 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 248.03/248.11 ** KEPT (pick-wt=11): 256 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 248.03/248.11 ** KEPT (pick-wt=13): 258 [copy,257,flip.3] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 248.03/248.11 ** KEPT (pick-wt=11): 259 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 248.03/248.11 ** KEPT (pick-wt=11): 260 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 248.03/248.11 ** KEPT (pick-wt=11): 261 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 248.03/248.11 ** KEPT (pick-wt=11): 262 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 248.03/248.11 Following clause subsumed by 255 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 248.03/248.11 Following clause subsumed by 246 during input processing: 0 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 248.03/248.11 ** KEPT (pick-wt=12): 263 [] -hBOOL(hAPP(A,B))|hBOOL(hAPP(A,c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))).
% 248.03/248.11 ** KEPT (pick-wt=12): 264 [] -hBOOL(hAPP(A,c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))|hBOOL(hAPP(A,B)).
% 248.03/248.11 ** KEPT (pick-wt=10): 266 [copy,265,factor_simp] hBOOL(hAPP(A,v_sko__List__Xlexn__Xinduct__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.11 ** KEPT (pick-wt=10): 268 [copy,267,factor_simp] hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)))| -hBOOL(hAPP(A,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(A))).
% 248.03/248.11 Following clause subsumed by 211 during input processing: 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=13): 269 [] hBOOL(hAPP(A,c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.11 Following clause subsumed by 269 during input processing: 0 [] -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)))|hBOOL(hAPP(A,c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))).
% 248.03/248.11 ** KEPT (pick-wt=13): 270 [] -hBOOL(hAPP(A,c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))|hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.11 ** KEPT (pick-wt=10): 272 [copy,271,factor_simp] hBOOL(hAPP(A,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.11 ** KEPT (pick-wt=15): 273 [] 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).
% 248.03/248.11 ** KEPT (pick-wt=13): 274 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=13): 275 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=16): 276 [] 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.
% 248.03/248.11 ** KEPT (pick-wt=16): 277 [] 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.
% 248.03/248.11 Following clause subsumed by 277 during input processing: 0 [] 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).
% 248.03/248.11 ** KEPT (pick-wt=12): 279 [copy,278,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.11 Following clause subsumed by 279 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=10): 281 [copy,280,factor_simp] hBOOL(hAPP(A,v_sko__List__Xreplicate__Xinduct__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.11 ** KEPT (pick-wt=10): 283 [copy,282,factor_simp] hBOOL(hAPP(A,v_sko__Nat__Xnat__Xinducts__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.11 ** KEPT (pick-wt=10): 285 [copy,284,factor_simp] hBOOL(hAPP(A,v_sko__Nat__Xnat__Xinduct__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.11 ** KEPT (pick-wt=5): 286 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 248.03/248.11 Following clause subsumed by 286 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=10): 288 [copy,287,factor_simp] hBOOL(hAPP(A,v_sko__List__Xupt__Xinduct__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.11 ** KEPT (pick-wt=19): 289 [] 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).
% 248.03/248.11 ** KEPT (pick-wt=19): 290 [] 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).
% 248.03/248.11 ** KEPT (pick-wt=21): 291 [] 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).
% 248.03/248.11 ** KEPT (pick-wt=14): 292 [] c_HOL_Otimes__class_Otimes(c_Suc(A),B,tc_nat)!=c_HOL_Otimes__class_Otimes(c_Suc(A),C,tc_nat)|B=C.
% 248.03/248.11 ** KEPT (pick-wt=9): 293 [] c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=9): 294 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=13): 295 [] 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).
% 248.03/248.11 ** KEPT (pick-wt=12): 296 [] A=B| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)|c_HOL_Oord__class_Oless(A,B,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=12): 297 [] A=B| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 248.03/248.11 Following clause subsumed by 296 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).
% 248.03/248.11 ** KEPT (pick-wt=13): 298 [] c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat)|c_Suc(A)=B| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=9): 299 [] -c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=10): 300 [] c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=10): 301 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat).
% 248.03/248.11 Following clause subsumed by 300 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).
% 248.03/248.11 ** KEPT (pick-wt=8): 302 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 248.03/248.11 ** KEPT (pick-wt=8): 303 [] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 248.03/248.11 ** KEPT (pick-wt=8): 304 [] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 248.03/248.11 ** KEPT (pick-wt=14): 305 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),hAPP(hAPP(c_Lambda_OdB_OApp,A),C))| -c_Lambda_Obeta(B,C).
% 248.03/248.11 ** KEPT (pick-wt=14): 306 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),hAPP(hAPP(c_Lambda_OdB_OApp,C),B))| -c_Lambda_Obeta(A,C).
% 248.03/248.11 ** KEPT (pick-wt=8): 307 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 248.03/248.11 ** KEPT (pick-wt=12): 308 [] c_List_Omap(A,B,C,D)!=c_List_Olist_ONil(D)|B=c_List_Olist_ONil(C).
% 248.03/248.11 ** KEPT (pick-wt=12): 309 [] c_List_Olist_ONil(A)!=c_List_Omap(B,C,D,A)|C=c_List_Olist_ONil(D).
% 248.03/248.11 ** KEPT (pick-wt=23): 310 [] A=B| -c_Type_Otyping(C,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(D),E,tc_Lambda_OdB,tc_Lambda_OdB),B)| -c_Type_Otyping(C,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(D),E,tc_Lambda_OdB,tc_Lambda_OdB),A).
% 248.03/248.11 ** KEPT (pick-wt=13): 311 [] c_Lambda_OdB_OAbs(A)!=c_List_Ofoldl(c_Lambda_OdB_OApp,B,C,tc_Lambda_OdB,tc_Lambda_OdB)|C=c_List_Olist_ONil(tc_Lambda_OdB).
% 248.03/248.11 ** KEPT (pick-wt=15): 312 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(C),D,tc_Lambda_OdB,tc_Lambda_OdB).
% 248.03/248.11 ** KEPT (pick-wt=13): 313 [] c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_Lambda_OdB_OAbs(C)|B=c_List_Olist_ONil(tc_Lambda_OdB).
% 248.03/248.11 ** KEPT (pick-wt=13): 314 [] c_Lambda_OdB_OVar(A)!=c_List_Ofoldl(c_Lambda_OdB_OApp,B,C,tc_Lambda_OdB,tc_Lambda_OdB)|C=c_List_Olist_ONil(tc_Lambda_OdB).
% 248.03/248.11 ** KEPT (pick-wt=14): 315 [] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(C),D,tc_Lambda_OdB,tc_Lambda_OdB).
% 248.03/248.11 ** KEPT (pick-wt=27): 317 [copy,316,flip.2] -class_OrderedGroup_Osemigroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,D,A,A))=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A,A).
% 248.03/248.11 ** KEPT (pick-wt=18): 318 [] c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C),hAPP(hAPP(hAPP(c_Lambda_Osubst,D),B),C))| -c_Lambda_Obeta(A,D).
% 248.03/248.11 ** KEPT (pick-wt=10): 319 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 248.03/248.11 ** KEPT (pick-wt=20): 320 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=17): 321 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),C,A),A)=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.11 Following clause subsumed by 43 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A).
% 248.03/248.11 ** KEPT (pick-wt=15): 323 [copy,322,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),B,A).
% 248.03/248.11 ** KEPT (pick-wt=16): 324 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A)=c_Divides_Odiv__class_Omod(B,C,A).
% 248.03/248.11 ** KEPT (pick-wt=16): 325 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),B,A)=c_Divides_Odiv__class_Omod(C,B,A).
% 248.03/248.11 ** KEPT (pick-wt=15): 326 [] hAPP(c_Type_Oshift(A,B,C,D),E)=hAPP(A,E)| -c_HOL_Oord__class_Oless(E,B,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=20): 327 [] -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).
% 248.03/248.11 ** KEPT (pick-wt=20): 328 [] -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).
% 248.03/248.11 Following clause subsumed by 327 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).
% 248.03/248.11 ** KEPT (pick-wt=13): 329 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(D,B,A),C,A).
% 248.03/248.11 ** KEPT (pick-wt=13): 330 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,D,A),C,A).
% 248.03/248.11 ** KEPT (pick-wt=13): 331 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(C,D,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,A).
% 248.03/248.11 ** KEPT (pick-wt=13): 332 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(C,D,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A).
% 248.03/248.11 ** KEPT (pick-wt=18): 333 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,c_Suc(D),tc_nat),tc_nat,A)=c_HOL_Ozero__class_Ozero(A)| -c_HOL_Oord__class_Oless(D,C,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=20): 334 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A).
% 248.03/248.11 ** KEPT (pick-wt=15): 335 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),C)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=18): 336 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,A),D,A)=c_Divides_Odiv__class_Omod(B,D,A)| -c_Ring__and__Field_Odvd__class_Odvd(D,C,A).
% 248.03/248.11 ** KEPT (pick-wt=21): 337 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A).
% 248.03/248.11 ** KEPT (pick-wt=21): 338 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A).
% 248.03/248.11 Following clause subsumed by 337 during input processing: 0 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A)| -c_HOL_Oord__class_Oless(C,D,tc_nat).
% 248.03/248.11 Following clause subsumed by 338 during input processing: 0 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A).
% 248.03/248.11 ** KEPT (pick-wt=9): 339 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=9): 340 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=20): 341 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A).
% 248.03/248.11 ** KEPT (pick-wt=20): 342 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(C,E,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A).
% 248.03/248.11 ** KEPT (pick-wt=27): 343 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat)),D),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(D,A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=30): 344 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Otimes__class_Otimes(C,D,A))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Otimes__class_Otimes(C,E,A))|D=E|C=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.11 ** KEPT (pick-wt=26): 345 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Otimes__class_Otimes(B,C,tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Otimes__class_Otimes(B,D,tc_nat))|C=D|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=21): 346 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,B,A)),c_HOL_Otimes__class_Otimes(C,C,A))!=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.11 ** KEPT (pick-wt=21): 347 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,B,A)),c_HOL_Otimes__class_Otimes(C,C,A))!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.11 ** KEPT (pick-wt=14): 348 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_Power_Opower__class_Opower(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=20): 349 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A)| -c_HOL_Oord__class_Oless(B,D,A).
% 248.03/248.11 ** KEPT (pick-wt=20): 350 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A)| -c_HOL_Oord__class_Oless(B,D,A).
% 248.03/248.11 ** KEPT (pick-wt=20): 351 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A).
% 248.03/248.11 ** KEPT (pick-wt=20): 352 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A)| -c_HOL_Oord__class_Oless(C,D,A).
% 248.03/248.11 ** KEPT (pick-wt=20): 353 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A)| -c_HOL_Oord__class_Oless(C,D,A).
% 248.03/248.11 ** KEPT (pick-wt=20): 354 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A).
% 248.03/248.11 ** KEPT (pick-wt=18): 355 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=18): 356 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=18): 357 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=11): 358 [] c_Type_Otyping(A,B,C)| -c_Lambda_Obeta(D,B)| -c_Type_Otyping(A,D,C).
% 248.03/248.11 ** KEPT (pick-wt=31): 359 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,c_Suc(D),tc_nat),tc_nat,A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,A)),hAPP(B,D))|c_HOL_Oord__class_Oless(D,C,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=16): 360 [] A=c_HOL_Oone__class_Oone(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,A,tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=16): 361 [] A=c_HOL_Oone__class_Oone(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,B,tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=8): 362 [] -class_OrderedGroup_Oab__semigroup__idem__mult(A)|c_HOL_Otimes__class_Otimes(B,B,A)=B.
% 248.03/248.11 ** KEPT (pick-wt=12): 363 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),C,A)=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.11 ** KEPT (pick-wt=12): 364 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.11 ** KEPT (pick-wt=8): 365 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OVar(B)|A=B.
% 248.03/248.11 ** KEPT (pick-wt=9): 366 [] A=c_HOL_Oone__class_Oone(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=5): 367 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 248.03/248.11 ** KEPT (pick-wt=19): 368 [] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A))=B.
% 248.03/248.11 ** KEPT (pick-wt=21): 369 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),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))=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.11 ** KEPT (pick-wt=21): 370 [] -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).
% 248.03/248.11 ** KEPT (pick-wt=21): 371 [] -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).
% 248.03/248.11 ** KEPT (pick-wt=21): 372 [] -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).
% 248.03/248.11 ** KEPT (pick-wt=21): 373 [] -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).
% 248.03/248.11 ** KEPT (pick-wt=17): 374 [] A=c_HOL_Ozero__class_Ozero(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_Power_Opower__class_Opower(B,A,tc_nat),tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=21): 375 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)).
% 248.03/248.11 ** KEPT (pick-wt=20): 376 [] -class_OrderedGroup_Ocomm__monoid__mult(A)|c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A).
% 248.03/248.11 ** KEPT (pick-wt=20): 377 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A).
% 248.03/248.11 Following clause subsumed by 23 during input processing: 0 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),D),C,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A).
% 248.03/248.11 Following clause subsumed by 21 during input processing: 0 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A).
% 248.03/248.11 ** KEPT (pick-wt=31): 379 [copy,378,flip.2] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,C)),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(C),D,tc_nat),tc_nat,A))=c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,A)| -c_HOL_Oord__class_Oless(C,D,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=17): 381 [copy,380,flip.2] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(B,C,A),D,A)=c_Power_Opower__class_Opower(B,c_HOL_Otimes__class_Otimes(C,D,tc_nat),A).
% 248.03/248.11 ** KEPT (pick-wt=19): 382 [] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,A),A)),c_Divides_Odiv__class_Omod(C,B,A))=C.
% 248.03/248.11 ** KEPT (pick-wt=19): 383 [] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A)),c_Divides_Odiv__class_Omod(B,C,A))=B.
% 248.03/248.11 Following clause subsumed by 383 during input processing: 0 [flip.2] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A)),c_Divides_Odiv__class_Omod(B,C,A))=B.
% 248.03/248.11 ** KEPT (pick-wt=20): 385 [copy,384,flip.2] -class_Divides_Osemiring__div(A)|c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,C,A),D,A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 248.03/248.11 ** KEPT (pick-wt=20): 387 [copy,386,flip.2] -class_Divides_Osemiring__div(A)|c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Omod(C,D,A),A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 248.03/248.11 ** KEPT (pick-wt=11): 388 [] c_HOL_Oone__class_Oone(tc_nat)!=c_HOL_Otimes__class_Otimes(A,B,tc_nat)|A=c_HOL_Oone__class_Oone(tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=11): 389 [] c_HOL_Oone__class_Oone(tc_nat)!=c_HOL_Otimes__class_Otimes(A,B,tc_nat)|B=c_HOL_Oone__class_Oone(tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=17): 390 [] -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).
% 248.03/248.11 ** KEPT (pick-wt=17): 391 [] -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).
% 248.03/248.11 ** KEPT (pick-wt=17): 392 [] -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).
% 248.03/248.11 Following clause subsumed by 392 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).
% 248.03/248.11 ** KEPT (pick-wt=17): 393 [] -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).
% 248.03/248.11 Following clause subsumed by 392 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).
% 248.03/248.11 Following clause subsumed by 142 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,D,A)),c_HOL_Otimes__class_Otimes(C,D,A))=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A).
% 248.03/248.11 ** KEPT (pick-wt=24): 395 [copy,394,flip.2] -class_Ring__and__Field_Ocomm__semiring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,C,A)),c_HOL_Otimes__class_Otimes(D,C,A))=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A).
% 248.03/248.11 ** KEPT (pick-wt=24): 397 [copy,396,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,C,A)),c_HOL_Otimes__class_Otimes(B,D,A))=c_HOL_Otimes__class_Otimes(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A).
% 248.03/248.11 ** KEPT (pick-wt=16): 398 [] c_Type_Otyping(c_Type_Oshift(A,B,C,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,D),B),E)| -c_Type_Otyping(A,D,E).
% 248.03/248.11 ** KEPT (pick-wt=10): 399 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 248.03/248.11 ** KEPT (pick-wt=10): 400 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 248.03/248.11 Following clause subsumed by 226 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 248.03/248.11 Following clause subsumed by 226 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=10): 401 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 248.03/248.11 Following clause subsumed by 401 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 248.03/248.11 ** KEPT (pick-wt=48): 402 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),hAPP(hAPP(c_Lambda_Olift,B),C)),c_Suc(D))),hAPP(hAPP(hAPP(c_Lambda_Osubst,E),B),D)),C)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),E),C)),B),D)| -c_HOL_Oord__class_Oless(C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=9): 403 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(A)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 248.03/248.11 ** KEPT (pick-wt=14): 404 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,A),B),hAPP(hAPP(c_Lambda_Olift,C),B))| -c_Lambda_Obeta(A,C).
% 248.03/248.11 ** KEPT (pick-wt=26): 405 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),A),B)))| -c_Type_Otyping(C,A,v_T____)| -hBOOL(hAPP(c_InductTermi_OIT,A))| -c_Type_Otyping(c_Type_Oshift(C,B,v_T____,tc_Type_Otype),v_a____,D).
% 248.03/248.11 ** KEPT (pick-wt=29): 406 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Ozero__class_Ozero(A)|c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_nat),tc_nat,A)=c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,A).
% 248.03/248.11 ** KEPT (pick-wt=14): 407 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)))| -c_List_Olistsp(c_InductTermi_OIT,B,tc_Lambda_OdB).
% 248.03/248.11 ** KEPT (pick-wt=20): 408 [] -class_Ring__and__Field_Ozero__ne_q__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.11 ** KEPT (pick-wt=16): 409 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.12 ** KEPT (pick-wt=16): 410 [] -class_Ring__and__Field_Ozero__ne_q__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A)!=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.12 ** KEPT (pick-wt=9): 411 [] -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).
% 248.03/248.12 ** KEPT (pick-wt=13): 412 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Suc(B),A)=c_HOL_Ozero__class_Ozero(A).
% 248.03/248.12 ** KEPT (pick-wt=18): 413 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.12 ** KEPT (pick-wt=20): 414 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.03/248.12 ** KEPT (pick-wt=15): 415 [] hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)))|hBOOL(hAPP(A,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(A))))| -hBOOL(hAPP(A,B)).
% 248.03/248.12 ** KEPT (pick-wt=17): 416 [] c_Power_Opower__class_Opower(A,B,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.12 ** KEPT (pick-wt=15): 417 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_Suc(v_sko__List__Xlexn__Xinduct__1(A))))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.12 ** KEPT (pick-wt=18): 418 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.12 ** KEPT (pick-wt=20): 419 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.03/248.12 ** KEPT (pick-wt=15): 420 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(A))))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.12 ** KEPT (pick-wt=13): 421 [] 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)).
% 248.03/248.12 ** KEPT (pick-wt=13): 422 [] 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)).
% 248.03/248.12 ** KEPT (pick-wt=15): 423 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_Suc(v_sko__List__Xreplicate__Xinduct__1(A))))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.12 ** KEPT (pick-wt=15): 424 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_Suc(v_sko__List__Xupt__Xinduct__1(A))))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.12 ** KEPT (pick-wt=15): 425 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_Suc(v_sko__Nat__Xnat__Xinduct__1(A))))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.12 ** KEPT (pick-wt=10): 426 [] 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).
% 248.03/248.12 ** KEPT (pick-wt=15): 427 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_Suc(v_sko__Nat__Xnat__Xinducts__1(A))))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.03/248.12 ** KEPT (pick-wt=19): 428 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.12 ** KEPT (pick-wt=19): 429 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|A=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.03/248.12 ** KEPT (pick-wt=15): 430 [] c_Suc(c_Divides_Odiv__class_Omod(A,B,tc_nat))!=B|c_Divides_Odiv__class_Omod(c_Suc(A),B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.12 ** KEPT (pick-wt=19): 431 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.03/248.12 ** KEPT (pick-wt=19): 432 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.07/248.12 ** KEPT (pick-wt=11): 433 [] A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))| -c_Ring__and__Field_Odvd__class_Odvd(A,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 248.07/248.12 ** KEPT (pick-wt=23): 434 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),C,A,A))=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A).
% 248.07/248.12 ** KEPT (pick-wt=18): 435 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(C),D,tc_Lambda_OdB,tc_Lambda_OdB)|A=C.
% 248.07/248.12 ** KEPT (pick-wt=18): 436 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(C),D,tc_Lambda_OdB,tc_Lambda_OdB)|B=D.
% 248.07/248.12 ** KEPT (pick-wt=20): 437 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_List_Ofoldl(c_Lambda_OdB_OApp,C,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)|hAPP(hAPP(c_Lambda_OdB_OApp,A),B)=C.
% 248.07/248.12 ** KEPT (pick-wt=13): 438 [] c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_Lambda_OdB_OAbs(C)|A=c_Lambda_OdB_OAbs(C).
% 248.07/248.12 ** KEPT (pick-wt=18): 439 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(C),D,tc_Lambda_OdB,tc_Lambda_OdB)|A=C.
% 248.07/248.12 ** KEPT (pick-wt=18): 440 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(C),D,tc_Lambda_OdB,tc_Lambda_OdB)|B=D.
% 248.07/248.12 ** KEPT (pick-wt=16): 441 [] c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,C,B,tc_Lambda_OdB,tc_Lambda_OdB))| -c_Lambda_Obeta(A,C).
% 248.07/248.12 ** KEPT (pick-wt=13): 442 [] c_Lambda_OdB_OVar(A)!=c_List_Ofoldl(c_Lambda_OdB_OApp,B,C,tc_Lambda_OdB,tc_Lambda_OdB)|c_Lambda_OdB_OVar(A)=B.
% 248.07/248.12 ** KEPT (pick-wt=13): 443 [] c_Lambda_OdB_OAbs(A)!=c_List_Ofoldl(c_Lambda_OdB_OApp,B,C,tc_Lambda_OdB,tc_Lambda_OdB)|c_Lambda_OdB_OAbs(A)=B.
% 248.07/248.12 ** KEPT (pick-wt=13): 444 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,A),c_Lambda_OdB_OVar(B))))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 248.07/248.12 ** KEPT (pick-wt=32): 445 [] c_Type_Otypings(A,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,B,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),C,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),D,tc_Lambda_OdB,tc_Lambda_OdB),E)| -c_Type_Otypings(c_Type_Oshift(A,C,F,tc_Type_Otype),D,E)| -c_Type_Otyping(A,B,F).
% 248.07/248.12 ** KEPT (pick-wt=15): 446 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),c_Lambda_OdB_OVar(B)),C)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 248.07/248.12 ** KEPT (pick-wt=21): 447 [] c_Type_Otypings(c_Type_Oshift(A,B,C,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,B,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),D,tc_Lambda_OdB,tc_Lambda_OdB),E)| -c_Type_Otypings(A,D,E).
% 248.07/248.12 ** KEPT (pick-wt=50): 448 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),A),B)))| -c_Type_Otyping(C,A,v_T____)| -hBOOL(hAPP(c_InductTermi_OIT,A))| -c_Type_Otyping(c_Type_Oshift(C,B,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),D).
% 248.07/248.12 ** KEPT (pick-wt=34): 449 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B),C,tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(c_InductTermi_OIT,B))| -hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_Lambda_OdB,tc_Lambda_OdB))).
% 248.07/248.12 ** KEPT (pick-wt=18): 450 [] c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),A,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)| -c_List_Olistsp(c_InductTermi_OIT,A,tc_Lambda_OdB).
% 248.07/248.12 ** KEPT (pick-wt=4): 452 [copy,451,flip.1] c_Suc(A)!=A.
% 248.07/248.12 Following clause subsumed by 452 during input processing: 0 [] c_Suc(A)!=A.
% 248.07/248.12 ** KEPT (pick-wt=5): 453 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.12 Following clause subsumed by 453 during input processing: 0 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.12 ** KEPT (pick-wt=14): 454 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|A=C.
% 248.07/248.12 ** KEPT (pick-wt=14): 455 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|B=D.
% 248.07/248.12 ** KEPT (pick-wt=12): 456 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,A),B)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 248.07/248.12 ** KEPT (pick-wt=8): 457 [] c_Suc(A)!=c_Suc(B)|A=B.
% 248.07/248.12 Following clause subsumed by 457 during input processing: 0 [] c_Suc(A)!=c_Suc(B)|A=B.
% 248.07/248.12 Following clause subsumed by 453 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.12 Following clause subsumed by 453 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.12 ** KEPT (pick-wt=16): 458 [] c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,C,B,tc_Lambda_OdB,tc_Lambda_OdB)|A=C.
% 248.07/248.12 ** KEPT (pick-wt=50): 459 [] -hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),hAPP(hAPP(c_Lambda_Olift,v_u____),c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(v_i____))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))).
% 248.07/248.12 ** KEPT (pick-wt=6): 460 [] class_Orderings_Opreorder(tc_fun(A,B))| -class_Orderings_Opreorder(B).
% 248.07/248.12 ** KEPT (pick-wt=6): 461 [] class_Orderings_Oorder(tc_fun(A,B))| -class_Orderings_Oorder(B).
% 248.07/248.12 ** KEPT (pick-wt=7): 462 [] A=B| -c_fe_qual(A,B,C).
% 248.07/248.12 106 back subsumes 85.
% 248.07/248.12 158 back subsumes 24.
% 248.07/248.12 Following clause subsumed by 367 during input processing: 0 [copy,174,flip.1] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 248.07/248.12 226 back subsumes 225.
% 248.07/248.12 226 back subsumes 158.
% 248.07/248.12 234 back subsumes 125.
% 248.07/248.12 234 back subsumes 94.
% 248.07/248.12 244 back subsumes 81.
% 248.07/248.12 Following clause subsumed by 303 during input processing: 0 [copy,302,flip.1] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 248.07/248.12 Following clause subsumed by 302 during input processing: 0 [copy,303,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 248.07/248.12 Following clause subsumed by 307 during input processing: 0 [copy,304,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 248.07/248.12 Following clause subsumed by 304 during input processing: 0 [copy,307,flip.1] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 248.07/248.12 ** KEPT (pick-wt=15): 510 [copy,312,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(C),D,tc_Lambda_OdB,tc_Lambda_OdB).
% 248.07/248.12 ** KEPT (pick-wt=14): 511 [copy,315,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(C)),D).
% 248.07/248.12 Following clause subsumed by 174 during input processing: 0 [copy,367,flip.1] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 248.07/248.12 392 back subsumes 203.
% 248.07/248.12 393 back subsumes 204.
% 248.07/248.12 Following clause subsumed by 312 during input processing: 0 [copy,510,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(C),D,tc_Lambda_OdB,tc_Lambda_OdB).
% 248.07/248.12 Following clause subsumed by 315 during input processing: 0 [copy,511,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(C),D,tc_Lambda_OdB,tc_Lambda_OdB).
% 248.07/248.12
% 248.07/248.12 ------------> process sos:
% 248.07/248.12 ** KEPT (pick-wt=3): 527 [] A=A.
% 248.07/248.12 ** KEPT (pick-wt=32): 529 [copy,528,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat)),D)).
% 248.07/248.13 ---> New Demodulator: 530 [new_demod,529] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat)),D)).
% 248.07/248.13 ** KEPT (pick-wt=7): 531 [] c_Type_Otyping(A,c_Lambda_OdB_OVar(B),hAPP(A,B)).
% 248.07/248.13 ** KEPT (pick-wt=10): 533 [copy,532,unit_del,211] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),A)=B.
% 248.07/248.13 ---> New Demodulator: 534 [new_demod,533] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),A)=B.
% 248.07/248.13 ** KEPT (pick-wt=19): 535 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(A)),B)=c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)))|c_HOL_Oord__class_Oless(A,B,tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=23): 536 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)).
% 248.07/248.13 ---> New Demodulator: 537 [new_demod,536] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)).
% 248.07/248.13 ** KEPT (pick-wt=23): 538 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)).
% 248.07/248.13 ** KEPT (pick-wt=9): 539 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)=c_HOL_Otimes__class_Otimes(B,A,tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=18): 540 [] hAPP(hAPP(hAPP(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).
% 248.07/248.13 ** KEPT (pick-wt=25): 541 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),c_HOL_Otimes__class_Otimes(A,C,tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat)),c_HOL_Otimes__class_Otimes(A,B,tc_nat)).
% 248.07/248.13 Following clause subsumed by 541 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),c_HOL_Otimes__class_Otimes(A,C,tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat)),c_HOL_Otimes__class_Otimes(A,B,tc_nat)).
% 248.07/248.13 ** KEPT (pick-wt=10): 542 [] c_Suc(A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)).
% 248.07/248.13 ---> New Demodulator: 543 [new_demod,542] c_Suc(A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)).
% 248.07/248.13 ** KEPT (pick-wt=15): 545 [copy,544,demod,543] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A).
% 248.07/248.13 ** KEPT (pick-wt=7): 546 [] c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=A.
% 248.07/248.13 ---> New Demodulator: 547 [new_demod,546] c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=A.
% 248.07/248.13 ** KEPT (pick-wt=7): 548 [] c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 248.07/248.13 ---> New Demodulator: 549 [new_demod,548] c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 248.07/248.13 ** KEPT (pick-wt=5): 550 [] c_List_Olistsp(A,c_List_Olist_ONil(B),B).
% 248.07/248.13 ** KEPT (pick-wt=15): 552 [copy,551,demod,543,537] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))),tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=15): 554 [copy,553,demod,543,537] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))),tc_nat).
% 248.07/248.13 Following clause subsumed by 552 during input processing: 0 [demod,543,537] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))),tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=6): 555 [] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(A))=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.13 ---> New Demodulator: 556 [new_demod,555] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(A))=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.13 Following clause subsumed by 527 during input processing: 0 [demod,549] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=17): 558 [copy,557,flip.1] c_Lambda_OdB_OAbs(c_Lambda_Osubstn(A,B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=c_Lambda_Osubstn(c_Lambda_OdB_OAbs(A),B,C).
% 248.07/248.13 ---> New Demodulator: 559 [new_demod,558] c_Lambda_OdB_OAbs(c_Lambda_Osubstn(A,B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=c_Lambda_Osubstn(c_Lambda_OdB_OAbs(A),B,C).
% 248.07/248.13 ** KEPT (pick-wt=13): 560 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 248.07/248.13 ** KEPT (pick-wt=6): 561 [] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=20): 563 [copy,562,demod,543] c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(A),tc_Lambda_OdB)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))).
% 248.07/248.13 ---> New Demodulator: 564 [new_demod,563] c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(A),tc_Lambda_OdB)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))).
% 248.07/248.13 Following clause subsumed by 527 during input processing: 0 [demod,549] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=11): 566 [copy,565,unit_del,211] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.07/248.13 ---> New Demodulator: 567 [new_demod,566] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.07/248.13 ** KEPT (pick-wt=18): 568 [] c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat).
% 248.07/248.13 ---> New Demodulator: 569 [new_demod,568] c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=18): 570 [] c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,B,tc_nat),C,tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat).
% 248.07/248.13 ---> New Demodulator: 571 [new_demod,570] c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,B,tc_nat),C,tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=41): 573 [copy,572,demod,537,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(C,B,tc_nat)),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),c_Divides_Odiv__class_Omod(C,B,tc_nat)),B,tc_nat)))=c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 248.07/248.13 ---> New Demodulator: 574 [new_demod,573] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(C,B,tc_nat)),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),c_Divides_Odiv__class_Omod(C,B,tc_nat)),B,tc_nat)))=c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=19): 575 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(B,C,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=17): 576 [] c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),C),B,tc_nat)=c_Divides_Odiv__class_Omod(C,B,tc_nat).
% 248.07/248.13 ---> New Demodulator: 577 [new_demod,576] c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),C),B,tc_nat)=c_Divides_Odiv__class_Omod(C,B,tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=9): 578 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=20): 580 [copy,579,demod,543] c_HOL_Otimes__class_Otimes(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Otimes__class_Otimes(A,B,tc_nat)).
% 248.07/248.13 ** KEPT (pick-wt=20): 582 [copy,581,demod,543] c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),B,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Otimes__class_Otimes(A,B,tc_nat)).
% 248.07/248.13 ** KEPT (pick-wt=9): 583 [] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 248.07/248.13 ---> New Demodulator: 584 [new_demod,583] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 248.07/248.13 ** KEPT (pick-wt=15): 585 [] 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).
% 248.07/248.13 Following clause subsumed by 527 during input processing: 0 [demod,543,537,577,543] c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),B,tc_nat)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),B,tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=17): 586 [] c_Lambda_Oliftn(A,c_Lambda_OdB_OVar(B),C)=c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A))|c_HOL_Oord__class_Oless(B,C,tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=17): 588 [copy,587,flip.1] c_Lambda_OdB_OAbs(c_Lambda_Oliftn(A,B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=c_Lambda_Oliftn(A,c_Lambda_OdB_OAbs(B),C).
% 248.07/248.13 ---> New Demodulator: 589 [new_demod,588] c_Lambda_OdB_OAbs(c_Lambda_Oliftn(A,B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=c_Lambda_Oliftn(A,c_Lambda_OdB_OAbs(B),C).
% 248.07/248.13 ** KEPT (pick-wt=11): 590 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 248.07/248.13 Following clause subsumed by 590 during input processing: 0 [] hBOOL(hAPP(hAPP(A,B),C))|c_HOL_Oord__class_Oless(B,C,tc_nat)|C=B|c_HOL_Oord__class_Oless(C,B,tc_nat).
% 248.07/248.13 Following clause subsumed by 590 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 248.07/248.13 ** KEPT (pick-wt=4): 591 [] c_Ring__and__Field_Odvd__class_Odvd(A,A,tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=12): 592 [] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=32): 594 [copy,593,demod,569,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,C,tc_nat),tc_nat)),c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat),C,tc_nat))=c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat).
% 248.07/248.13 ---> New Demodulator: 595 [new_demod,594] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,C,tc_nat),tc_nat)),c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat),C,tc_nat))=c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=8): 596 [] c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 248.07/248.13 ---> New Demodulator: 597 [new_demod,596] c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=11): 598 [] c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=11): 599 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=7): 600 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 248.07/248.13 ---> New Demodulator: 601 [new_demod,600] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 248.07/248.13 ** KEPT (pick-wt=9): 602 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=8): 603 [] c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.13 ---> New Demodulator: 604 [new_demod,603] c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=8): 605 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.13 ---> New Demodulator: 606 [new_demod,605] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=11): 607 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.13 ---> New Demodulator: 608 [new_demod,607] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=9): 610 [copy,609,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 248.07/248.13 ---> New Demodulator: 611 [new_demod,610] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 248.07/248.13 ** KEPT (pick-wt=9): 612 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 248.07/248.13 ---> New Demodulator: 613 [new_demod,612] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 248.07/248.13 Following clause subsumed by 527 during input processing: 0 [demod,611] A=A.
% 248.07/248.13 ** KEPT (pick-wt=24): 615 [copy,614,demod,543,543,flip.1] c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),B,tc_nat)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),B,tc_nat).
% 248.07/248.13 ---> New Demodulator: 616 [new_demod,615] c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),B,tc_nat)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),B,tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=10): 618 [copy,617,demod,543] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 248.07/248.13 Following clause subsumed by 618 during input processing: 0 [demod,543] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=25): 620 [copy,619,demod,543,537,543,537] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))).
% 248.07/248.13 Following clause subsumed by 527 during input processing: 0 [demod,543,543,537] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))).
% 248.07/248.13 ** KEPT (pick-wt=33): 622 [copy,621,demod,543,543,543,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),c_HOL_Oone__class_Oone(tc_nat))=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),B,tc_nat)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),c_HOL_Oone__class_Oone(tc_nat))=B.
% 248.07/248.13 Following clause subsumed by 620 during input processing: 0 [demod,543,537,543] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))).
% 248.07/248.13 Following clause subsumed by 618 during input processing: 0 [demod,543,unit_del,211] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=14): 624 [copy,623,demod,543] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=20): 626 [copy,625,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(A,B,C)),c_Lambda_Oliftn(A,D,C))=c_Lambda_Oliftn(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),D),C).
% 248.07/248.13 ---> New Demodulator: 627 [new_demod,626] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(A,B,C)),c_Lambda_Oliftn(A,D,C))=c_Lambda_Oliftn(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),D),C).
% 248.07/248.13 ** KEPT (pick-wt=20): 629 [copy,628,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(A,B,C)),c_Lambda_Osubstn(D,B,C))=c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,A),D),B,C).
% 248.07/248.13 ---> New Demodulator: 630 [new_demod,629] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(A,B,C)),c_Lambda_Osubstn(D,B,C))=c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,A),D),B,C).
% 248.07/248.13 ** KEPT (pick-wt=16): 632 [copy,631,flip.1] hAPP(hAPP(hAPP(c_Lambda_Osubst,A),c_Lambda_Oliftn(B,C,c_HOL_Ozero__class_Ozero(tc_nat))),B)=c_Lambda_Osubstn(A,C,B).
% 248.07/248.13 ---> New Demodulator: 633 [new_demod,632] hAPP(hAPP(hAPP(c_Lambda_Osubst,A),c_Lambda_Oliftn(B,C,c_HOL_Ozero__class_Ozero(tc_nat))),B)=c_Lambda_Osubstn(A,C,B).
% 248.07/248.13 ** KEPT (pick-wt=9): 634 [] c_List_Omap(A,c_List_Olist_ONil(B),B,C)=c_List_Olist_ONil(C).
% 248.07/248.13 ** KEPT (pick-wt=9): 635 [] c_List_Olist_ONil(A)=c_List_Omap(B,c_List_Olist_ONil(C),C,A).
% 248.07/248.13 ** KEPT (pick-wt=11): 637 [copy,636,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OVar(A).
% 248.07/248.13 ---> New Demodulator: 638 [new_demod,637] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OVar(A).
% 248.07/248.13 ** KEPT (pick-wt=11): 640 [copy,639,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OAbs(A).
% 248.07/248.13 ---> New Demodulator: 641 [new_demod,640] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OAbs(A).
% 248.07/248.13 Following clause subsumed by 527 during input processing: 0 [demod,641] c_Lambda_OdB_OAbs(A)=c_Lambda_OdB_OAbs(A).
% 248.07/248.13 ** KEPT (pick-wt=9): 642 [] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 248.07/248.13 ---> New Demodulator: 643 [new_demod,642] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 248.07/248.13 Following clause subsumed by 527 during input processing: 0 [demod,534] B=B.
% 248.07/248.13 ** KEPT (pick-wt=9): 645 [copy,644,demod,606,606] c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.13 ---> New Demodulator: 646 [new_demod,645] c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=29): 648 [copy,647,demod,569,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)),c_Divides_Odiv__class_Omod(B,A,tc_nat))=c_Divides_Odiv__class_Omod(B,c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat).
% 248.07/248.13 ---> New Demodulator: 649 [new_demod,648] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)),c_Divides_Odiv__class_Omod(B,A,tc_nat))=c_Divides_Odiv__class_Omod(B,c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=15): 650 [] c_Divides_Odiv__class_Odiv(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(A,B,tc_nat),C,tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=10): 651 [] c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=7): 652 [] c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(A),tc_Lambda_OdB)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.13 ---> New Demodulator: 653 [new_demod,652] c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(A),tc_Lambda_OdB)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=4): 654 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 248.07/248.13 ** KEPT (pick-wt=19): 656 [copy,655,flip.1] c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(A)),B).
% 248.07/248.13 ---> New Demodulator: 657 [new_demod,656] c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(A)),B).
% 248.07/248.13 ** KEPT (pick-wt=12): 659 [copy,658,demod,543,613] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(A))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),c_HOL_Oone__class_Oone(tc_nat)).
% 248.07/248.13 ---> New Demodulator: 660 [new_demod,659] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(A))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),c_HOL_Oone__class_Oone(tc_nat)).
% 248.07/248.13 ** KEPT (pick-wt=15): 661 [] 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).
% 248.07/248.13 ---> New Demodulator: 662 [new_demod,661] 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).
% 248.07/248.13 ** KEPT (pick-wt=22): 664 [copy,663,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),c_HOL_Otimes__class_Otimes(C,B,tc_nat))=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 248.07/248.13 ---> New Demodulator: 665 [new_demod,664] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),c_HOL_Otimes__class_Otimes(C,B,tc_nat))=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=22): 667 [copy,666,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),c_HOL_Otimes__class_Otimes(A,C,tc_nat))=c_HOL_Otimes__class_Otimes(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat).
% 248.07/248.13 ---> New Demodulator: 668 [new_demod,667] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),c_HOL_Otimes__class_Otimes(A,C,tc_nat))=c_HOL_Otimes__class_Otimes(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=28): 670 [copy,669,flip.1] c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,A),hAPP(hAPP(c_Lambda_Olift,B),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(A)),B),C).
% 248.07/248.13 ---> New Demodulator: 671 [new_demod,670] c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,A),hAPP(hAPP(c_Lambda_Olift,B),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(A)),B),C).
% 248.07/248.13 ** KEPT (pick-wt=5): 672 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(A))).
% 248.07/248.13 ** KEPT (pick-wt=4): 673 [] hBOOL(hAPP(c_InductTermi_OIT,v_ua______)).
% 248.07/248.13 ** KEPT (pick-wt=21): 675 [copy,674,demod,543,613,537] c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(B)),c_HOL_Oone__class_Oone(tc_nat))).
% 248.07/248.13 ---> New Demodulator: 676 [new_demod,675] c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(B)),c_HOL_Oone__class_Oone(tc_nat))).
% 248.07/248.13 ** KEPT (pick-wt=24): 678 [copy,677,demod,543,613,537,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(B,tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat)))=c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),tc_Lambda_OdB).
% 248.07/248.13 ---> New Demodulator: 679 [new_demod,678] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(B,tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat)))=c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),tc_Lambda_OdB).
% 248.07/248.13 ** KEPT (pick-wt=15): 680 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat))).
% 248.07/248.13 ** KEPT (pick-wt=18): 681 [] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____).
% 248.07/248.13 ** KEPT (pick-wt=14): 683 [copy,682,demod,543,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(A)),c_HOL_Oone__class_Oone(tc_nat))=A|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.13 Following clause subsumed by 527 during input processing: 0 [demod,543,613,613,543,613] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 248.07/248.13 Following clause subsumed by 527 during input processing: 0 [demod,543,613,543,613,611] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=8): 685 [copy,684,demod,543,613] c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.13 Following clause subsumed by 527 during input processing: 0 [demod,543,613,543,613,549,543,613] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 248.07/248.13 Following clause subsumed by 591 during input processing: 0 [demod,543,613,543,613] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=6): 687 [copy,686,demod,543,613] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 248.07/248.13 Following clause subsumed by 527 during input processing: 0 [demod,543,613] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=27): 689 [copy,688,demod,543] c_Type_Oshift(c_Type_Oshift(A,B,C,D),c_HOL_Ozero__class_Ozero(tc_nat),E,D)=c_Type_Oshift(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),E,D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)),C,D).
% 248.07/248.13 ** KEPT (pick-wt=14): 691 [copy,690,demod,543,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(A)),c_HOL_Oone__class_Oone(tc_nat))=A|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.13 Following clause subsumed by 527 during input processing: 0 [demod,597,543,613] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 248.07/248.13 Following clause subsumed by 527 during input processing: 0 [demod,543,613,611,543,613] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=14): 693 [copy,692,demod,543,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(A)),c_HOL_Oone__class_Oone(tc_nat))=A|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=5): 695 [copy,694,demod,543,613] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat).
% 248.07/248.13 Following clause subsumed by 527 during input processing: 0 [demod,543,613,543,613,613] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=11): 697 [copy,696,demod,543] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 248.07/248.13 Following clause subsumed by 697 during input processing: 0 [demod,543] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=8): 699 [copy,698,demod,543,613,543,613] c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 248.07/248.13 ---> New Demodulator: 700 [new_demod,699] c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 248.07/248.13 Following clause subsumed by 527 during input processing: 0 [demod,543,613,700,543,613] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=7): 702 [copy,701,demod,543,613] c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 248.07/248.13 ---> New Demodulator: 703 [new_demod,702] c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 248.07/248.13 ** KEPT (pick-wt=14): 705 [copy,704,flip.1] hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.07/248.13 ---> New Demodulator: 706 [new_demod,705] hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 248.07/248.13 Following clause subsumed by 527 during input processing: 0 [demod,643] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)=hAPP(hAPP(c_Lambda_OdB_OApp,A),B).
% 248.07/248.13 ** KEPT (pick-wt=19): 708 [copy,707,demod,543] c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),B,C)=hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(A,B,C)),C).
% 248.07/248.13 ** KEPT (pick-wt=4): 709 [] hBOOL(hAPP(c_InductTermi_OIT,v_a____)).
% 248.07/248.13 ** KEPT (pick-wt=29): 710 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),C),D)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),C),D)),hAPP(hAPP(hAPP(c_Lambda_Osubst,B),C),D)).
% 248.07/248.13 ** KEPT (pick-wt=13): 712 [copy,711,demod,706] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))).
% 248.07/248.13 ** KEPT (pick-wt=30): 713 [] hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,A),C),c_List_Omap(c_COMBC(c_Lambda_Olift,C,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),B,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 248.07/248.13 ---> New Demodulator: 714 [new_demod,713] hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,A),C),c_List_Omap(c_COMBC(c_Lambda_Olift,C,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),B,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 248.07/248.13 ** KEPT (pick-wt=23): 715 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),C)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,A),C)),hAPP(hAPP(c_Lambda_Olift,B),C)).
% 248.07/248.13 ** KEPT (pick-wt=41): 716 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C),D)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),C),D),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,C,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),D,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),B,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 248.07/248.13 ** KEPT (pick-wt=14): 717 [] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 248.07/248.13 ** KEPT (pick-wt=4): 718 [] hBOOL(hAPP(c_InductTermi_OIT,v_u____)).
% 248.07/248.13 ** KEPT (pick-wt=13): 719 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),B)),C),B)=A.
% 248.07/248.13 ---> New Demodulator: 720 [new_demod,719] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),B)),C),B)=A.
% 248.07/248.13 ** KEPT (pick-wt=19): 722 [copy,721,demod,706] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))).
% 248.07/248.13 ** KEPT (pick-wt=2): 723 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 248.07/248.13 ** KEPT (pick-wt=2): 724 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 725 [] class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 726 [] class_Ring__and__Field_Oordered__semiring__strict(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 727 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 728 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 729 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 730 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 731 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 732 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 733 [] class_OrderedGroup_Oab__semigroup__mult(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 734 [] class_OrderedGroup_Ocomm__monoid__mult(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 735 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 736 [] class_Ring__and__Field_Ocomm__semiring(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 737 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 738 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 739 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 740 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 741 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 742 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 743 [] class_OrderedGroup_Omonoid__mult(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 744 [] class_Ring__and__Field_Osemiring(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 745 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 746 [] class_Divides_Osemiring__div(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 747 [] class_Nat_Osemiring__char__0(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 748 [] class_Ring__and__Field_Odvd(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 749 [] class_Orderings_Opreorder(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 750 [] class_Orderings_Olinorder(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 751 [] class_Orderings_Oorder(tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=2): 752 [] class_Power_Opower(tc_nat).
% 248.07/248.14 Following clause subsumed by 717 during input processing: 0 [] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 248.07/248.14 ** KEPT (pick-wt=13): 753 [] c_COMBB(A,B,C,D,E,F)=hAPP(A,hAPP(B,C)).
% 248.07/248.14 ** KEPT (pick-wt=4): 754 [] c_fe_qual(A,A,B).
% 248.07/248.14 Following clause subsumed by 527 during input processing: 0 [copy,527,flip.1] A=A.
% 248.07/248.14 527 back subsumes 509.
% 248.07/248.14 527 back subsumes 500.
% 248.07/248.14 527 back subsumes 499.
% 248.07/248.14 527 back subsumes 498.
% 248.07/248.14 >>>> Starting back demodulation with 530.
% 248.07/248.14 >>>> Starting back demodulation with 534.
% 248.07/248.14 >>>> Starting back demodulation with 537.
% 248.07/248.14 Following clause subsumed by 538 during input processing: 0 [copy,538,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)).
% 248.07/248.14 Following clause subsumed by 539 during input processing: 0 [copy,539,flip.1] c_HOL_Otimes__class_Otimes(A,B,tc_nat)=c_HOL_Otimes__class_Otimes(B,A,tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=19): 755 [copy,541,flip.1,demod,668,668] c_HOL_Otimes__class_Otimes(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)=c_HOL_Otimes__class_Otimes(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat).
% 248.07/248.14 >>>> Starting back demodulation with 543.
% 248.07/248.14 >> back demodulating 526 with 543.
% 248.07/248.14 >> back demodulating 525 with 543.
% 248.07/248.14 >> back demodulating 524 with 543.
% 248.07/248.14 >> back demodulating 523 with 543.
% 248.07/248.14 >> back demodulating 508 with 543.
% 248.07/248.14 >> back demodulating 507 with 543.
% 248.07/248.14 >> back demodulating 459 with 543.
% 248.07/248.14 >> back demodulating 457 with 543.
% 248.07/248.14 >> back demodulating 453 with 543.
% 248.07/248.14 >> back demodulating 452 with 543.
% 248.07/248.14 >> back demodulating 433 with 543.
% 248.07/248.14 >> back demodulating 432 with 543.
% 248.07/248.14 >> back demodulating 431 with 543.
% 248.07/248.14 >> back demodulating 430 with 543.
% 248.07/248.14 >> back demodulating 429 with 543.
% 248.07/248.14 >> back demodulating 428 with 543.
% 248.07/248.14 >> back demodulating 427 with 543.
% 248.07/248.14 >> back demodulating 426 with 543.
% 248.07/248.14 >> back demodulating 425 with 543.
% 248.07/248.14 >> back demodulating 424 with 543.
% 248.07/248.14 >> back demodulating 423 with 543.
% 248.07/248.14 >> back demodulating 422 with 543.
% 248.07/248.14 >> back demodulating 421 with 543.
% 248.07/248.14 >> back demodulating 420 with 543.
% 248.07/248.14 >> back demodulating 419 with 543.
% 248.07/248.14 >> back demodulating 418 with 543.
% 248.07/248.14 >> back demodulating 417 with 543.
% 248.07/248.14 >> back demodulating 416 with 543.
% 248.07/248.14 >> back demodulating 415 with 543.
% 248.07/248.14 >> back demodulating 414 with 543.
% 248.07/248.14 >> back demodulating 413 with 543.
% 248.07/248.14 >> back demodulating 412 with 543.
% 248.07/248.14 >> back demodulating 406 with 543.
% 248.07/248.14 >> back demodulating 402 with 543.
% 248.07/248.14 >> back demodulating 379 with 543.
% 248.07/248.14 >> back demodulating 359 with 543.
% 248.07/248.14 >> back demodulating 333 with 543.
% 248.07/248.14 >> back demodulating 323 with 543.
% 248.07/248.14 >> back demodulating 301 with 543.
% 248.07/248.14 >> back demodulating 300 with 543.
% 248.07/248.14 >> back demodulating 299 with 543.
% 248.07/248.14 >> back demodulating 298 with 543.
% 248.07/248.14 >> back demodulating 297 with 543.
% 248.07/248.14 >> back demodulating 296 with 543.
% 248.07/248.14 >> back demodulating 295 with 543.
% 248.07/248.14 >> back demodulating 294 with 543.
% 248.07/248.14 >> back demodulating 293 with 543.
% 248.07/248.14 >> back demodulating 292 with 543.
% 248.07/248.14 >> back demodulating 291 with 543.
% 248.07/248.14 >> back demodulating 290 with 543.
% 248.07/248.14 >> back demodulating 289 with 543.
% 248.07/248.14 >> back demodulating 227 with 543.
% 248.07/248.14 >> back demodulating 143 with 543.
% 248.07/248.14 >> back demodulating 122 with 543.
% 248.07/248.14 >> back demodulating 77 with 543.
% 248.07/248.14 >> back demodulating 45 with 543.
% 248.07/248.14 >> back demodulating 44 with 543.
% 248.07/248.14 >> back demodulating 43 with 543.
% 248.07/248.14 >> back demodulating 39 with 543.
% 248.07/248.14 >> back demodulating 18 with 543.
% 248.07/248.14 >> back demodulating 6 with 543.
% 248.07/248.14 Following clause subsumed by 560 during input processing: 0 [copy,545,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)).
% 248.07/248.14 >>>> Starting back demodulation with 547.
% 248.07/248.14 >> back demodulating 48 with 547.
% 248.07/248.14 >>>> Starting back demodulation with 549.
% 248.07/248.14 >> back demodulating 47 with 549.
% 248.07/248.14 >>>> Starting back demodulation with 556.
% 248.07/248.14 >>>> Starting back demodulation with 559.
% 248.07/248.14 Following clause subsumed by 560 during input processing: 0 [copy,560,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 248.07/248.14 560 back subsumes 545.
% 248.07/248.14 560 back subsumes 541.
% 248.07/248.14 >>>> Starting back demodulation with 564.
% 248.07/248.14 >>>> Starting back demodulation with 567.
% 248.07/248.14 >>>> Starting back demodulation with 569.
% 248.07/248.14 >> back demodulating 516 with 569.
% 248.07/248.14 >> back demodulating 343 with 569.
% 248.07/248.14 >>>> Starting back demodulation with 571.
% 248.07/248.14 >>>> Starting back demodulation with 574.
% 248.07/248.14 >>>> Starting back demodulation with 577.
% 248.07/248.14 ** KEPT (pick-wt=20): 806 [copy,580,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Otimes__class_Otimes(A,B,tc_nat))=c_HOL_Otimes__class_Otimes(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=20): 807 [copy,582,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Otimes__class_Otimes(B,A,tc_nat))=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)),A,tc_nat).
% 248.07/248.14 >>>> Starting back demodulation with 584.
% 248.07/248.14 >>>> Starting back demodulation with 589.
% 248.07/248.14 591 back subsumes 561.
% 248.07/248.14 >>>> Starting back demodulation with 595.
% 248.07/248.14 >>>> Starting back demodulation with 597.
% 248.07/248.14 >> back demodulating 578 with 597.
% 248.07/248.14 >> back demodulating 467 with 597.
% 248.07/248.14 Following clause subsumed by 527 during input processing: 0 [copy,598,flip.1,demod,604,604] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.14 Following clause subsumed by 527 during input processing: 0 [copy,599,flip.1,demod,606,606] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 248.07/248.14 >>>> Starting back demodulation with 601.
% 248.07/248.14 >>>> Starting back demodulation with 604.
% 248.07/248.14 >> back demodulating 598 with 604.
% 248.07/248.14 >> back demodulating 518 with 604.
% 248.07/248.14 >> back demodulating 506 with 604.
% 248.07/248.14 >> back demodulating 479 with 604.
% 248.07/248.14 >>>> Starting back demodulation with 606.
% 248.07/248.14 >> back demodulating 599 with 606.
% 248.07/248.14 >> back demodulating 592 with 606.
% 248.07/248.14 >> back demodulating 505 with 606.
% 248.07/248.14 >> back demodulating 478 with 606.
% 248.07/248.14 >>>> Starting back demodulation with 608.
% 248.07/248.14 >>>> Starting back demodulation with 611.
% 248.07/248.14 >> back demodulating 607 with 611.
% 248.07/248.14 >>>> Starting back demodulation with 613.
% 248.07/248.14 >> back demodulating 563 with 613.
% 248.07/248.14 >>>> Starting back demodulation with 616.
% 248.07/248.14 ** KEPT (pick-wt=25): 812 [copy,620,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),B)).
% 248.07/248.14 >>>> Starting back demodulation with 627.
% 248.07/248.14 >>>> Starting back demodulation with 630.
% 248.07/248.14 >>>> Starting back demodulation with 633.
% 248.07/248.14 Following clause subsumed by 635 during input processing: 0 [copy,634,flip.1] c_List_Olist_ONil(A)=c_List_Omap(B,c_List_Olist_ONil(C),C,A).
% 248.07/248.14 Following clause subsumed by 634 during input processing: 0 [copy,635,flip.1] c_List_Omap(A,c_List_Olist_ONil(B),B,C)=c_List_Olist_ONil(C).
% 248.07/248.14 >>>> Starting back demodulation with 638.
% 248.07/248.14 >>>> Starting back demodulation with 641.
% 248.07/248.14 >>>> Starting back demodulation with 643.
% 248.07/248.14 >> back demodulating 640 with 643.
% 248.07/248.14 >> back demodulating 637 with 643.
% 248.07/248.14 >> back demodulating 437 with 643.
% 248.07/248.14 >>>> Starting back demodulation with 646.
% 248.07/248.14 >>>> Starting back demodulation with 649.
% 248.07/248.14 ** KEPT (pick-wt=15): 813 [copy,650,flip.1] c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(A,B,tc_nat),C,tc_nat)=c_Divides_Odiv__class_Odiv(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=10): 814 [copy,651,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),A,tc_nat).
% 248.07/248.14 >>>> Starting back demodulation with 653.
% 248.07/248.14 >>>> Starting back demodulation with 657.
% 248.07/248.14 >>>> Starting back demodulation with 660.
% 248.07/248.14 >>>> Starting back demodulation with 662.
% 248.07/248.14 >>>> Starting back demodulation with 665.
% 248.07/248.14 >>>> Starting back demodulation with 668.
% 248.07/248.14 >>>> Starting back demodulation with 671.
% 248.07/248.14 >>>> Starting back demodulation with 676.
% 248.07/248.14 >>>> Starting back demodulation with 679.
% 248.07/248.14 ** KEPT (pick-wt=8): 815 [copy,685,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)=c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 248.07/248.14 ** KEPT (pick-wt=27): 816 [copy,689,flip.1] c_Type_Oshift(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),B,C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)),E,C)=c_Type_Oshift(c_Type_Oshift(A,D,E,C),c_HOL_Ozero__class_Ozero(tc_nat),B,C).
% 248.07/248.14 >>>> Starting back demodulation with 700.
% 248.07/248.14 >>>> Starting back demodulation with 703.
% 248.07/248.14 >>>> Starting back demodulation with 706.
% 248.07/248.14 >> back demodulating 680 with 706.
% 248.07/248.14 >> back demodulating 449 with 706.
% 248.07/248.14 >> back demodulating 448 with 706.
% 248.07/248.14 ** KEPT (pick-wt=19): 820 [copy,708,flip.1] hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(A,B,C)),C)=c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),B,C).
% 248.07/248.14 ** KEPT (pick-wt=29): 821 [copy,710,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),hAPP(hAPP(hAPP(c_Lambda_Osubst,D),B),C))=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,A),D)),B),C).
% 248.07/248.14 >>>> Starting back demodulation with 714.
% 248.07/248.14 ** KEPT (pick-wt=23): 822 [copy,715,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,A),B)),hAPP(hAPP(c_Lambda_Olift,C),B))=hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,A),C)),B).
% 248.07/248.14 ** KEPT (pick-wt=41): 823 [copy,716,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,B,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),C,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),D,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,A,D,tc_Lambda_OdB,tc_Lambda_OdB)),B),C).
% 248.07/248.14 ** KEPT (pick-wt=14): 824 [copy,717,flip.1] hAPP(hAPP(A,B),C)=hAPP(c_COMBC(A,C,D,E,F),B).
% 248.07/248.14 >>>> Starting back demodulation with 720.
% 248.07/248.14 ** KEPT (pick-wt=13): 825 [copy,753,flip.1] hAPP(A,hAPP(B,C))=c_COMBB(A,B,C,D,E,F).
% 248.07/248.14 Following clause subsumed by 755 during input processing: 0 [copy,755,flip.1] c_HOL_Otimes__class_Otimes(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)=c_HOL_Otimes__class_Otimes(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat).
% 249.58/249.67 ** KEPT (pick-wt=10): 826 [copy,761,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)).
% 249.58/249.67 Following clause subsumed by 580 during input processing: 0 [copy,806,flip.1] c_HOL_Otimes__class_Otimes(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Otimes__class_Otimes(A,B,tc_nat)).
% 249.58/249.67 Following clause subsumed by 582 during input processing: 0 [copy,807,flip.1] c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),B,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Otimes__class_Otimes(A,B,tc_nat)).
% 249.58/249.67 >>>> Starting back demodulation with 811.
% 249.58/249.67 Following clause subsumed by 620 during input processing: 0 [copy,812,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))).
% 249.58/249.67 Following clause subsumed by 650 during input processing: 0 [copy,813,flip.1] c_Divides_Odiv__class_Odiv(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(A,B,tc_nat),C,tc_nat).
% 249.58/249.67 Following clause subsumed by 651 during input processing: 0 [copy,814,flip.1] c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 249.58/249.67 Following clause subsumed by 685 during input processing: 0 [copy,815,flip.1] c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 249.58/249.67 Following clause subsumed by 689 during input processing: 0 [copy,816,flip.1] c_Type_Oshift(c_Type_Oshift(A,B,C,D),c_HOL_Ozero__class_Ozero(tc_nat),E,D)=c_Type_Oshift(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),E,D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)),C,D).
% 249.58/249.67 Following clause subsumed by 708 during input processing: 0 [copy,820,flip.1] c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),B,C)=hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(A,B,C)),C).
% 249.58/249.67 Following clause subsumed by 710 during input processing: 0 [copy,821,flip.1] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),C),D)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),C),D)),hAPP(hAPP(hAPP(c_Lambda_Osubst,B),C),D)).
% 249.58/249.67 Following clause subsumed by 715 during input processing: 0 [copy,822,flip.1] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),C)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,A),C)),hAPP(hAPP(c_Lambda_Olift,B),C)).
% 249.58/249.67 Following clause subsumed by 716 during input processing: 0 [copy,823,flip.1] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C),D)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),C),D),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,C,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),D,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),B,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 249.58/249.67 Following clause subsumed by 717 during input processing: 0 [copy,824,flip.1] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 249.58/249.67 Following clause subsumed by 753 during input processing: 0 [copy,825,flip.1] c_COMBB(A,B,C,D,E,F)=hAPP(A,hAPP(B,C)).
% 249.58/249.67 Following clause subsumed by 761 during input processing: 0 [copy,826,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))!=c_HOL_Ozero__class_Ozero(tc_nat).
% 249.58/249.67
% 249.58/249.67 ======= end of input processing =======
% 249.58/249.67
% 249.58/249.67 =========== start of search ===========
% 249.58/249.67
% 249.58/249.67
% 249.58/249.67 Resetting weight limit to 2.
% 249.58/249.67
% 249.58/249.67
% 249.58/249.67 Resetting weight limit to 2.
% 249.58/249.67
% 249.58/249.67 sos_size=192
% 249.58/249.67
% 249.58/249.67 Search stopped in tp_alloc by max_mem option.
% 249.58/249.67
% 249.58/249.67 Search stopped in tp_alloc by max_mem option.
% 249.58/249.67
% 249.58/249.67 ============ end of search ============
% 249.58/249.67
% 249.58/249.67 -------------- statistics -------------
% 249.58/249.67 clauses given 161
% 249.58/249.67 clauses generated 150870
% 249.58/249.67 clauses kept 700
% 249.58/249.67 clauses forward subsumed 169
% 249.58/249.67 clauses back subsumed 16
% 249.58/249.67 Kbytes malloced 11718
% 249.58/249.67
% 249.58/249.67 ----------- times (seconds) -----------
% 249.58/249.67 user CPU time 1.63 (0 hr, 0 min, 1 sec)
% 249.58/249.67 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 249.58/249.67 wall-clock time 249 (0 hr, 4 min, 9 sec)
% 249.58/249.67
% 249.58/249.67 Process 5760 finished Wed Jul 27 09:16:14 2022
% 249.58/249.67 Otter interrupted
% 249.58/249.67 PROOF NOT FOUND
%------------------------------------------------------------------------------