TSTP Solution File: LCL833-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL833-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.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 13:05:34 EDT 2022
% Result : Unknown 193.91s 193.97s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL833-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 09:15:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 192.01/192.06 ----- Otter 3.3f, August 2004 -----
% 192.01/192.06 The process was started by sandbox on n004.cluster.edu,
% 192.01/192.06 Wed Jul 27 09:15:21 2022
% 192.01/192.06 The command was "./otter". The process ID is 13774.
% 192.01/192.06
% 192.01/192.06 set(prolog_style_variables).
% 192.01/192.06 set(auto).
% 192.01/192.06 dependent: set(auto1).
% 192.01/192.06 dependent: set(process_input).
% 192.01/192.06 dependent: clear(print_kept).
% 192.01/192.06 dependent: clear(print_new_demod).
% 192.01/192.06 dependent: clear(print_back_demod).
% 192.01/192.06 dependent: clear(print_back_sub).
% 192.01/192.06 dependent: set(control_memory).
% 192.01/192.06 dependent: assign(max_mem, 12000).
% 192.01/192.06 dependent: assign(pick_given_ratio, 4).
% 192.01/192.06 dependent: assign(stats_level, 1).
% 192.01/192.06 dependent: assign(max_seconds, 10800).
% 192.01/192.06 clear(print_given).
% 192.01/192.06
% 192.01/192.06 list(usable).
% 192.01/192.06 0 [] A=A.
% 192.01/192.06 0 [] c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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)).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat).
% 192.01/192.06 0 [] c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)!=c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)|V_m=V_n.
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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.
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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.
% 192.01/192.06 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).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_z,V_x,T_a)| -c_HOL_Oord__class_Oless(V_z,V_y,T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 192.01/192.06 0 [] -class_Orderings_Opreorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_z,T_a)| -c_HOL_Oord__class_Oless(V_y,V_z,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)=c_HOL_Otimes__class_Otimes(V_b,V_a,T_a).
% 192.01/192.06 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)=c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat).
% 192.01/192.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_x,V_y,T_a)=c_HOL_Otimes__class_Otimes(V_y,V_x,T_a).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 0 [] c_Suc(V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Oone__class_Oone(tc_nat)).
% 192.01/192.06 0 [] c_Suc(V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),V_n).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat)=V_n.
% 192.01/192.06 0 [] c_HOL_Otimes__class_Otimes(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=V_n.
% 192.01/192.06 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.
% 192.01/192.06 0 [] c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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)))).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_Nat_Osemiring__char__0(T_a)|c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)!=c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)|V_m=V_n.
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat).
% 192.01/192.06 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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)).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 192.01/192.06 0 [] c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k)=c_Lambda_OdB_OVar(V_i)| -c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)|c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_x),V_s,V_x)=c_Lambda_Oliftn(V_x,V_s,c_HOL_Ozero__class_Ozero(tc_nat)).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_j,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_k,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__comm__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 192.01/192.06 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)).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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.
% 192.01/192.06 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)).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Omult__zero(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Omult__zero(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oring__no__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oring__no__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_Ring__and__Field_Ono__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Ono__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oring__no__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] hAPP(V_e,V_i)=V_T| -c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 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).
% 192.01/192.06 0 [] hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x)=V_T.
% 192.01/192.06 0 [] c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_i),V_s,V_k)=c_Lambda_OdB_OVar(V_i)|V_i=V_k|c_HOL_Oord__class_Oless(V_k,V_i,tc_nat).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a)=c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 192.01/192.06 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).
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_ry,T_a),T_a).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -c_HOL_Oord__class_Oless(V_x,V_x,tc_nat).
% 192.01/192.06 0 [] -c_HOL_Oord__class_Oless(V_n,V_n,tc_nat).
% 192.01/192.06 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 192.01/192.06 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 192.01/192.06 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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)))).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|V_x=V_y.
% 192.01/192.06 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)|V_m=V_n.
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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.
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(V_y,V_x,tc_nat)|c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)|V_x=V_y.
% 192.01/192.06 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|V_x=V_y.
% 192.01/192.06 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 192.01/192.06 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,V_a,T_a).
% 192.01/192.06 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,V_x,tc_nat).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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)).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_OrderedGroup_Oab__semigroup__idem__mult(T_a)|c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_x,V_y,T_a).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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.
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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)).
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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).
% 192.01/192.06 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))).
% 192.01/192.06 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)).
% 192.01/192.06 0 [] c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Otimes__class_Otimes(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 192.01/192.06 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)=c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 192.01/192.06 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))).
% 192.01/192.06 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)).
% 192.01/192.06 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 192.01/192.06 0 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k)=V_t.
% 192.01/192.06 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))).
% 192.01/192.06 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))).
% 192.01/192.06 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))).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.01/192.06 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))).
% 192.01/192.06 0 [] c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.01/192.06 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.01/192.06 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat)!=c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat)|V_k=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=V_n.
% 192.01/192.06 0 [] c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)!=c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)|V_k=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=V_n.
% 192.01/192.06 0 [] c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)!=c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)|V_m=V_n|V_k=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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))).
% 192.01/192.06 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))).
% 192.01/192.06 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).
% 192.01/192.06 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))).
% 192.01/192.06 0 [] -c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 192.01/192.06 0 [] -c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 192.01/192.06 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))).
% 192.01/192.06 0 [] V_x=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)).
% 192.01/192.06 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)=V_n.
% 192.01/192.06 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat))=V_m.
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat).
% 192.01/192.06 0 [] c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat)!=c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat)|V_m=V_n.
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat).
% 192.01/192.06 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).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat).
% 192.01/192.06 0 [] V_n=V_m| -c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)|c_HOL_Oord__class_Oless(V_n,V_m,tc_nat).
% 192.01/192.06 0 [] V_m=V_n| -c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)|c_HOL_Oord__class_Oless(V_n,V_m,tc_nat).
% 192.01/192.06 0 [] V_m=V_n|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 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.
% 192.01/192.06 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)).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat)|c_Suc(V_m)=V_n| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)|c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat).
% 192.01/192.06 0 [] -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_n,tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 192.01/192.06 0 [] c_Lambda_OdB_OVar(V_nat)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)!=c_Lambda_OdB_OVar(V_nat).
% 192.01/192.06 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).
% 192.01/192.06 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=c_Lambda_OdB_OVar(V_nat).
% 192.01/192.06 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OAbs(V_dB_H).
% 192.01/192.06 0 [] c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t))| -c_Lambda_Obeta(V_s,V_t).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a)=c_List_Olist_ONil(T_a).
% 192.01/192.06 0 [] c_List_Olist_ONil(T_a)=c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b)=V_a.
% 192.01/192.06 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)).
% 192.01/192.06 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k)=V_u.
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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)))).
% 192.01/192.06 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 192.01/192.06 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).
% 192.01/192.06 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.
% 192.01/192.06 0 [] c_Power_Opower__class_Opower(V_p,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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)).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_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).
% 192.01/192.06 0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat).
% 192.01/192.06 0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_OrderedGroup_Oab__semigroup__idem__mult(T_a)|c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)=V_x.
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OVar(V_nat_H)|V_nat=V_nat_H.
% 192.01/192.06 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).
% 192.01/192.06 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.
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 192.01/192.06 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).
% 192.01/192.06 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)).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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)).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_OrderedGroup_Oab__semigroup__mult(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)=c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a)=c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,V_rx,T_a),T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ry,T_a).
% 192.01/192.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a).
% 192.01/192.06 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_k,tc_nat)=c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat).
% 192.01/192.06 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a).
% 192.01/192.06 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 192.01/192.06 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 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).
% 192.01/192.06 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)).
% 192.01/192.06 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))).
% 192.01/192.06 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).
% 192.01/192.06 0 [] c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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)).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 192.01/192.06 0 [] c_HOL_Oone__class_Oone(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 192.01/192.06 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).
% 192.01/192.06 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))).
% 192.01/192.06 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 192.01/192.06 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 192.01/192.06 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))).
% 192.01/192.06 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))).
% 192.01/192.06 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).
% 192.01/192.06 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)).
% 192.01/192.06 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))).
% 192.01/192.06 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)).
% 192.01/192.06 0 [] V_n=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 192.01/192.06 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))).
% 192.01/192.06 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).
% 192.01/192.06 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_k,tc_nat).
% 192.01/192.06 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))).
% 192.01/192.06 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).
% 192.01/192.06 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)).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat).
% 192.01/192.06 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 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)).
% 192.01/192.06 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).
% 192.01/192.06 0 [] c_Divides_Odiv__class_Odiv(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=V_m.
% 192.01/192.06 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).
% 192.01/192.06 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)).
% 192.01/192.06 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).
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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.
% 192.01/192.06 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).
% 192.01/192.06 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.
% 192.01/192.06 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)).
% 192.01/192.06 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)))).
% 192.01/192.06 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).
% 192.01/192.06 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____).
% 192.01/192.06 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).
% 192.01/192.06 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)).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.06 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).
% 192.01/192.07 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).
% 192.01/192.07 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))).
% 192.01/192.07 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).
% 192.01/192.07 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_a____)).
% 192.01/192.07 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)).
% 192.01/192.07 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=c_Lambda_OdB_OAbs(V_dB_H).
% 192.01/192.07 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))).
% 192.01/192.07 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2).
% 192.01/192.07 0 [] V_n!=c_Suc(V_n).
% 192.01/192.07 0 [] c_Suc(V_n)!=V_n.
% 192.01/192.07 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).
% 192.01/192.07 0 [] c_Suc(V_m)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.01/192.07 0 [] c_Suc(V_nat_H)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.01/192.07 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).
% 192.01/192.07 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.
% 192.01/192.07 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.
% 192.01/192.07 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.
% 192.01/192.07 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.
% 192.01/192.07 0 [] c_Lambda_OdB_OAbs(V_dB)!=c_Lambda_OdB_OAbs(V_dB_H)|V_dB=V_dB_H.
% 192.01/192.07 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)))| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 192.01/192.07 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))).
% 192.01/192.07 0 [] c_Suc(V_nat)!=c_Suc(V_nat_H)|V_nat=V_nat_H.
% 192.01/192.07 0 [] c_Suc(V_x)!=c_Suc(V_y)|V_x=V_y.
% 192.01/192.07 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)).
% 192.01/192.07 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).
% 192.01/192.07 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_m).
% 192.01/192.07 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_nat_H).
% 192.01/192.07 0 [] hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R)=hAPP(hAPP(V_P,V_R),V_Q).
% 192.01/192.07 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.
% 192.01/192.07 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.
% 192.01/192.07 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r)))| -hBOOL(hAPP(c_InductTermi_OIT,V_r)).
% 192.01/192.07 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_u____)).
% 192.01/192.07 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k)=V_t.
% 192.01/192.07 0 [] -hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(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_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))).
% 192.01/192.07 0 [] class_Orderings_Opreorder(tc_fun(T_2,T_1))| -class_Orderings_Opreorder(T_1).
% 192.01/192.07 0 [] class_Orderings_Oorder(tc_fun(T_2,T_1))| -class_Orderings_Oorder(T_1).
% 192.01/192.07 0 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 192.01/192.07 0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 192.01/192.07 0 [] class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat).
% 192.01/192.07 0 [] class_Ring__and__Field_Oordered__semiring__strict(tc_nat).
% 192.01/192.07 0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 192.01/192.07 0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 192.01/192.07 0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 192.01/192.07 0 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 192.01/192.07 0 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 192.01/192.07 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 192.01/192.07 0 [] class_OrderedGroup_Oab__semigroup__mult(tc_nat).
% 192.01/192.07 0 [] class_OrderedGroup_Ocomm__monoid__mult(tc_nat).
% 192.01/192.07 0 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 192.01/192.07 0 [] class_Ring__and__Field_Ocomm__semiring(tc_nat).
% 192.01/192.07 0 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 192.01/192.07 0 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 192.01/192.07 0 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 192.01/192.07 0 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 192.01/192.07 0 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 192.01/192.07 0 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 192.01/192.07 0 [] class_OrderedGroup_Omonoid__mult(tc_nat).
% 192.01/192.07 0 [] class_Ring__and__Field_Osemiring(tc_nat).
% 192.01/192.07 0 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 192.01/192.07 0 [] class_Divides_Osemiring__div(tc_nat).
% 192.01/192.07 0 [] class_Nat_Osemiring__char__0(tc_nat).
% 192.01/192.07 0 [] class_Ring__and__Field_Odvd(tc_nat).
% 192.01/192.07 0 [] class_Orderings_Opreorder(tc_nat).
% 192.01/192.07 0 [] class_Orderings_Olinorder(tc_nat).
% 192.01/192.07 0 [] class_Orderings_Oorder(tc_nat).
% 192.01/192.07 0 [] class_Power_Opower(tc_nat).
% 192.01/192.07 0 [] hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R)=hAPP(hAPP(V_P,V_R),V_Q).
% 192.01/192.07 0 [] c_COMBB(V_P,V_Q,V_R,T_b,T_a,T_c)=hAPP(V_P,hAPP(V_Q,V_R)).
% 192.01/192.07 0 [] c_fe_qual(V_x,V_x,T_a).
% 192.01/192.07 0 [] V_X=V_Y| -c_fe_qual(V_X,V_Y,T_a).
% 192.01/192.07 end_of_list.
% 192.01/192.07
% 192.01/192.07 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 192.01/192.07
% 192.01/192.07 This ia a non-Horn set with equality. The strategy will be
% 192.01/192.07 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 192.01/192.07 deletion, with positive clauses in sos and nonpositive
% 192.01/192.07 clauses in usable.
% 192.01/192.07
% 192.01/192.07 dependent: set(knuth_bendix).
% 192.01/192.07 dependent: set(anl_eq).
% 192.01/192.07 dependent: set(para_from).
% 192.01/192.07 dependent: set(para_into).
% 192.01/192.07 dependent: clear(para_from_right).
% 192.01/192.07 dependent: clear(para_into_right).
% 192.01/192.07 dependent: set(para_from_vars).
% 192.01/192.07 dependent: set(eq_units_both_ways).
% 192.01/192.07 dependent: set(dynamic_demod_all).
% 192.01/192.07 dependent: set(dynamic_demod).
% 192.01/192.07 dependent: set(order_eq).
% 192.01/192.07 dependent: set(back_demod).
% 192.01/192.07 dependent: set(lrpo).
% 192.01/192.07 dependent: set(hyper_res).
% 192.01/192.07 dependent: set(unit_deletion).
% 192.01/192.07 dependent: set(factor).
% 192.01/192.07
% 192.01/192.07 ------------> process usable:
% 192.01/192.07 ** KEPT (pick-wt=13): 1 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=13): 2 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=22): 3 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=13): 4 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=13): 5 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=21): 6 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=10): 7 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=43): 8 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=34): 10 [copy,9,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)).
% 192.01/192.07 ** KEPT (pick-wt=20): 11 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=16): 12 [] -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)).
% 192.01/192.07 ** KEPT (pick-wt=15): 13 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=15): 14 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=17): 15 [] 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.
% 192.01/192.07 ** KEPT (pick-wt=9): 16 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=11): 17 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|A=c_HOL_Oone__class_Oone(tc_nat).
% 192.01/192.07 ** KEPT (pick-wt=11): 18 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|B=c_HOL_Oone__class_Oone(tc_nat).
% 192.01/192.07 ** KEPT (pick-wt=24): 20 [copy,19,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).
% 192.01/192.07 ** KEPT (pick-wt=24): 22 [copy,21,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).
% 192.01/192.07 ** KEPT (pick-wt=20): 23 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=12): 24 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=10): 25 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A)=c_HOL_Oone__class_Oone(A).
% 192.01/192.07 ** KEPT (pick-wt=28): 26 [] -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.
% 192.01/192.07 ** KEPT (pick-wt=22): 27 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=20): 28 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=25): 29 [] -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)).
% 192.01/192.07 ** KEPT (pick-wt=25): 30 [] -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)).
% 192.01/192.07 ** KEPT (pick-wt=25): 31 [] -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).
% 192.01/192.07 Following clause subsumed by 29 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)).
% 192.01/192.07 ** KEPT (pick-wt=25): 32 [] -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)).
% 192.01/192.07 ** KEPT (pick-wt=25): 33 [] -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)).
% 192.01/192.07 ** KEPT (pick-wt=25): 34 [] -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)).
% 192.01/192.07 ** KEPT (pick-wt=25): 35 [] -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)).
% 192.01/192.07 Following clause subsumed by 29 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)).
% 192.01/192.07 ** KEPT (pick-wt=14): 36 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=14): 37 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=21): 38 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=27): 40 [copy,39,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).
% 192.01/192.07 ** KEPT (pick-wt=11): 41 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,C,A)=c_HOL_Otimes__class_Otimes(C,B,A).
% 192.01/192.07 Following clause subsumed by 41 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).
% 192.01/192.07 ** KEPT (pick-wt=15): 42 [] -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).
% 192.01/192.07 Following clause subsumed by 42 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).
% 192.01/192.07 ** KEPT (pick-wt=15): 43 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=15): 44 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=17): 45 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=13): 46 [] -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).
% 192.01/192.07 ** 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(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat),A,tc_nat).
% 192.01/192.07 ** KEPT (pick-wt=29): 48 [] -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)).
% 192.01/192.07 Following clause subsumed by 48 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)).
% 192.01/192.07 ** KEPT (pick-wt=14): 49 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=15): 50 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=13): 51 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=9): 52 [] -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).
% 192.01/192.07 ** 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(B,C,A),A).
% 192.01/192.07 ** KEPT (pick-wt=9): 54 [] -class_Ring__and__Field_Odvd(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(B,C,A),A).
% 192.01/192.07 ** KEPT (pick-wt=9): 55 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A)=B.
% 192.01/192.07 ** KEPT (pick-wt=9): 56 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oone__class_Oone(A),A)=B.
% 192.01/192.07 ** KEPT (pick-wt=9): 57 [] -class_OrderedGroup_Omonoid__mult(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oone__class_Oone(A),A)=B.
% 192.01/192.07 ** KEPT (pick-wt=9): 58 [] -class_OrderedGroup_Omonoid__mult(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A)=B.
% 192.01/192.07 ** KEPT (pick-wt=9): 59 [] -class_OrderedGroup_Ocomm__monoid__mult(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A)=B.
% 192.01/192.07 Following clause subsumed by 55 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.
% 192.01/192.07 ** KEPT (pick-wt=14): 60 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=14): 61 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=16): 62 [] -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).
% 192.01/192.07 ** 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(B,D,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(C,D,A).
% 192.01/192.07 ** KEPT (pick-wt=14): 64 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=20): 65 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=32): 67 [copy,66,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).
% 192.01/192.07 ** KEPT (pick-wt=29): 68 [] -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).
% 192.01/192.07 ** 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(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).
% 192.01/192.07 ** KEPT (pick-wt=26): 70 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=13): 71 [] 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).
% 192.01/192.07 ** 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,C,tc_nat).
% 192.01/192.07 ** KEPT (pick-wt=13): 73 [] 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).
% 192.01/192.07 Following clause subsumed by 71 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).
% 192.01/192.07 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,C,tc_nat).
% 192.01/192.07 ** KEPT (pick-wt=17): 74 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=17): 75 [] -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).
% 192.01/192.07 Following clause subsumed by 74 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).
% 192.01/192.07 Following clause subsumed by 75 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).
% 192.01/192.07 ** KEPT (pick-wt=16): 76 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=15): 77 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=15): 78 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=21): 79 [] 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).
% 192.01/192.07 Following clause subsumed by 77 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).
% 192.01/192.07 ** KEPT (pick-wt=11): 80 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=12): 81 [] -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.
% 192.01/192.07 ** KEPT (pick-wt=16): 82 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=16): 83 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=16): 84 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)|B=C.
% 192.01/192.07 ** KEPT (pick-wt=16): 85 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B)|A=C.
% 192.01/192.07 Following clause subsumed by 84 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.
% 192.01/192.07 ** KEPT (pick-wt=20): 86 [] -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.
% 192.01/192.07 ** KEPT (pick-wt=18): 87 [] -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.
% 192.01/192.07 ** KEPT (pick-wt=18): 88 [] -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.
% 192.01/192.07 ** KEPT (pick-wt=18): 89 [] -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.
% 192.01/192.07 ** KEPT (pick-wt=16): 90 [] -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).
% 192.01/192.07 Following clause subsumed by 65 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).
% 192.01/192.07 ** KEPT (pick-wt=20): 92 [copy,91,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).
% 192.01/192.07 ** KEPT (pick-wt=24): 93 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=24): 94 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=11): 95 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=22): 96 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=22): 97 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=35): 98 [] -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)).
% 192.01/192.07 ** KEPT (pick-wt=9): 99 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=12): 100 [] c_Lambda_Oliftn(A,c_Lambda_OdB_OVar(B),C)=c_Lambda_OdB_OVar(B)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 192.01/192.07 ** KEPT (pick-wt=19): 101 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=22): 102 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=20): 103 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=22): 104 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=20): 105 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=15): 106 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=15): 107 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=13): 108 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=25): 109 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=43): 110 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=30): 111 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=19): 112 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=19): 113 [] 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).
% 192.01/192.07 Following clause subsumed by 113 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).
% 192.01/192.07 Following clause subsumed by 112 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).
% 192.01/192.07 ** KEPT (pick-wt=19): 114 [] 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).
% 192.01/192.07 Following clause subsumed by 113 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).
% 192.01/192.07 ** KEPT (pick-wt=21): 115 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=21): 116 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=21): 117 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=21): 118 [] -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).
% 192.01/192.07 Following clause subsumed by 116 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).
% 192.01/192.07 ** KEPT (pick-wt=21): 119 [] -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).
% 192.01/192.07 Following clause subsumed by 118 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).
% 192.01/192.07 Following clause subsumed by 116 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).
% 192.01/192.07 ** KEPT (pick-wt=21): 120 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=21): 121 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=21): 122 [] -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).
% 192.01/192.07 Following clause subsumed by 120 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).
% 192.01/192.07 ** KEPT (pick-wt=21): 123 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=19): 124 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=21): 125 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=21): 126 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=22): 127 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=14): 128 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=19): 129 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=19): 130 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=24): 131 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=16): 132 [] -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).
% 192.01/192.07 ** KEPT (pick-wt=18): 133 [] 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).
% 192.01/192.07 ** KEPT (pick-wt=20): 134 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=20): 135 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=26): 137 [copy,136,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).
% 192.01/192.08 ** KEPT (pick-wt=26): 139 [copy,138,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).
% 192.01/192.08 ** KEPT (pick-wt=22): 140 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=20): 141 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=9): 142 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(B,c_HOL_Oone__class_Oone(A),A)=B.
% 192.01/192.08 ** KEPT (pick-wt=27): 143 [] -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)).
% 192.01/192.08 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),B,tc_nat).
% 192.01/192.08 Following clause subsumed by 71 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).
% 192.01/192.08 ** KEPT (pick-wt=17): 144 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=17): 145 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=16): 146 [] -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).
% 192.01/192.08 Following clause subsumed by 146 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).
% 192.01/192.08 ** KEPT (pick-wt=19): 147 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=13): 148 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=10): 149 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=10): 150 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=10): 151 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=10): 152 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=10): 153 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=10): 154 [] -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).
% 192.01/192.08 Following clause subsumed by 149 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).
% 192.01/192.08 ** KEPT (pick-wt=7): 155 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ozero__class_Ozero(A),A).
% 192.01/192.08 ** KEPT (pick-wt=7): 157 [copy,156,flip.2] -class_Ring__and__Field_Ozero__ne_q__one(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Oone__class_Oone(A).
% 192.01/192.08 ** KEPT (pick-wt=17): 158 [] -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).
% 192.01/192.08 Following clause subsumed by 158 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).
% 192.01/192.08 ** KEPT (pick-wt=17): 159 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=10): 160 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 192.01/192.08 ** KEPT (pick-wt=10): 161 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 192.01/192.08 ** KEPT (pick-wt=15): 162 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=10): 163 [] hAPP(A,B)=C| -c_Type_Otyping(A,c_Lambda_OdB_OVar(B),C).
% 192.01/192.08 ** KEPT (pick-wt=12): 164 [] -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).
% 192.01/192.08 Following clause subsumed by 95 during input processing: 0 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=23): 166 [copy,165,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).
% 192.01/192.08 ** KEPT (pick-wt=17): 167 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=22): 169 [copy,168,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).
% 192.01/192.08 ** KEPT (pick-wt=28): 170 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=28): 171 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=20): 172 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=9): 173 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A)=B.
% 192.01/192.08 ** KEPT (pick-wt=9): 174 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A)=B.
% 192.01/192.08 ** KEPT (pick-wt=39): 175 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=17): 176 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=17): 177 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=17): 178 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=17): 179 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=20): 180 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=20): 181 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=20): 182 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=20): 183 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=18): 184 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=15): 185 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=13): 186 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=27): 187 [] -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)).
% 192.01/192.08 ** KEPT (pick-wt=24): 188 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=8): 189 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=18): 190 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=17): 191 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=35): 192 [] -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.
% 192.01/192.08 Following clause subsumed by 192 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.
% 192.01/192.08 ** KEPT (pick-wt=31): 193 [] 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.
% 192.01/192.08 Following clause subsumed by 193 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.
% 192.01/192.08 ** KEPT (pick-wt=15): 194 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=15): 195 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=14): 197 [copy,196,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).
% 192.01/192.08 ** KEPT (pick-wt=35): 198 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=23): 199 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=23): 200 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=23): 201 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=22): 202 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=22): 203 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=10): 204 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,c_HOL_Oone__class_Oone(A),A)=c_HOL_Ozero__class_Ozero(A).
% 192.01/192.08 ** KEPT (pick-wt=13): 205 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=13): 206 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=10): 207 [] c_Divides_Odiv__class_Omod(A,B,tc_nat)=A| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 192.01/192.08 ** KEPT (pick-wt=4): 208 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 192.01/192.08 Following clause subsumed by 208 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 192.01/192.08 ** KEPT (pick-wt=6): 209 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 192.01/192.08 ** KEPT (pick-wt=6): 210 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 192.01/192.08 ** KEPT (pick-wt=6): 211 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 192.01/192.08 ** KEPT (pick-wt=22): 212 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=18): 213 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=13): 214 [] -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.
% 192.01/192.08 ** KEPT (pick-wt=13): 215 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(C,B,A)|c_HOL_Oord__class_Oless(B,C,A).
% 192.01/192.08 ** KEPT (pick-wt=11): 216 [] A=B| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 192.01/192.08 Following clause subsumed by 216 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).
% 192.01/192.08 Following clause subsumed by 216 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).
% 192.01/192.08 Following clause subsumed by 216 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).
% 192.01/192.08 Following clause subsumed by 216 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).
% 192.01/192.08 Following clause subsumed by 216 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).
% 192.01/192.08 Following clause subsumed by 216 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.
% 192.01/192.08 Following clause subsumed by 215 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.
% 192.01/192.08 Following clause subsumed by 215 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).
% 192.01/192.08 Following clause subsumed by 215 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).
% 192.01/192.08 ** KEPT (pick-wt=13): 217 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=24): 218 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=22): 219 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=14): 220 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=6): 221 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,B,A).
% 192.01/192.08 ** KEPT (pick-wt=20): 222 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=12): 223 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=16): 224 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=4): 225 [] -c_Lambda_Obeta(c_Lambda_OdB_OVar(A),B).
% 192.01/192.08 ** KEPT (pick-wt=14): 226 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=14): 227 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=14): 228 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=14): 229 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=8): 230 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=14): 231 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=14): 232 [] 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).
% 192.01/192.08 Following clause subsumed by 64 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).
% 192.01/192.08 ** KEPT (pick-wt=19): 233 [] 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).
% 192.01/192.08 Following clause subsumed by 233 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).
% 192.01/192.08 ** KEPT (pick-wt=12): 234 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=17): 235 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=14): 236 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=31): 237 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=16): 239 [copy,238,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).
% 192.01/192.08 ** KEPT (pick-wt=9): 240 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 192.01/192.08 ** KEPT (pick-wt=9): 241 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 192.01/192.08 ** KEPT (pick-wt=10): 242 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 192.01/192.08 ** KEPT (pick-wt=13): 243 [] -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).
% 192.01/192.08 Following clause subsumed by 157 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).
% 192.01/192.08 ** KEPT (pick-wt=11): 244 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=11): 245 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 192.01/192.08 ** KEPT (pick-wt=11): 246 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 192.01/192.08 ** KEPT (pick-wt=13): 248 [copy,247,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.
% 192.01/192.08 ** KEPT (pick-wt=11): 249 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 192.01/192.08 ** KEPT (pick-wt=11): 250 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 192.01/192.08 ** KEPT (pick-wt=11): 251 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 192.01/192.08 ** KEPT (pick-wt=11): 252 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 192.01/192.08 Following clause subsumed by 245 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.
% 192.01/192.08 ** KEPT (pick-wt=13): 253 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=12): 254 [] -hBOOL(hAPP(A,B))|hBOOL(hAPP(A,c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))).
% 192.01/192.08 ** KEPT (pick-wt=12): 255 [] -hBOOL(hAPP(A,c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))|hBOOL(hAPP(A,B)).
% 192.01/192.08 ** KEPT (pick-wt=10): 257 [copy,256,factor_simp] hBOOL(hAPP(A,v_sko__List__Xlexn__Xinduct__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 192.01/192.08 ** KEPT (pick-wt=10): 259 [copy,258,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))).
% 192.01/192.08 Following clause subsumed by 208 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).
% 192.01/192.08 ** KEPT (pick-wt=13): 260 [] 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))).
% 192.01/192.08 Following clause subsumed by 260 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))).
% 192.01/192.08 ** KEPT (pick-wt=13): 261 [] -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))).
% 192.01/192.08 ** KEPT (pick-wt=10): 263 [copy,262,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))).
% 192.01/192.08 ** KEPT (pick-wt=15): 264 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=13): 265 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=13): 266 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=16): 267 [] 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.
% 192.01/192.08 ** KEPT (pick-wt=16): 268 [] 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.
% 192.01/192.08 Following clause subsumed by 268 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).
% 192.01/192.08 ** KEPT (pick-wt=12): 270 [copy,269,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.01/192.08 Following clause subsumed by 270 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.01/192.08 ** KEPT (pick-wt=10): 272 [copy,271,factor_simp] hBOOL(hAPP(A,v_sko__List__Xreplicate__Xinduct__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 192.01/192.08 ** KEPT (pick-wt=10): 274 [copy,273,factor_simp] hBOOL(hAPP(A,v_sko__Nat__Xnat__Xinducts__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 192.01/192.08 ** KEPT (pick-wt=10): 276 [copy,275,factor_simp] hBOOL(hAPP(A,v_sko__Nat__Xnat__Xinduct__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 192.01/192.08 ** KEPT (pick-wt=5): 277 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 192.01/192.08 Following clause subsumed by 277 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 192.01/192.08 ** KEPT (pick-wt=10): 279 [copy,278,factor_simp] hBOOL(hAPP(A,v_sko__List__Xupt__Xinduct__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 192.01/192.08 ** KEPT (pick-wt=19): 280 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=19): 281 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=21): 282 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=14): 283 [] c_HOL_Otimes__class_Otimes(c_Suc(A),B,tc_nat)!=c_HOL_Otimes__class_Otimes(c_Suc(A),C,tc_nat)|B=C.
% 192.01/192.08 ** KEPT (pick-wt=9): 284 [] c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 192.01/192.08 ** KEPT (pick-wt=9): 285 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat).
% 192.01/192.08 ** KEPT (pick-wt=13): 286 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=12): 287 [] A=B| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)|c_HOL_Oord__class_Oless(A,B,tc_nat).
% 192.01/192.08 ** KEPT (pick-wt=12): 288 [] A=B| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 192.01/192.08 Following clause subsumed by 287 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).
% 192.01/192.08 ** KEPT (pick-wt=13): 289 [] c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat)|c_Suc(A)=B| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 192.01/192.08 ** KEPT (pick-wt=9): 290 [] -c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat).
% 192.01/192.08 ** KEPT (pick-wt=10): 291 [] c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 192.01/192.08 ** KEPT (pick-wt=10): 292 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat).
% 192.01/192.08 Following clause subsumed by 291 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).
% 192.01/192.08 ** KEPT (pick-wt=8): 293 [] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 192.01/192.08 ** KEPT (pick-wt=14): 294 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),hAPP(hAPP(c_Lambda_OdB_OApp,A),C))| -c_Lambda_Obeta(B,C).
% 192.01/192.08 ** KEPT (pick-wt=14): 295 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),hAPP(hAPP(c_Lambda_OdB_OApp,C),B))| -c_Lambda_Obeta(A,C).
% 192.01/192.08 ** KEPT (pick-wt=8): 296 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 192.01/192.08 ** KEPT (pick-wt=5): 297 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 192.01/192.08 ** KEPT (pick-wt=5): 298 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 192.01/192.08 ** KEPT (pick-wt=8): 299 [] c_Lambda_Obeta(c_Lambda_OdB_OAbs(A),c_Lambda_OdB_OAbs(B))| -c_Lambda_Obeta(A,B).
% 192.01/192.08 ** KEPT (pick-wt=12): 300 [] c_List_Omap(A,B,C,D)!=c_List_Olist_ONil(D)|B=c_List_Olist_ONil(C).
% 192.01/192.08 ** KEPT (pick-wt=12): 301 [] c_List_Olist_ONil(A)!=c_List_Omap(B,C,D,A)|C=c_List_Olist_ONil(D).
% 192.01/192.08 ** KEPT (pick-wt=23): 302 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=13): 303 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=27): 305 [copy,304,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).
% 192.01/192.08 ** KEPT (pick-wt=18): 306 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=48): 307 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=14): 308 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,A),B),hAPP(hAPP(c_Lambda_Olift,C),B))| -c_Lambda_Obeta(A,C).
% 192.01/192.08 ** KEPT (pick-wt=26): 309 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=14): 310 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=28): 311 [] 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).
% 192.01/192.08 ** KEPT (pick-wt=14): 312 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=14): 313 [] -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).
% 192.01/192.08 ** KEPT (pick-wt=7): 314 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(A),B,A).
% 192.01/192.08 ** KEPT (pick-wt=19): 315 [] -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.
% 192.01/192.09 ** KEPT (pick-wt=10): 316 [] -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 192.01/192.09 ** KEPT (pick-wt=10): 317 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=20): 318 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=17): 319 [] -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).
% 192.01/192.09 Following clause subsumed by 42 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).
% 192.01/192.09 ** KEPT (pick-wt=15): 321 [copy,320,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).
% 192.01/192.09 ** KEPT (pick-wt=16): 322 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=16): 323 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=15): 324 [] hAPP(c_Type_Oshift(A,B,C,D),E)=hAPP(A,E)| -c_HOL_Oord__class_Oless(E,B,tc_nat).
% 192.01/192.09 ** KEPT (pick-wt=20): 325 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=20): 326 [] -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).
% 192.01/192.09 Following clause subsumed by 325 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).
% 192.01/192.09 ** KEPT (pick-wt=13): 327 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=13): 328 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=13): 329 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=13): 330 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=20): 331 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=15): 332 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=18): 333 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=21): 334 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=21): 335 [] -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).
% 192.01/192.09 Following clause subsumed by 334 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).
% 192.01/192.09 Following clause subsumed by 335 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).
% 192.01/192.09 ** KEPT (pick-wt=9): 336 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat).
% 192.01/192.09 ** KEPT (pick-wt=9): 337 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat).
% 192.01/192.09 ** KEPT (pick-wt=20): 338 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=20): 339 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=27): 340 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=30): 341 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=26): 342 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=21): 343 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=21): 344 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=14): 345 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=20): 346 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=20): 347 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=20): 348 [] -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).
% 192.01/192.09 ** 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),B),D),A)| -c_HOL_Oord__class_Oless(C,D,A).
% 192.01/192.09 ** 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),B),D),A)| -c_HOL_Oord__class_Oless(C,D,A).
% 192.01/192.09 ** 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),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A).
% 192.01/192.09 ** KEPT (pick-wt=18): 352 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=18): 353 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=18): 354 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=11): 355 [] c_Type_Otyping(A,B,C)| -c_Lambda_Obeta(D,B)| -c_Type_Otyping(A,D,C).
% 192.01/192.09 ** KEPT (pick-wt=16): 356 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=16): 357 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=8): 358 [] -class_OrderedGroup_Oab__semigroup__idem__mult(A)|c_HOL_Otimes__class_Otimes(B,B,A)=B.
% 192.01/192.09 ** KEPT (pick-wt=12): 359 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=12): 360 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=8): 361 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OVar(B)|A=B.
% 192.01/192.09 ** KEPT (pick-wt=9): 362 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=19): 363 [] -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.
% 192.01/192.09 ** KEPT (pick-wt=21): 364 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=21): 365 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=21): 366 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=21): 367 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=21): 368 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=17): 369 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=21): 370 [] -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)).
% 192.01/192.09 ** KEPT (pick-wt=20): 371 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=20): 372 [] -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).
% 192.01/192.09 Following clause subsumed by 22 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).
% 192.01/192.09 Following clause subsumed by 20 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).
% 192.01/192.09 ** KEPT (pick-wt=17): 374 [copy,373,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).
% 192.01/192.09 ** KEPT (pick-wt=19): 375 [] -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.
% 192.01/192.09 ** KEPT (pick-wt=19): 376 [] -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.
% 192.01/192.09 Following clause subsumed by 376 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.
% 192.01/192.09 ** KEPT (pick-wt=20): 378 [copy,377,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).
% 192.01/192.09 ** KEPT (pick-wt=20): 380 [copy,379,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).
% 192.01/192.09 ** KEPT (pick-wt=11): 381 [] c_HOL_Oone__class_Oone(tc_nat)!=c_HOL_Otimes__class_Otimes(A,B,tc_nat)|A=c_HOL_Oone__class_Oone(tc_nat).
% 192.01/192.09 ** KEPT (pick-wt=11): 382 [] c_HOL_Oone__class_Oone(tc_nat)!=c_HOL_Otimes__class_Otimes(A,B,tc_nat)|B=c_HOL_Oone__class_Oone(tc_nat).
% 192.01/192.09 ** KEPT (pick-wt=17): 383 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=17): 384 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=17): 385 [] -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).
% 192.01/192.09 Following clause subsumed by 385 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).
% 192.01/192.09 ** KEPT (pick-wt=17): 386 [] -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).
% 192.01/192.09 Following clause subsumed by 385 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).
% 192.01/192.09 Following clause subsumed by 131 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).
% 192.01/192.09 ** KEPT (pick-wt=24): 388 [copy,387,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).
% 192.01/192.09 ** KEPT (pick-wt=24): 390 [copy,389,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).
% 192.01/192.09 ** KEPT (pick-wt=16): 391 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=10): 392 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 192.01/192.09 ** KEPT (pick-wt=10): 393 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 192.01/192.09 Following clause subsumed by 223 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).
% 192.01/192.09 Following clause subsumed by 223 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).
% 192.01/192.09 ** KEPT (pick-wt=10): 394 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 192.01/192.09 Following clause subsumed by 394 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 192.01/192.09 ** KEPT (pick-wt=20): 395 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=16): 396 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=16): 397 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=9): 398 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=13): 399 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=18): 400 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=20): 401 [] 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)).
% 192.01/192.09 ** KEPT (pick-wt=15): 402 [] 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)).
% 192.01/192.09 ** KEPT (pick-wt=17): 403 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=15): 404 [] 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))).
% 192.01/192.09 ** KEPT (pick-wt=18): 405 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=20): 406 [] 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)).
% 192.01/192.09 ** KEPT (pick-wt=15): 407 [] 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))).
% 192.01/192.09 ** KEPT (pick-wt=13): 408 [] 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)).
% 192.01/192.09 ** KEPT (pick-wt=13): 409 [] 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)).
% 192.01/192.09 ** KEPT (pick-wt=15): 410 [] 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))).
% 192.01/192.09 ** KEPT (pick-wt=15): 411 [] 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))).
% 192.01/192.09 ** KEPT (pick-wt=15): 412 [] 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))).
% 192.01/192.09 ** KEPT (pick-wt=10): 413 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=15): 414 [] 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))).
% 192.01/192.09 ** KEPT (pick-wt=19): 415 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=19): 416 [] 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)).
% 192.01/192.09 ** KEPT (pick-wt=15): 417 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=19): 418 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=19): 419 [] 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)).
% 192.01/192.09 ** KEPT (pick-wt=11): 420 [] 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).
% 192.01/192.09 ** KEPT (pick-wt=23): 421 [] -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).
% 192.01/192.09 ** KEPT (pick-wt=18): 422 [] 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.
% 192.01/192.09 ** KEPT (pick-wt=18): 423 [] 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.
% 192.01/192.09 ** KEPT (pick-wt=20): 424 [] 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.
% 192.08/192.10 ** KEPT (pick-wt=16): 425 [] 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).
% 192.08/192.10 ** KEPT (pick-wt=13): 426 [] 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.
% 192.08/192.10 ** KEPT (pick-wt=13): 427 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,A),c_Lambda_OdB_OVar(B))))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 192.08/192.10 ** KEPT (pick-wt=32): 428 [] 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).
% 192.08/192.10 ** KEPT (pick-wt=15): 429 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),c_Lambda_OdB_OVar(B)),C)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 192.08/192.10 ** KEPT (pick-wt=21): 430 [] 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).
% 192.08/192.10 ** KEPT (pick-wt=13): 431 [] 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).
% 192.08/192.10 ** KEPT (pick-wt=15): 432 [] 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).
% 192.08/192.10 ** KEPT (pick-wt=13): 433 [] 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).
% 192.08/192.10 ** KEPT (pick-wt=14): 434 [] 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).
% 192.08/192.10 ** KEPT (pick-wt=50): 435 [] 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).
% 192.08/192.10 ** KEPT (pick-wt=18): 436 [] 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).
% 192.08/192.10 ** KEPT (pick-wt=8): 437 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 192.08/192.10 ** KEPT (pick-wt=8): 438 [] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 192.08/192.10 ** KEPT (pick-wt=4): 440 [copy,439,flip.1] c_Suc(A)!=A.
% 192.08/192.10 Following clause subsumed by 440 during input processing: 0 [] c_Suc(A)!=A.
% 192.08/192.10 ** KEPT (pick-wt=5): 441 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.08/192.10 Following clause subsumed by 441 during input processing: 0 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.08/192.10 ** KEPT (pick-wt=13): 442 [] 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).
% 192.08/192.10 ** KEPT (pick-wt=18): 443 [] 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.
% 192.08/192.10 ** KEPT (pick-wt=18): 444 [] 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.
% 192.08/192.10 ** KEPT (pick-wt=14): 445 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|A=C.
% 192.08/192.10 ** KEPT (pick-wt=14): 446 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|B=D.
% 192.08/192.10 ** KEPT (pick-wt=8): 447 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OAbs(B)|A=B.
% 192.08/192.10 ** KEPT (pick-wt=12): 448 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,A),B)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 192.08/192.10 ** 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))).
% 192.08/192.10 ** KEPT (pick-wt=8): 450 [] c_Suc(A)!=c_Suc(B)|A=B.
% 192.08/192.10 Following clause subsumed by 450 during input processing: 0 [] c_Suc(A)!=c_Suc(B)|A=B.
% 192.08/192.10 Following clause subsumed by 441 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.08/192.10 Following clause subsumed by 441 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.08/192.10 ** KEPT (pick-wt=13): 451 [] 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.
% 192.08/192.10 ** KEPT (pick-wt=16): 452 [] 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.
% 192.08/192.10 ** KEPT (pick-wt=9): 453 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(A)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 192.08/192.10 ** KEPT (pick-wt=48): 454 [] -hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(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_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))).
% 192.08/192.10 ** KEPT (pick-wt=6): 455 [] class_Orderings_Opreorder(tc_fun(A,B))| -class_Orderings_Opreorder(B).
% 192.08/192.10 ** KEPT (pick-wt=6): 456 [] class_Orderings_Oorder(tc_fun(A,B))| -class_Orderings_Oorder(B).
% 192.08/192.10 ** KEPT (pick-wt=7): 457 [] A=B| -c_fe_qual(A,B,C).
% 192.08/192.10 146 back subsumes 23.
% 192.08/192.10 223 back subsumes 222.
% 192.08/192.10 223 back subsumes 146.
% 192.08/192.10 231 back subsumes 114.
% 192.08/192.10 231 back subsumes 83.
% 192.08/192.10 Following clause subsumed by 296 during input processing: 0 [copy,293,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 192.08/192.10 Following clause subsumed by 293 during input processing: 0 [copy,296,flip.1] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 192.08/192.10 Following clause subsumed by 298 during input processing: 0 [copy,297,flip.1] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 192.08/192.10 Following clause subsumed by 297 during input processing: 0 [copy,298,flip.1] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 192.08/192.10 314 back subsumes 80.
% 192.08/192.10 316 back subsumes 253.
% 192.08/192.10 385 back subsumes 200.
% 192.08/192.10 386 back subsumes 201.
% 192.08/192.10 ** KEPT (pick-wt=15): 520 [copy,432,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).
% 192.08/192.10 ** KEPT (pick-wt=14): 521 [copy,434,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).
% 192.08/192.10 Following clause subsumed by 438 during input processing: 0 [copy,437,flip.1] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 192.08/192.10 Following clause subsumed by 437 during input processing: 0 [copy,438,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 192.08/192.10 Following clause subsumed by 432 during input processing: 0 [copy,520,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).
% 192.08/192.10 Following clause subsumed by 434 during input processing: 0 [copy,521,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).
% 192.08/192.10
% 192.08/192.10 ------------> process sos:
% 192.08/192.10 ** KEPT (pick-wt=3): 522 [] A=A.
% 192.08/192.10 ** KEPT (pick-wt=7): 523 [] c_Type_Otyping(A,c_Lambda_OdB_OVar(B),hAPP(A,B)).
% 192.08/192.10 ** KEPT (pick-wt=32): 525 [copy,524,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)).
% 192.08/192.10 ---> New Demodulator: 526 [new_demod,525] 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)).
% 192.08/192.10 ** KEPT (pick-wt=10): 528 [copy,527,unit_del,208] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),A)=B.
% 192.08/192.10 ---> New Demodulator: 529 [new_demod,528] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),A)=B.
% 192.08/192.10 ** KEPT (pick-wt=19): 530 [] 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).
% 192.08/192.10 ** KEPT (pick-wt=23): 531 [] 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)).
% 192.08/192.10 ---> New Demodulator: 532 [new_demod,531] 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)).
% 192.08/192.10 ** KEPT (pick-wt=23): 533 [] 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)).
% 192.08/192.10 ** KEPT (pick-wt=9): 534 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)=c_HOL_Otimes__class_Otimes(B,A,tc_nat).
% 192.08/192.10 ** KEPT (pick-wt=18): 535 [] 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).
% 192.08/192.10 ** KEPT (pick-wt=25): 536 [] 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)).
% 192.08/192.10 Following clause subsumed by 536 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)).
% 192.08/192.10 ** KEPT (pick-wt=10): 537 [] c_Suc(A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)).
% 192.08/192.10 ---> New Demodulator: 538 [new_demod,537] c_Suc(A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)).
% 192.08/192.10 ** KEPT (pick-wt=15): 540 [copy,539,demod,538] 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).
% 192.08/192.10 ** KEPT (pick-wt=7): 541 [] c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=A.
% 192.08/192.10 ---> New Demodulator: 542 [new_demod,541] c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=A.
% 192.08/192.10 ** KEPT (pick-wt=7): 543 [] c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 192.08/192.10 ---> New Demodulator: 544 [new_demod,543] c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 192.08/192.10 ** KEPT (pick-wt=5): 545 [] c_List_Olistsp(A,c_List_Olist_ONil(B),B).
% 192.08/192.10 ** KEPT (pick-wt=15): 547 [copy,546,demod,538,532] 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).
% 192.08/192.10 ** KEPT (pick-wt=15): 549 [copy,548,demod,538,532] 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).
% 192.08/192.10 Following clause subsumed by 547 during input processing: 0 [demod,538,532] 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).
% 192.08/192.10 Following clause subsumed by 522 during input processing: 0 [demod,544] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 192.08/192.10 ** KEPT (pick-wt=17): 551 [copy,550,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).
% 192.08/192.10 ---> New Demodulator: 552 [new_demod,551] 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).
% 192.08/192.10 ** KEPT (pick-wt=13): 553 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 192.08/192.10 ** KEPT (pick-wt=6): 554 [] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 192.08/192.10 Following clause subsumed by 522 during input processing: 0 [demod,544] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 192.08/192.10 ** KEPT (pick-wt=11): 556 [copy,555,unit_del,208] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 192.08/192.10 ---> New Demodulator: 557 [new_demod,556] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 192.08/192.10 ** KEPT (pick-wt=18): 558 [] 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).
% 192.08/192.10 ---> New Demodulator: 559 [new_demod,558] 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).
% 192.08/192.10 ** KEPT (pick-wt=18): 560 [] 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).
% 192.08/192.10 ---> New Demodulator: 561 [new_demod,560] 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).
% 192.08/192.10 ** KEPT (pick-wt=41): 563 [copy,562,demod,532,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).
% 192.08/192.10 ---> New Demodulator: 564 [new_demod,563] 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).
% 192.08/192.10 ** KEPT (pick-wt=19): 565 [] 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).
% 192.08/192.10 ** KEPT (pick-wt=17): 566 [] 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).
% 192.08/192.10 ---> New Demodulator: 567 [new_demod,566] 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).
% 192.08/192.10 ** KEPT (pick-wt=9): 568 [] 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).
% 192.08/192.10 ** KEPT (pick-wt=20): 570 [copy,569,demod,538] 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)).
% 192.08/192.10 ** KEPT (pick-wt=20): 572 [copy,571,demod,538] 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)).
% 192.08/192.10 ** KEPT (pick-wt=9): 573 [] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 192.08/192.10 ---> New Demodulator: 574 [new_demod,573] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 192.08/192.10 ** KEPT (pick-wt=15): 575 [] 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).
% 192.08/192.10 Following clause subsumed by 522 during input processing: 0 [demod,538,532,567,538] 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).
% 192.08/192.10 ** KEPT (pick-wt=17): 576 [] 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).
% 192.08/192.10 ** KEPT (pick-wt=17): 578 [copy,577,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).
% 192.08/192.10 ---> New Demodulator: 579 [new_demod,578] 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).
% 192.08/192.10 ** KEPT (pick-wt=11): 580 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 192.08/192.10 Following clause subsumed by 580 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).
% 192.08/192.10 Following clause subsumed by 580 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 192.08/192.10 ** KEPT (pick-wt=4): 581 [] c_Ring__and__Field_Odvd__class_Odvd(A,A,tc_nat).
% 192.08/192.10 ** KEPT (pick-wt=12): 582 [] 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).
% 192.08/192.10 ** KEPT (pick-wt=32): 584 [copy,583,demod,559,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).
% 192.08/192.10 ---> New Demodulator: 585 [new_demod,584] 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).
% 192.08/192.10 ** KEPT (pick-wt=11): 586 [] 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).
% 192.08/192.10 ** KEPT (pick-wt=11): 587 [] 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).
% 192.08/192.10 ** KEPT (pick-wt=7): 588 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 192.08/192.10 ---> New Demodulator: 589 [new_demod,588] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 192.08/192.10 ** KEPT (pick-wt=9): 590 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.08/192.10 ** KEPT (pick-wt=8): 591 [] c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.08/192.10 ---> New Demodulator: 592 [new_demod,591] c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.08/192.10 ** KEPT (pick-wt=8): 593 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.08/192.10 ---> New Demodulator: 594 [new_demod,593] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.08/192.10 ** KEPT (pick-wt=11): 595 [] 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).
% 192.08/192.10 ---> New Demodulator: 596 [new_demod,595] 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).
% 192.08/192.10 ** KEPT (pick-wt=9): 598 [copy,597,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 192.08/192.10 ---> New Demodulator: 599 [new_demod,598] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 192.08/192.10 ** KEPT (pick-wt=9): 600 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 192.08/192.10 ---> New Demodulator: 601 [new_demod,600] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 192.08/192.10 Following clause subsumed by 522 during input processing: 0 [demod,599] A=A.
% 192.08/192.10 ** KEPT (pick-wt=24): 603 [copy,602,demod,538,538,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).
% 192.08/192.10 ---> New Demodulator: 604 [new_demod,603] 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).
% 192.08/192.10 ** KEPT (pick-wt=10): 606 [copy,605,demod,538] 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).
% 192.08/192.10 Following clause subsumed by 606 during input processing: 0 [demod,538] 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).
% 192.08/192.10 ** KEPT (pick-wt=25): 608 [copy,607,demod,538,532,538,532] 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))).
% 192.08/192.10 Following clause subsumed by 522 during input processing: 0 [demod,538,538,532] 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))).
% 192.08/192.10 ** KEPT (pick-wt=33): 610 [copy,609,demod,538,538,538,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.
% 192.08/192.10 Following clause subsumed by 608 during input processing: 0 [demod,538,532,538] 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))).
% 192.08/192.10 Following clause subsumed by 606 during input processing: 0 [demod,538,unit_del,208] 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).
% 192.08/192.10 ** KEPT (pick-wt=14): 612 [copy,611,demod,538] 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).
% 192.08/192.10 ** KEPT (pick-wt=20): 614 [copy,613,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).
% 192.08/192.10 ---> New Demodulator: 615 [new_demod,614] 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).
% 192.08/192.10 ** KEPT (pick-wt=20): 617 [copy,616,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).
% 192.08/192.10 ---> New Demodulator: 618 [new_demod,617] 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).
% 192.08/192.10 ** KEPT (pick-wt=16): 620 [copy,619,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).
% 192.08/192.10 ---> New Demodulator: 621 [new_demod,620] 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).
% 192.08/192.10 ** KEPT (pick-wt=9): 622 [] c_List_Omap(A,c_List_Olist_ONil(B),B,C)=c_List_Olist_ONil(C).
% 192.08/192.10 ** KEPT (pick-wt=9): 623 [] c_List_Olist_ONil(A)=c_List_Omap(B,c_List_Olist_ONil(C),C,A).
% 192.08/192.10 ** KEPT (pick-wt=11): 625 [copy,624,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).
% 192.08/192.10 ---> New Demodulator: 626 [new_demod,625] 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).
% 192.08/192.10 ** KEPT (pick-wt=9): 627 [] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 192.08/192.10 ---> New Demodulator: 628 [new_demod,627] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 192.08/192.10 Following clause subsumed by 522 during input processing: 0 [demod,529] B=B.
% 192.08/192.10 ** KEPT (pick-wt=19): 630 [copy,629,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).
% 192.08/192.10 ---> New Demodulator: 631 [new_demod,630] 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).
% 192.08/192.10 ** KEPT (pick-wt=5): 632 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(A))).
% 192.08/192.10 ** KEPT (pick-wt=8): 633 [] c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 192.08/192.10 ---> New Demodulator: 634 [new_demod,633] c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 192.08/192.10 ** KEPT (pick-wt=9): 636 [copy,635,demod,594,594] 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).
% 192.08/192.10 ---> New Demodulator: 637 [new_demod,636] 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).
% 192.08/192.10 ** KEPT (pick-wt=29): 639 [copy,638,demod,559,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).
% 192.08/192.10 ---> New Demodulator: 640 [new_demod,639] 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).
% 192.08/192.10 ** KEPT (pick-wt=15): 641 [] 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).
% 192.08/192.10 ** KEPT (pick-wt=10): 642 [] c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.08/192.10 ** KEPT (pick-wt=4): 643 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 192.08/192.10 ** KEPT (pick-wt=15): 644 [] 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).
% 192.08/192.10 ---> New Demodulator: 645 [new_demod,644] 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).
% 192.08/192.11 ** KEPT (pick-wt=22): 647 [copy,646,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).
% 192.08/192.11 ---> New Demodulator: 648 [new_demod,647] 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).
% 192.08/192.11 ** KEPT (pick-wt=22): 650 [copy,649,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).
% 192.08/192.11 ---> New Demodulator: 651 [new_demod,650] 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).
% 192.08/192.11 ** KEPT (pick-wt=14): 653 [copy,652,demod,538,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).
% 192.08/192.11 Following clause subsumed by 522 during input processing: 0 [demod,538,601,601,538,601] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 192.08/192.11 Following clause subsumed by 522 during input processing: 0 [demod,538,601,538,601,599] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=8): 655 [copy,654,demod,538,601] c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.08/192.11 Following clause subsumed by 522 during input processing: 0 [demod,538,601,538,601,544,538,601] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 192.08/192.11 Following clause subsumed by 581 during input processing: 0 [demod,538,601,538,601] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=6): 657 [copy,656,demod,538,601] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 192.08/192.11 Following clause subsumed by 522 during input processing: 0 [demod,538,601] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=27): 659 [copy,658,demod,538] 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).
% 192.08/192.11 ** KEPT (pick-wt=14): 661 [copy,660,demod,538,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).
% 192.08/192.11 Following clause subsumed by 522 during input processing: 0 [demod,634,538,601] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 192.08/192.11 Following clause subsumed by 522 during input processing: 0 [demod,538,601,599,538,601] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=14): 663 [copy,662,demod,538,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).
% 192.08/192.11 ** KEPT (pick-wt=5): 665 [copy,664,demod,538,601] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat).
% 192.08/192.11 Following clause subsumed by 522 during input processing: 0 [demod,538,601,538,601,601] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=11): 667 [copy,666,demod,538] 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).
% 192.08/192.11 Following clause subsumed by 667 during input processing: 0 [demod,538] 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).
% 192.08/192.11 ** KEPT (pick-wt=8): 669 [copy,668,demod,538,601,538,601] c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 192.08/192.11 ---> New Demodulator: 670 [new_demod,669] c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 192.08/192.11 Following clause subsumed by 522 during input processing: 0 [demod,538,601,670,538,601] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=7): 672 [copy,671,demod,538,601] c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 192.08/192.11 ---> New Demodulator: 673 [new_demod,672] c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 192.08/192.11 ** KEPT (pick-wt=14): 675 [copy,674,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)).
% 192.08/192.11 ---> New Demodulator: 676 [new_demod,675] 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)).
% 192.08/192.11 Following clause subsumed by 522 during input processing: 0 [demod,628] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)=hAPP(hAPP(c_Lambda_OdB_OApp,A),B).
% 192.08/192.11 ** KEPT (pick-wt=28): 678 [copy,677,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).
% 192.08/192.11 ---> New Demodulator: 679 [new_demod,678] 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).
% 192.08/192.11 ** KEPT (pick-wt=18): 680 [] 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____).
% 192.08/192.11 ** KEPT (pick-wt=19): 682 [copy,681,demod,538] 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).
% 192.08/192.11 Following clause subsumed by 522 during input processing: 0 [demod,628] c_Lambda_OdB_OAbs(A)=c_Lambda_OdB_OAbs(A).
% 192.08/192.11 Following clause subsumed by 522 during input processing: 0 [demod,628] c_Lambda_OdB_OAbs(A)=c_Lambda_OdB_OAbs(A).
% 192.08/192.11 ** KEPT (pick-wt=12): 684 [copy,683,demod,676] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B),c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat))).
% 192.08/192.11 ** KEPT (pick-wt=4): 685 [] hBOOL(hAPP(c_InductTermi_OIT,v_a____)).
% 192.08/192.11 ** KEPT (pick-wt=29): 686 [] 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)).
% 192.08/192.11 ** KEPT (pick-wt=13): 688 [copy,687,demod,676] 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))).
% 192.08/192.11 ** KEPT (pick-wt=30): 689 [] 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).
% 192.08/192.11 ---> New Demodulator: 690 [new_demod,689] 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).
% 192.08/192.11 ** KEPT (pick-wt=23): 691 [] 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)).
% 192.08/192.11 ** KEPT (pick-wt=41): 692 [] 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).
% 192.08/192.11 ** KEPT (pick-wt=14): 693 [] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 192.08/192.11 ** KEPT (pick-wt=4): 694 [] hBOOL(hAPP(c_InductTermi_OIT,v_u____)).
% 192.08/192.11 ** KEPT (pick-wt=13): 695 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),B)),C),B)=A.
% 192.08/192.11 ---> New Demodulator: 696 [new_demod,695] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),B)),C),B)=A.
% 192.08/192.11 ** KEPT (pick-wt=2): 697 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 698 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 699 [] class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 700 [] class_Ring__and__Field_Oordered__semiring__strict(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 701 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 702 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 703 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 704 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 705 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 706 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 707 [] class_OrderedGroup_Oab__semigroup__mult(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 708 [] class_OrderedGroup_Ocomm__monoid__mult(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 709 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 710 [] class_Ring__and__Field_Ocomm__semiring(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 711 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 712 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 713 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 714 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 715 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 716 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 717 [] class_OrderedGroup_Omonoid__mult(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 718 [] class_Ring__and__Field_Osemiring(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 719 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 720 [] class_Divides_Osemiring__div(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 721 [] class_Nat_Osemiring__char__0(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 722 [] class_Ring__and__Field_Odvd(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 723 [] class_Orderings_Opreorder(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 724 [] class_Orderings_Olinorder(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 725 [] class_Orderings_Oorder(tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=2): 726 [] class_Power_Opower(tc_nat).
% 192.08/192.11 Following clause subsumed by 693 during input processing: 0 [] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 192.08/192.11 ** KEPT (pick-wt=13): 727 [] c_COMBB(A,B,C,D,E,F)=hAPP(A,hAPP(B,C)).
% 192.08/192.11 ** KEPT (pick-wt=4): 728 [] c_fe_qual(A,A,B).
% 192.08/192.11 Following clause subsumed by 522 during input processing: 0 [copy,522,flip.1] A=A.
% 192.08/192.11 522 back subsumes 504.
% 192.08/192.11 522 back subsumes 495.
% 192.08/192.11 522 back subsumes 494.
% 192.08/192.11 522 back subsumes 493.
% 192.08/192.11 >>>> Starting back demodulation with 526.
% 192.08/192.11 >>>> Starting back demodulation with 529.
% 192.08/192.11 >>>> Starting back demodulation with 532.
% 192.08/192.11 Following clause subsumed by 533 during input processing: 0 [copy,533,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)).
% 192.08/192.11 Following clause subsumed by 534 during input processing: 0 [copy,534,flip.1] c_HOL_Otimes__class_Otimes(A,B,tc_nat)=c_HOL_Otimes__class_Otimes(B,A,tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=19): 729 [copy,536,flip.1,demod,651,651] 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).
% 192.08/192.11 >>>> Starting back demodulation with 538.
% 192.08/192.11 >> back demodulating 519 with 538.
% 192.08/192.11 >> back demodulating 518 with 538.
% 192.08/192.11 >> back demodulating 517 with 538.
% 192.08/192.11 >> back demodulating 516 with 538.
% 192.08/192.11 >> back demodulating 503 with 538.
% 192.08/192.11 >> back demodulating 502 with 538.
% 192.08/192.11 >> back demodulating 454 with 538.
% 192.08/192.11 >> back demodulating 450 with 538.
% 192.08/192.11 >> back demodulating 441 with 538.
% 192.08/192.11 >> back demodulating 440 with 538.
% 192.08/192.11 >> back demodulating 420 with 538.
% 192.08/192.11 >> back demodulating 419 with 538.
% 192.08/192.11 >> back demodulating 418 with 538.
% 192.08/192.11 >> back demodulating 417 with 538.
% 192.08/192.11 >> back demodulating 416 with 538.
% 192.08/192.11 >> back demodulating 415 with 538.
% 192.08/192.11 >> back demodulating 414 with 538.
% 192.08/192.11 >> back demodulating 413 with 538.
% 192.08/192.11 >> back demodulating 412 with 538.
% 192.08/192.11 >> back demodulating 411 with 538.
% 192.08/192.11 >> back demodulating 410 with 538.
% 192.08/192.11 >> back demodulating 409 with 538.
% 192.08/192.11 >> back demodulating 408 with 538.
% 192.08/192.11 >> back demodulating 407 with 538.
% 192.08/192.11 >> back demodulating 406 with 538.
% 192.08/192.11 >> back demodulating 405 with 538.
% 192.08/192.11 >> back demodulating 404 with 538.
% 192.08/192.11 >> back demodulating 403 with 538.
% 192.08/192.11 >> back demodulating 402 with 538.
% 192.08/192.11 >> back demodulating 401 with 538.
% 192.08/192.11 >> back demodulating 400 with 538.
% 192.08/192.11 >> back demodulating 399 with 538.
% 192.08/192.11 >> back demodulating 321 with 538.
% 192.08/192.11 >> back demodulating 307 with 538.
% 192.08/192.11 >> back demodulating 292 with 538.
% 192.08/192.11 >> back demodulating 291 with 538.
% 192.08/192.11 >> back demodulating 290 with 538.
% 192.08/192.11 >> back demodulating 289 with 538.
% 192.08/192.11 >> back demodulating 288 with 538.
% 192.08/192.11 >> back demodulating 287 with 538.
% 192.08/192.11 >> back demodulating 286 with 538.
% 192.08/192.11 >> back demodulating 285 with 538.
% 192.08/192.11 >> back demodulating 284 with 538.
% 192.08/192.11 >> back demodulating 283 with 538.
% 192.08/192.11 >> back demodulating 282 with 538.
% 192.08/192.11 >> back demodulating 281 with 538.
% 192.08/192.11 >> back demodulating 280 with 538.
% 192.08/192.11 >> back demodulating 224 with 538.
% 192.08/192.11 >> back demodulating 132 with 538.
% 192.08/192.11 >> back demodulating 111 with 538.
% 192.08/192.11 >> back demodulating 82 with 538.
% 192.08/192.11 >> back demodulating 76 with 538.
% 192.08/192.11 >> back demodulating 44 with 538.
% 192.08/192.11 >> back demodulating 43 with 538.
% 192.08/192.11 >> back demodulating 42 with 538.
% 192.08/192.11 >> back demodulating 38 with 538.
% 192.08/192.11 >> back demodulating 12 with 538.
% 192.08/192.11 Following clause subsumed by 553 during input processing: 0 [copy,540,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)).
% 192.08/192.11 >>>> Starting back demodulation with 542.
% 192.08/192.11 >> back demodulating 47 with 542.
% 192.08/192.11 >>>> Starting back demodulation with 544.
% 192.08/192.11 >> back demodulating 46 with 544.
% 192.08/192.11 >>>> Starting back demodulation with 552.
% 192.08/192.11 Following clause subsumed by 553 during input processing: 0 [copy,553,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 192.08/192.11 553 back subsumes 540.
% 192.08/192.11 553 back subsumes 536.
% 192.08/192.11 >>>> Starting back demodulation with 557.
% 192.08/192.11 >>>> Starting back demodulation with 559.
% 192.08/192.11 >> back demodulating 509 with 559.
% 192.08/192.11 >> back demodulating 340 with 559.
% 192.08/192.11 >>>> Starting back demodulation with 561.
% 192.08/192.11 >>>> Starting back demodulation with 564.
% 192.08/192.11 >>>> Starting back demodulation with 567.
% 192.08/192.11 ** KEPT (pick-wt=20): 776 [copy,570,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).
% 192.08/192.11 ** KEPT (pick-wt=20): 777 [copy,572,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).
% 192.08/192.11 >>>> Starting back demodulation with 574.
% 192.08/192.11 >>>> Starting back demodulation with 579.
% 192.08/192.11 581 back subsumes 554.
% 192.08/192.11 >>>> Starting back demodulation with 585.
% 192.08/192.11 Following clause subsumed by 522 during input processing: 0 [copy,586,flip.1,demod,592,592] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.08/192.11 Following clause subsumed by 522 during input processing: 0 [copy,587,flip.1,demod,594,594] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.08/192.11 >>>> Starting back demodulation with 589.
% 192.08/192.11 >>>> Starting back demodulation with 592.
% 192.08/192.11 >> back demodulating 586 with 592.
% 192.08/192.11 >> back demodulating 511 with 592.
% 192.08/192.11 >> back demodulating 501 with 592.
% 192.08/192.11 >> back demodulating 474 with 592.
% 192.08/192.11 >>>> Starting back demodulation with 594.
% 192.08/192.11 >> back demodulating 587 with 594.
% 192.08/192.11 >> back demodulating 582 with 594.
% 192.08/192.11 >> back demodulating 500 with 594.
% 192.08/192.11 >> back demodulating 473 with 594.
% 192.08/192.11 >>>> Starting back demodulation with 596.
% 192.08/192.11 >>>> Starting back demodulation with 599.
% 192.08/192.11 >> back demodulating 595 with 599.
% 192.08/192.11 >>>> Starting back demodulation with 601.
% 192.08/192.11 >>>> Starting back demodulation with 604.
% 192.08/192.11 ** KEPT (pick-wt=25): 779 [copy,608,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)).
% 192.08/192.11 >>>> Starting back demodulation with 615.
% 192.08/192.11 >>>> Starting back demodulation with 618.
% 192.08/192.11 >>>> Starting back demodulation with 621.
% 192.08/192.11 Following clause subsumed by 623 during input processing: 0 [copy,622,flip.1] c_List_Olist_ONil(A)=c_List_Omap(B,c_List_Olist_ONil(C),C,A).
% 192.08/192.11 Following clause subsumed by 622 during input processing: 0 [copy,623,flip.1] c_List_Omap(A,c_List_Olist_ONil(B),B,C)=c_List_Olist_ONil(C).
% 192.08/192.11 >>>> Starting back demodulation with 626.
% 192.08/192.11 >>>> Starting back demodulation with 628.
% 192.08/192.11 >> back demodulating 625 with 628.
% 192.08/192.11 >> back demodulating 424 with 628.
% 192.08/192.11 >>>> Starting back demodulation with 631.
% 192.08/192.11 >>>> Starting back demodulation with 634.
% 192.08/192.11 >> back demodulating 568 with 634.
% 192.08/192.11 >> back demodulating 462 with 634.
% 192.08/192.11 >>>> Starting back demodulation with 637.
% 192.08/192.11 >>>> Starting back demodulation with 640.
% 192.08/192.11 ** KEPT (pick-wt=15): 781 [copy,641,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).
% 192.08/192.11 ** KEPT (pick-wt=10): 782 [copy,642,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).
% 192.08/192.11 >>>> Starting back demodulation with 645.
% 192.08/192.11 >>>> Starting back demodulation with 648.
% 192.08/192.11 >>>> Starting back demodulation with 651.
% 192.08/192.11 ** KEPT (pick-wt=8): 783 [copy,655,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)=c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 192.08/192.11 ** KEPT (pick-wt=27): 784 [copy,659,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).
% 192.08/192.11 >>>> Starting back demodulation with 670.
% 192.08/192.11 >>>> Starting back demodulation with 673.
% 192.08/192.11 >>>> Starting back demodulation with 676.
% 192.08/192.11 >> back demodulating 449 with 676.
% 192.08/192.11 >> back demodulating 435 with 676.
% 192.08/192.11 >>>> Starting back demodulation with 679.
% 192.08/192.11 ** KEPT (pick-wt=19): 787 [copy,682,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).
% 192.08/192.11 ** KEPT (pick-wt=29): 788 [copy,686,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).
% 192.08/192.11 >>>> Starting back demodulation with 690.
% 192.08/192.11 ** KEPT (pick-wt=23): 789 [copy,691,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).
% 192.08/192.11 ** KEPT (pick-wt=41): 790 [copy,692,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).
% 192.08/192.11 ** KEPT (pick-wt=14): 791 [copy,693,flip.1] hAPP(hAPP(A,B),C)=hAPP(c_COMBC(A,C,D,E,F),B).
% 192.08/192.11 >>>> Starting back demodulation with 696.
% 192.08/192.11 ** KEPT (pick-wt=13): 792 [copy,727,flip.1] hAPP(A,hAPP(B,C))=c_COMBB(A,B,C,D,E,F).
% 192.08/192.11 Following clause subsumed by 729 during input processing: 0 [copy,729,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).
% 192.08/192.11 ** KEPT (pick-wt=10): 793 [copy,735,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)).
% 192.08/192.11 Following clause subsumed by 570 during input processing: 0 [copy,776,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)).
% 192.08/192.11 Following clause subsumed by 572 during input processing: 0 [copy,777,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)).
% 192.08/192.11 Following clause subsumed by 608 during input processing: 0 [copy,779,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))).
% 192.08/192.11 Following clause subsumed by 641 during input processing: 0 [copy,781,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).
% 192.08/192.11 Following clause subsumed by 642 during input processing: 0 [copy,782,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).
% 192.08/192.11 Following clause subsumed by 655 during input processing: 0 [copy,783,flip.1] c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 192.08/192.11 Following clause subsumed by 659 during input processing: 0 [copy,784,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).
% 192.08/192.11 Following clause subsumed by 682 during input processing: 0 [copy,787,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).
% 192.08/192.11 Following clause subsumed by 686 during input processing: 0 [copy,788,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)).
% 192.08/192.11 Following clause subsumed by 691 during input processing: 0 [copy,789,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)).
% 192.08/192.11 Following clause subsumed by 692 during input processing: 0 [copy,790,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).
% 192.08/192.11 Following clause subsumed by 693 during input processing: 0 [copy,791,flip.1] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 192.08/192.11 Following clause subsumed by 727 during input processing: 0 [copy,792,flip.1] c_COMBB(A,B,C,D,E,F)=hAPP(A,hAPP(B,C)).
% 192.08/192.11 Following clause subsumed by 735 during input processing: 0 [copy,793,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).
% 192.08/192.11
% 192.08/192.11 ======= end of input processing =======
% 192.08/192.11
% 192.08/192.11 =========== start of search ===========
% 192.08/192.11
% 192.08/192.11
% 193.91/193.97 Resetting weight limit to 2.
% 193.91/193.97
% 193.91/193.97
% 193.91/193.97 Resetting weight limit to 2.
% 193.91/193.97
% 193.91/193.97 sos_size=180
% 193.91/193.97
% 193.91/193.97 Search stopped in tp_alloc by max_mem option.
% 193.91/193.97
% 193.91/193.97 Search stopped in tp_alloc by max_mem option.
% 193.91/193.97
% 193.91/193.97 ============ end of search ============
% 193.91/193.97
% 193.91/193.97 -------------- statistics -------------
% 193.91/193.97 clauses given 178
% 193.91/193.97 clauses generated 182736
% 193.91/193.97 clauses kept 681
% 193.91/193.97 clauses forward subsumed 168
% 193.91/193.97 clauses back subsumed 16
% 193.91/193.97 Kbytes malloced 11718
% 193.91/193.97
% 193.91/193.97 ----------- times (seconds) -----------
% 193.91/193.97 user CPU time 1.94 (0 hr, 0 min, 1 sec)
% 193.91/193.97 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 193.91/193.97 wall-clock time 194 (0 hr, 3 min, 14 sec)
% 193.91/193.97
% 193.91/193.97 Process 13774 finished Wed Jul 27 09:18:35 2022
% 193.91/193.97 Otter interrupted
% 193.91/193.97 PROOF NOT FOUND
%------------------------------------------------------------------------------