TSTP Solution File: LCL781-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL781-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 13:05:24 EDT 2022
% Result : Unknown 39.40s 39.54s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL781-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n014.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 09:18:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 38.60/38.71 ----- Otter 3.3f, August 2004 -----
% 38.60/38.71 The process was started by sandbox2 on n014.cluster.edu,
% 38.60/38.71 Wed Jul 27 09:18:24 2022
% 38.60/38.71 The command was "./otter". The process ID is 4018.
% 38.60/38.71
% 38.60/38.71 set(prolog_style_variables).
% 38.60/38.71 set(auto).
% 38.60/38.71 dependent: set(auto1).
% 38.60/38.71 dependent: set(process_input).
% 38.60/38.71 dependent: clear(print_kept).
% 38.60/38.71 dependent: clear(print_new_demod).
% 38.60/38.71 dependent: clear(print_back_demod).
% 38.60/38.71 dependent: clear(print_back_sub).
% 38.60/38.71 dependent: set(control_memory).
% 38.60/38.71 dependent: assign(max_mem, 12000).
% 38.60/38.71 dependent: assign(pick_given_ratio, 4).
% 38.60/38.71 dependent: assign(stats_level, 1).
% 38.60/38.71 dependent: assign(max_seconds, 10800).
% 38.60/38.71 clear(print_given).
% 38.60/38.71
% 38.60/38.71 list(usable).
% 38.60/38.71 0 [] A=A.
% 38.60/38.71 0 [] V_n=c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 38.60/38.71 0 [] c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat))=V_n| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 38.60/38.71 0 [] c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=V_n.
% 38.60/38.71 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)))).
% 38.60/38.71 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).
% 38.60/38.71 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)).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_j,V_k,tc_nat).
% 38.60/38.71 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)=c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),V_n))|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.71 0 [] V_n=V_m| -c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)|c_HOL_Oord__class_Oless(V_n,V_m,tc_nat).
% 38.60/38.71 0 [] V_m=V_n| -c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)|c_HOL_Oord__class_Oless(V_n,V_m,tc_nat).
% 38.60/38.71 0 [] V_m=V_n|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat).
% 38.60/38.71 0 [] c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat)=c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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)).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y))| -hBOOL(hAPP(hAPP(V_r,V_x),V_y)).
% 38.60/38.71 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.
% 38.60/38.71 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.
% 38.60/38.71 0 [] c_HOL_Oone__class_Oone(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.60/38.71 0 [] -class_OrderedGroup_Oab__semigroup__add(T_a)|c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,V_a,T_a,T_a)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_a,V_xs,T_a,T_a).
% 38.60/38.71 0 [] c_Suc(V_nat)!=c_Suc(V_nat_H)|V_nat=V_nat_H.
% 38.60/38.71 0 [] c_Suc(V_x)!=c_Suc(V_y)|V_x=V_y.
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 0 [] c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=V_m.
% 38.60/38.71 0 [] c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.71 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 38.60/38.71 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 38.60/38.71 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=V_a.
% 38.60/38.71 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 38.60/38.71 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 0 [] -class_Nat_Osemiring__char__0(T_a)|c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)!=c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)|V_m=V_n.
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_l,tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 38.60/38.71 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)).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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)))).
% 38.60/38.71 0 [] c_HOL_Ominus__class_Ominus(c_Suc(V_n),c_HOL_Oone__class_Oone(tc_nat),tc_nat)=V_n.
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 0 [] c_Suc(V_nat_H)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.71 0 [] c_Suc(V_m)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.71 0 [] hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1(V_P,V_n)))| -hBOOL(hAPP(V_P,V_n))|hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 38.60/38.71 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).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 38.60/38.71 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_xs,T_a,T_a)=c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a).
% 38.60/38.71 0 [] hAPP(c_Type_Oshift(V_e,V_i,V_T,T_a),V_j)=hAPP(V_e,c_HOL_Ominus__class_Ominus(V_j,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),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)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)).
% 38.60/38.71 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.
% 38.60/38.71 0 [] c_Power_Opower__class_Opower(V_p,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 0 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k)=V_t.
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat).
% 38.60/38.71 0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat).
% 38.60/38.71 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).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat)| -c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat).
% 38.60/38.71 0 [] c_Suc(V_n)!=V_n.
% 38.60/38.71 0 [] V_n!=c_Suc(V_n).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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)).
% 38.60/38.71 0 [] hBOOL(hAPP(V_P,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xex__least__nat__less__1__1(V_P,V_n)),c_HOL_Oone__class_Oone(tc_nat))))| -hBOOL(hAPP(V_P,V_n))|hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 38.60/38.71 0 [] c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))=V_n| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 38.60/38.71 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)).
% 38.60/38.71 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_y,T_a)!=c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)|c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 38.60/38.71 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_y,T_a)!=c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)| -c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a).
% 38.60/38.71 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat))=V_m|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_n,c_Suc(V_i),tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 38.60/38.71 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)).
% 38.60/38.71 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).
% 38.60/38.71 0 [] c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB1)),c_Lambda_OdB_OdB__size(V_dB2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 38.60/38.71 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)))).
% 38.60/38.71 0 [] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(V_dB))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_c))| -hBOOL(hAPP(hAPP(V_r,V_a),V_b)).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c))| -hBOOL(hAPP(hAPP(V_r,V_b),V_c))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_b)).
% 38.60/38.71 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).
% 38.60/38.71 0 [] c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T,V_e,V_i,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)|c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_x),V_s,V_x)=c_Lambda_Oliftn(V_x,V_s,c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.60/38.71 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_j)),V_u),V_i)=c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(V_j,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 38.60/38.71 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i)),V_s),V_k)=c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(V_i,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(V_k,V_i,tc_nat).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 0 [] V_T=hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(V_T,V_e,V_t)),c_Type_Osko__Type__Xtyping__elims__3__2(V_T,V_e,V_t))| -c_Type_Otyping(V_e,c_Lambda_OdB_OAbs(V_t),V_T).
% 38.60/38.71 0 [] V_U=c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(V_T,V_U,V_e,V_us),V_T,tc_Type_Otype,tc_Type_Otype)| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_U)| -c_Type_Otypings(V_e,V_ts,V_Ts)| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_us,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 38.60/38.71 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 38.60/38.71 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat).
% 38.60/38.71 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).
% 38.60/38.71 0 [] V_n=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 38.60/38.71 0 [] hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat)))| -c_HOL_Oord__class_Oless(V_i,V_p,tc_nat)| -hBOOL(hAPP(V_P,V_i))|hBOOL(hAPP(V_P,c_List_Osko__Divides__Xmod__induct__0__1__1(V_P,V_p))).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_m).
% 38.60/38.71 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_nat_H).
% 38.60/38.71 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)).
% 38.60/38.71 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)).
% 38.60/38.71 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)).
% 38.60/38.71 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).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_z))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_z))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y)).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)).
% 38.60/38.71 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).
% 38.60/38.71 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)).
% 38.60/38.71 0 [] c_Suc(V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),V_n).
% 38.60/38.71 0 [] c_Suc(V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Oone__class_Oone(tc_nat)).
% 38.60/38.71 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).
% 38.60/38.71 0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ominus__class_Ominus(V_a,V_b,T_a)),V_b)=V_a.
% 38.60/38.71 0 [] -hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_b),V_x),V_b,tc_nat)))|hBOOL(hAPP(V_P,V_x)).
% 38.60/38.71 0 [] -hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_b),V_d),V_b,tc_nat)))|hBOOL(hAPP(V_P,V_d)).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_Suc(V_m),tc_nat).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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)).
% 38.60/38.71 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)).
% 38.60/38.71 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)).
% 38.60/38.71 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)).
% 38.60/38.71 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)).
% 38.60/38.71 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)).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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)).
% 38.60/38.71 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)).
% 38.60/38.71 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.
% 38.60/38.71 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).
% 38.60/38.71 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))).
% 38.60/38.71 0 [] c_HOL_Ominus__class_Ominus(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.71 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat)=c_HOL_Ominus__class_Ominus(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k),tc_nat).
% 38.60/38.71 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).
% 38.60/38.71 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a)!=c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)|V_xa=V_y.
% 38.60/38.71 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)!=c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)|V_x_H=V_y_H.
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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)).
% 38.60/38.71 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)).
% 38.60/38.71 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)).
% 38.60/38.71 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.71 0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k),tc_nat)=c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat).
% 38.60/38.71 0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat)=c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat).
% 38.60/38.71 0 [] c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),tc_Lambda_OdB)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(V_dB2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 38.60/38.71 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_y,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_x=V_y.
% 38.60/38.71 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=V_b.
% 38.60/38.71 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=V_b.
% 38.60/38.71 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_k,tc_nat),V_j,tc_nat).
% 38.60/38.71 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_a,V_xs,T_a,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a)).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat)|c_Suc(V_m)=V_n| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 38.60/38.71 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.
% 38.60/38.71 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.
% 38.60/38.71 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.
% 38.60/38.71 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.
% 38.60/38.71 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.
% 38.60/38.71 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.
% 38.60/38.71 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.
% 38.60/38.71 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).
% 38.60/38.71 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.
% 38.60/38.71 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).
% 38.60/38.71 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)).
% 38.60/38.71 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat),c_Suc(V_k),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat).
% 38.60/38.71 0 [] c_HOL_Ominus__class_Ominus(V_m,c_Suc(V_n),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_n,tc_nat).
% 38.60/38.71 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)).
% 38.60/38.71 0 [] c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(V_dB),tc_Lambda_OdB)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 38.60/38.71 0 [] c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_i),V_s,V_k)=c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(V_i,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(V_k,V_i,tc_nat).
% 38.60/38.71 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)).
% 38.60/38.71 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)).
% 38.60/38.71 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)).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)|c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat).
% 38.60/38.71 0 [] -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 0 [] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a)=c_Transitive__Closure_Ortranclp(V_r,T_a).
% 38.60/38.71 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.
% 38.60/38.71 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.
% 38.60/38.71 0 [] V_x=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.60/38.71 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)=V_n.
% 38.60/38.71 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat))=V_m.
% 38.60/38.71 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)).
% 38.60/38.71 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.
% 38.60/38.71 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.
% 38.60/38.71 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.
% 38.60/38.71 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.
% 38.60/38.71 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.
% 38.60/38.71 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)).
% 38.60/38.71 0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),V_n,tc_nat)=V_m.
% 38.60/38.71 0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_n,tc_nat)=V_m.
% 38.60/38.71 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_b,T_a)=V_a.
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_n,tc_nat).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xex__least__nat__less__1__1(V_P,V_n),V_n,tc_nat)| -hBOOL(hAPP(V_P,V_n))|hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 38.60/38.71 0 [] hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat)))| -c_HOL_Oord__class_Oless(V_a,V_b,tc_nat)| -hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(V_a,V_b,tc_nat))).
% 38.60/38.71 0 [] -hBOOL(hAPP(V_P,V_i))| -c_HOL_Oord__class_Oless(V_i,c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1(V_P,V_n),tc_nat)| -hBOOL(hAPP(V_P,V_n))|hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 38.60/38.71 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).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 38.60/38.71 0 [] hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat)))| -c_HOL_Oord__class_Oless(V_i,V_p,tc_nat)| -hBOOL(hAPP(V_P,V_i))|c_HOL_Oord__class_Oless(c_List_Osko__Divides__Xmod__induct__0__1__1(V_P,V_p),V_p,tc_nat).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s_H),V_t_H)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s_H),V_t)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t_H)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)).
% 38.60/38.71 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.
% 38.60/38.71 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.
% 38.60/38.71 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.
% 38.60/38.71 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).
% 38.60/38.71 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)).
% 38.60/38.71 0 [] V_s=c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_r)),V_s)).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(V_s)),c_Lambda_OdB_OAbs(V_s_H)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_r)),V_s)).
% 38.60/38.71 0 [] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(V_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.71 0 [] c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(V_nat),tc_Lambda_OdB)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.71 0 [] c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k)=c_Lambda_OdB_OVar(V_i)| -c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 38.60/38.71 0 [] c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_i),V_s,V_k)=c_Lambda_OdB_OVar(V_i)|V_i=V_k|c_HOL_Oord__class_Oless(V_k,V_i,tc_nat).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_r),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_i)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_t),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),V_i)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_r),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_i)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)).
% 38.60/38.71 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.
% 38.60/38.71 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.
% 38.60/38.71 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.
% 38.60/38.71 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)))).
% 38.60/38.71 0 [] c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u))| -c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T).
% 38.60/38.71 0 [] c_Type_Otyping(V_e,V_t_H,V_T)| -c_Type_Otyping(V_e,V_t,V_T)| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,V_r),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)).
% 38.60/38.71 0 [] c_Type_Otypings(V_e,V_us,c_Type_Osko__Type__Xvar__app__types__1__1(V_T,V_U,V_e,V_us))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_U)| -c_Type_Otypings(V_e,V_ts,V_Ts)| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_us,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 38.60/38.71 0 [] c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T,V_e,V_i,V_ts))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 38.60/38.71 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).
% 38.60/38.71 0 [] c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T)| -c_Type_Otypings(V_e,V_ts,V_Ts)| -c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,V_T,tc_Type_Otype,tc_Type_Otype)).
% 38.60/38.71 0 [] c_Type_Otyping(c_Type_Oshift(V_e,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(V_T,V_e,V_t),tc_Type_Otype),V_t,c_Type_Osko__Type__Xtyping__elims__3__2(V_T,V_e,V_t))| -c_Type_Otyping(V_e,c_Lambda_OdB_OAbs(V_t),V_T).
% 38.60/38.71 0 [] c_Type_Otyping(c_Type_Oshift(V_e,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(V_e,V_t),tc_Type_Otype),V_t,c_Type_Osko__Type__Xabs__typeE__1__2(V_e,V_t))| -c_Type_Otyping(V_e,c_Lambda_OdB_OAbs(V_t),V_T).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 0 [] c_Type_Otyping(V_e,V_t,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)),V_T))| -c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T).
% 38.60/38.71 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 38.60/38.71 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 38.60/38.71 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))).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)!=c_Lambda_OdB_OVar(V_nat).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_s)),c_Lambda_OdB_OAbs(V_t)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)).
% 38.60/38.71 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)).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,V_r),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)).
% 38.60/38.71 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).
% 38.60/38.71 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).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_u)),hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_s)),hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_t)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)).
% 38.60/38.71 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.
% 38.60/38.71 0 [] hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R)=hAPP(hAPP(V_P,V_R),V_Q).
% 38.60/38.71 0 [] -c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 38.60/38.71 0 [] -c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 38.60/38.71 0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_z,V_x,T_a)| -c_HOL_Oord__class_Oless(V_z,V_y,T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 38.60/38.71 0 [] -class_Orderings_Opreorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_z,T_a)| -c_HOL_Oord__class_Oless(V_y,V_z,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 38.60/38.71 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).
% 38.60/38.71 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)).
% 38.60/38.71 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OAbs(V_dB_H).
% 38.60/38.71 0 [] c_Lambda_OdB_OAbs(V_dB)!=c_Lambda_OdB_OAbs(V_dB_H)|V_dB=V_dB_H.
% 38.60/38.71 0 [] c_Lambda_OdB_OVar(V_nat)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H).
% 38.60/38.71 0 [] -c_HOL_Oord__class_Oless(V_x,V_x,tc_nat).
% 38.60/38.71 0 [] -c_HOL_Oord__class_Oless(V_n,V_n,tc_nat).
% 38.60/38.71 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 38.60/38.71 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 38.60/38.71 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(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)))).
% 38.60/38.71 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|V_x=V_y.
% 38.60/38.71 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)|V_m=V_n.
% 38.60/38.71 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).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(V_y,V_x,tc_nat)|c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)|V_x=V_y.
% 38.60/38.71 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|V_x=V_y.
% 38.60/38.71 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 38.60/38.71 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 38.60/38.71 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.
% 38.60/38.71 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.
% 38.60/38.71 0 [] c_Type_Otyping(V_env,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_U)| -c_Type_Otyping(V_env,V_t,V_T)| -c_Type_Otyping(V_env,V_s,hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U)).
% 38.60/38.71 0 [] -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)).
% 38.60/38.71 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.71 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 38.60/38.71 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).
% 38.60/38.71 0 [] hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2)!=hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H)|V_type2=V_type2_H.
% 38.60/38.71 0 [] hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2)!=hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H)|V_type1=V_type1_H.
% 38.60/38.71 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2).
% 38.60/38.71 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OVar(V_nat_H)|V_nat=V_nat_H.
% 38.60/38.71 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=c_Lambda_OdB_OAbs(V_dB_H).
% 38.60/38.71 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=c_Lambda_OdB_OVar(V_nat).
% 38.60/38.71 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a).
% 38.60/38.71 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 38.60/38.71 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 38.60/38.71 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 38.60/38.71 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).
% 38.60/38.71 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)).
% 38.60/38.71 0 [] c_Type_Otyping(V_e,V_t_H,V_T)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H))| -c_Type_Otyping(V_e,V_t,V_T).
% 38.60/38.71 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k)=V_u.
% 38.60/38.71 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)).
% 38.60/38.71 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).
% 38.60/38.71 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)))| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 38.60/38.71 0 [] v_T____!=hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2)|hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i)))| -c_Type_Otyping(V_e,V_u,V_T2)| -hBOOL(hAPP(c_InductTermi_OIT,V_u))| -c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_T2,tc_Type_Otype),V_t,V_Ta)| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 38.60/38.71 0 [] v_T____!=hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2)|hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i)))| -c_Type_Otyping(V_e,V_u,V_T1)| -hBOOL(hAPP(c_InductTermi_OIT,V_u))| -c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_T1,tc_Type_Otype),V_t,V_Ta)| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 38.60/38.71 0 [] hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x)=V_T.
% 38.60/38.71 0 [] c_Type_Otyping(V_env,c_Lambda_OdB_OAbs(V_t),hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U))| -c_Type_Otyping(c_Type_Oshift(V_env,c_HOL_Ozero__class_Ozero(tc_nat),V_T,tc_Type_Otype),V_t,V_U).
% 38.60/38.71 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))).
% 38.60/38.71 0 [] hAPP(V_e,V_i)=V_T| -c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T).
% 38.60/38.71 0 [] hBOOL(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)).
% 38.60/38.71 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).
% 38.60/38.71 0 [] c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)).
% 38.60/38.71 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r)))| -hBOOL(hAPP(c_InductTermi_OIT,V_r)).
% 38.60/38.71 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k)=V_t.
% 38.60/38.71 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).
% 38.60/38.71 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_t____)).
% 38.60/38.71 0 [] c_Type_Otyping(c_Type_Oshift(v_e,v_i,v_T____,tc_Type_Otype),v_t____,v_T_H).
% 38.60/38.71 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_u)).
% 38.60/38.71 0 [] c_Type_Otyping(v_e,v_u,v_T____).
% 38.60/38.71 0 [] -hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_t____),v_u),v_i))).
% 38.60/38.71 0 [] class_Orderings_Opreorder(tc_fun(T_2,T_1))| -class_Orderings_Opreorder(T_1).
% 38.60/38.71 0 [] class_Orderings_Oorder(tc_fun(T_2,T_1))| -class_Orderings_Oorder(T_1).
% 38.60/38.71 0 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 38.60/38.71 0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 38.60/38.71 0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 38.60/38.71 0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 38.60/38.71 0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 38.60/38.71 0 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 38.60/38.71 0 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 38.60/38.71 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 38.60/38.71 0 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 38.60/38.71 0 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 38.60/38.71 0 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 38.60/38.71 0 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 38.60/38.71 0 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 38.60/38.71 0 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 38.60/38.71 0 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 38.60/38.71 0 [] class_OrderedGroup_Omonoid__mult(tc_nat).
% 38.60/38.71 0 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 38.60/38.71 0 [] class_Nat_Osemiring__char__0(tc_nat).
% 38.60/38.71 0 [] class_Orderings_Opreorder(tc_nat).
% 38.60/38.71 0 [] class_Orderings_Olinorder(tc_nat).
% 38.60/38.71 0 [] class_Orderings_Oorder(tc_nat).
% 38.60/38.71 0 [] class_Power_Opower(tc_nat).
% 38.60/38.71 0 [] class_Orderings_Opreorder(tc_bool).
% 38.60/38.71 0 [] class_Orderings_Oorder(tc_bool).
% 38.60/38.71 0 [] c_fe_qual(V_x,V_x,T_a).
% 38.60/38.71 0 [] V_X=V_Y| -c_fe_qual(V_X,V_Y,T_a).
% 38.60/38.71 end_of_list.
% 38.60/38.71
% 38.60/38.71 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 38.60/38.72
% 38.60/38.72 This ia a non-Horn set with equality. The strategy will be
% 38.60/38.72 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 38.60/38.72 deletion, with positive clauses in sos and nonpositive
% 38.60/38.72 clauses in usable.
% 38.60/38.72
% 38.60/38.72 dependent: set(knuth_bendix).
% 38.60/38.72 dependent: set(anl_eq).
% 38.60/38.72 dependent: set(para_from).
% 38.60/38.72 dependent: set(para_into).
% 38.60/38.72 dependent: clear(para_from_right).
% 38.60/38.72 dependent: clear(para_into_right).
% 38.60/38.72 dependent: set(para_from_vars).
% 38.60/38.72 dependent: set(eq_units_both_ways).
% 38.60/38.72 dependent: set(dynamic_demod_all).
% 38.60/38.72 dependent: set(dynamic_demod).
% 38.60/38.72 dependent: set(order_eq).
% 38.60/38.72 dependent: set(back_demod).
% 38.60/38.72 dependent: set(lrpo).
% 38.60/38.72 dependent: set(hyper_res).
% 38.60/38.72 dependent: set(unit_deletion).
% 38.60/38.72 dependent: set(factor).
% 38.60/38.72
% 38.60/38.72 ------------> process usable:
% 38.60/38.72 ** KEPT (pick-wt=13): 2 [copy,1,flip.1] c_Suc(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat))=A| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 38.60/38.72 Following clause subsumed by 2 during input processing: 0 [] c_Suc(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat))=A| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=17): 3 [] c_HOL_Ominus__class_Ominus(A,B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Ominus__class_Ominus(B,A,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|B=A.
% 38.60/38.72 ** KEPT (pick-wt=11): 4 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=12): 5 [] A=B| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)|c_HOL_Oord__class_Oless(A,B,tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=12): 6 [] A=B| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 38.60/38.72 Following clause subsumed by 5 during input processing: 0 [] A=B|c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=7): 8 [copy,7,flip.2] -class_Ring__and__Field_Ozero__ne_q__one(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Oone__class_Oone(A).
% 38.60/38.72 ** KEPT (pick-wt=23): 9 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=18): 10 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=20): 11 [] 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)).
% 38.60/38.72 ** KEPT (pick-wt=14): 12 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(A,C),D)).
% 38.60/38.72 ** KEPT (pick-wt=9): 13 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A)=B.
% 38.60/38.72 ** KEPT (pick-wt=9): 14 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A)=B.
% 38.60/38.72 ** KEPT (pick-wt=17): 15 [] -class_OrderedGroup_Oab__semigroup__add(A)|c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,C,A,A)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,B,A,A).
% 38.60/38.72 ** KEPT (pick-wt=8): 16 [] c_Suc(A)!=c_Suc(B)|A=B.
% 38.60/38.72 Following clause subsumed by 16 during input processing: 0 [] c_Suc(A)!=c_Suc(B)|A=B.
% 38.60/38.72 ** KEPT (pick-wt=15): 17 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=13): 18 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=13): 19 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=11): 20 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 38.60/38.72 ** KEPT (pick-wt=9): 21 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 38.60/38.72 ** KEPT (pick-wt=9): 22 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 38.60/38.72 Following clause subsumed by 21 during input processing: 0 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 38.60/38.72 ** KEPT (pick-wt=9): 23 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 38.60/38.72 ** KEPT (pick-wt=12): 25 [copy,24,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.72 Following clause subsumed by 25 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=16): 27 [copy,26,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).
% 38.60/38.72 ** KEPT (pick-wt=12): 28 [] -class_Nat_Osemiring__char__0(A)|c_Nat_Osemiring__1__class_Oof__nat(B,A)!=c_Nat_Osemiring__1__class_Oof__nat(C,A)|B=C.
% 38.60/38.72 ** KEPT (pick-wt=18): 29 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_HOL_Ominus__class_Ominus(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(C,A,tc_nat)| -c_HOL_Oord__class_Oless(C,B,tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=27): 31 [copy,30,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).
% 38.60/38.72 ** KEPT (pick-wt=15): 32 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=21): 33 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=15): 34 [] -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).
% 38.60/38.72 Following clause subsumed by 32 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).
% 38.60/38.72 ** KEPT (pick-wt=13): 35 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=13): 36 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=13): 37 [] 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).
% 38.60/38.72 Following clause subsumed by 35 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).
% 38.60/38.72 Following clause subsumed by 36 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).
% 38.60/38.72 ** KEPT (pick-wt=26): 38 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=24): 39 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=22): 40 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=5): 41 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.72 Following clause subsumed by 41 during input processing: 0 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=15): 42 [] hBOOL(hAPP(A,c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1(A,B)))| -hBOOL(hAPP(A,B))|hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 38.60/38.72 ** KEPT (pick-wt=16): 43 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=13): 44 [] c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat)| -c_HOL_Oord__class_Oless(C,B,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=19): 46 [copy,45,flip.2] -class_OrderedGroup_Omonoid__add(A)|c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,c_HOL_Ozero__class_Ozero(A),A,A)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),B,A,A).
% 38.60/38.72 ** KEPT (pick-wt=19): 47 [] hAPP(c_Type_Oshift(A,B,C,D),E)=hAPP(A,c_HOL_Ominus__class_Ominus(E,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(B,E,tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=12): 48 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=13): 49 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=19): 50 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=26): 51 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),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)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),C)).
% 38.60/38.72 ** KEPT (pick-wt=19): 52 [] -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.
% 38.60/38.72 ** KEPT (pick-wt=10): 53 [] -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 38.60/38.72 ** KEPT (pick-wt=10): 54 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=21): 55 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=21): 56 [] -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).
% 38.60/38.72 Following clause subsumed by 55 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).
% 38.60/38.72 Following clause subsumed by 56 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).
% 38.60/38.72 ** KEPT (pick-wt=9): 57 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=9): 58 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=17): 59 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=16): 60 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat)| -c_HOL_Oord__class_Oless(A,c_HOL_Ominus__class_Ominus(C,B,tc_nat),tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=16): 61 [] c_HOL_Oord__class_Oless(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=4): 62 [] c_Suc(A)!=A.
% 38.60/38.72 Following clause subsumed by 62 during input processing: 0 [flip.1] c_Suc(A)!=A.
% 38.60/38.72 ** KEPT (pick-wt=20): 63 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=20): 64 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=20): 65 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=20): 66 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=20): 67 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=20): 68 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=18): 69 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=18): 70 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=18): 71 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=21): 72 [] hBOOL(hAPP(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xex__least__nat__less__1__1(A,B)),c_HOL_Oone__class_Oone(tc_nat))))| -hBOOL(hAPP(A,B))|hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 38.60/38.72 ** KEPT (pick-wt=9): 73 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=9): 74 [] c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=14): 75 [] c_Suc(c_HOL_Ominus__class_Ominus(A,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))=A| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=21): 76 [] -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)).
% 38.60/38.72 ** KEPT (pick-wt=19): 77 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,E,A)|c_HOL_Oord__class_Oless(D,E,A)| -c_HOL_Oord__class_Oless(B,C,A).
% 38.60/38.72 ** KEPT (pick-wt=19): 78 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,E,A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(D,E,A).
% 38.60/38.72 ** KEPT (pick-wt=13): 79 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,c_Suc(B),tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=20): 80 [] 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)).
% 38.60/38.72 ** KEPT (pick-wt=18): 81 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=22): 82 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),E),D))| -hBOOL(hAPP(hAPP(A,C),E)).
% 38.60/38.72 ** KEPT (pick-wt=22): 83 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(A,E),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),E)).
% 38.60/38.72 ** KEPT (pick-wt=20): 84 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=24): 85 [] c_Type_Otyping(A,c_Lambda_OdB_OVar(B),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(C,A,B,D),C,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(B),D,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 38.60/38.72 ** KEPT (pick-wt=19): 86 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),C)=c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(C,A,tc_nat).
% 38.60/38.72 Following clause subsumed by 86 during input processing: 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),C)=c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(C,A,tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=14): 87 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=43): 88 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=43): 89 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=18): 91 [copy,90,flip.1] hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(A,B,C)),c_Type_Osko__Type__Xtyping__elims__3__2(A,B,C))=A| -c_Type_Otyping(B,c_Lambda_OdB_OAbs(C),A).
% 38.60/38.72 ** KEPT (pick-wt=41): 93 [copy,92,flip.1] c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(A,B,C,D),A,tc_Type_Otype,tc_Type_Otype)=B| -c_Type_Otyping(C,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(E),F,tc_Lambda_OdB,tc_Lambda_OdB),B)| -c_Type_Otypings(C,F,G)| -c_Type_Otyping(C,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(E),F,tc_Lambda_OdB,tc_Lambda_OdB),D,tc_Lambda_OdB,tc_Lambda_OdB),A).
% 38.60/38.72 ** KEPT (pick-wt=17): 94 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=17): 95 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=9): 96 [] -class_Ring__and__Field_Oordered__semidom(A)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_HOL_Ozero__class_Ozero(A),A).
% 38.60/38.72 ** KEPT (pick-wt=22): 97 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=17): 98 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=17): 99 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=17): 100 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=17): 101 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=15): 102 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=8): 103 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=22): 104 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=14): 105 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A).
% 38.60/38.72 ** KEPT (pick-wt=14): 106 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,C,A).
% 38.60/38.72 ** KEPT (pick-wt=8): 107 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=20): 108 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=9): 109 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Ozero__class_Ozero(A).
% 38.60/38.72 ** KEPT (pick-wt=16): 110 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=16): 111 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=20): 112 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=14): 113 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=14): 114 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A).
% 38.60/38.72 Following clause subsumed by 36 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).
% 38.60/38.72 Following clause subsumed by 35 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).
% 38.60/38.72 ** KEPT (pick-wt=19): 115 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=20): 116 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=10): 117 [] A=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(A,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=19): 118 [] hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)))| -c_HOL_Oord__class_Oless(B,C,tc_nat)| -hBOOL(hAPP(A,B))|hBOOL(hAPP(A,c_List_Osko__Divides__Xmod__induct__0__1__1(A,C))).
% 38.60/38.72 ** KEPT (pick-wt=13): 119 [] 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).
% 38.60/38.72 Following clause subsumed by 41 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.72 Following clause subsumed by 41 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=13): 120 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=24): 121 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),E),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),E)).
% 38.60/38.72 ** KEPT (pick-wt=15): 122 [] -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).
% 38.60/38.72 Following clause subsumed by 53 during input processing: 0 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 38.60/38.72 ** KEPT (pick-wt=13): 123 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ominus__class_Ominus(B,C,A)),C)=B.
% 38.60/38.72 ** KEPT (pick-wt=16): 124 [] -hBOOL(hAPP(A,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),B,tc_nat)))|hBOOL(hAPP(A,C)).
% 38.60/38.72 Following clause subsumed by 124 during input processing: 0 [] -hBOOL(hAPP(A,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),B,tc_nat)))|hBOOL(hAPP(A,C)).
% 38.60/38.72 ** KEPT (pick-wt=13): 125 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=21): 126 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=25): 128 [copy,127,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)).
% 38.60/38.72 ** KEPT (pick-wt=25): 129 [] -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)).
% 38.60/38.72 ** KEPT (pick-wt=25): 130 [] -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)).
% 38.60/38.72 ** KEPT (pick-wt=25): 131 [] -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)).
% 38.60/38.72 ** KEPT (pick-wt=25): 132 [] -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)).
% 38.60/38.72 Following clause subsumed by 128 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)).
% 38.60/38.72 ** KEPT (pick-wt=25): 133 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=25): 134 [] -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)).
% 38.60/38.72 Following clause subsumed by 128 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 38.60/38.72 ** KEPT (pick-wt=28): 135 [] -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.
% 38.60/38.72 ** KEPT (pick-wt=10): 136 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A)=c_HOL_Oone__class_Oone(A).
% 38.60/38.72 ** KEPT (pick-wt=9): 137 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=14): 138 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,D,A)|B=C.
% 38.60/38.72 ** KEPT (pick-wt=14): 139 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)!=c_HOL_Ominus__class_Ominus(C,D,A)|C=D.
% 38.60/38.72 Following clause subsumed by 8 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).
% 38.60/38.72 ** KEPT (pick-wt=19): 140 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=19): 141 [] 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)).
% 38.60/38.72 ** KEPT (pick-wt=16): 142 [] -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)).
% 38.60/38.72 ** KEPT (pick-wt=14): 143 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 38.60/38.72 ** KEPT (pick-wt=12): 144 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 38.60/38.72 ** KEPT (pick-wt=12): 145 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 38.60/38.72 ** KEPT (pick-wt=23): 147 [copy,146,flip.2] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),C,c_HOL_Ozero__class_Ozero(A),A,A))=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A).
% 38.60/38.72 ** KEPT (pick-wt=13): 148 [] c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat)|c_Suc(A)=B| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=16): 149 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)|B=C.
% 38.60/38.72 ** KEPT (pick-wt=16): 150 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B)|A=C.
% 38.60/38.72 Following clause subsumed by 149 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.
% 38.60/38.72 ** KEPT (pick-wt=20): 151 [] -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.
% 38.60/38.72 ** KEPT (pick-wt=18): 152 [] -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.
% 38.60/38.72 ** KEPT (pick-wt=18): 153 [] -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.
% 38.60/38.72 ** KEPT (pick-wt=18): 154 [] -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.
% 38.60/38.72 ** KEPT (pick-wt=48): 155 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=16): 156 [] 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.
% 38.60/38.72 ** KEPT (pick-wt=19): 157 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=19): 158 [] 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)).
% 38.60/38.72 ** KEPT (pick-wt=35): 159 [] -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)).
% 38.60/38.72 ** KEPT (pick-wt=16): 160 [] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,C)=c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(C,A,tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=9): 161 [] -c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=30): 162 [] 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).
% 38.60/38.72 ** KEPT (pick-wt=14): 163 [] -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).
% 38.60/38.72 ** KEPT (pick-wt=11): 164 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 38.60/38.72 ** KEPT (pick-wt=11): 165 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 38.60/38.72 ** KEPT (pick-wt=13): 167 [copy,166,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.
% 38.60/38.72 ** KEPT (pick-wt=11): 168 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 38.60/38.72 ** KEPT (pick-wt=11): 169 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 38.60/38.72 ** KEPT (pick-wt=11): 170 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 38.60/38.72 ** KEPT (pick-wt=11): 171 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 38.60/38.72 Following clause subsumed by 164 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.
% 38.60/38.72 ** KEPT (pick-wt=13): 172 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A)=B.
% 38.60/38.72 ** KEPT (pick-wt=10): 173 [] c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=10): 174 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat).
% 38.60/38.72 Following clause subsumed by 173 during input processing: 0 [] c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 38.60/38.72 ** KEPT (pick-wt=15): 175 [] c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xex__least__nat__less__1__1(A,B),B,tc_nat)| -hBOOL(hAPP(A,B))|hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 38.60/38.73 ** KEPT (pick-wt=16): 176 [] hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)))| -c_HOL_Oord__class_Oless(B,C,tc_nat)| -hBOOL(hAPP(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat))).
% 38.60/38.73 ** KEPT (pick-wt=19): 177 [] -hBOOL(hAPP(A,B))| -c_HOL_Oord__class_Oless(B,c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1(A,C),tc_nat)| -hBOOL(hAPP(A,C))|hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 38.60/38.73 ** KEPT (pick-wt=12): 178 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(B,A,tc_nat),tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=12): 179 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(B,A,tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=17): 180 [] 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).
% 38.60/38.73 ** KEPT (pick-wt=17): 181 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=19): 182 [] hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)))| -c_HOL_Oord__class_Oless(B,C,tc_nat)| -hBOOL(hAPP(A,B))|c_HOL_Oord__class_Oless(c_List_Osko__Divides__Xmod__induct__0__1__1(A,C),C,tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=32): 183 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),hAPP(hAPP(c_Lambda_OdB_OApp,C),D)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),B),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),C)).
% 38.60/38.73 ** KEPT (pick-wt=24): 184 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),hAPP(hAPP(c_Lambda_OdB_OApp,C),B)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),C)).
% 38.60/38.73 ** KEPT (pick-wt=24): 185 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),hAPP(hAPP(c_Lambda_OdB_OApp,A),C)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),B),C)).
% 38.60/38.73 ** KEPT (pick-wt=22): 186 [] hBOOL(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),C)).
% 38.60/38.73 ** KEPT (pick-wt=13): 187 [] 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.
% 38.60/38.73 ** KEPT (pick-wt=18): 188 [] 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.
% 38.60/38.73 ** KEPT (pick-wt=18): 189 [] 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.
% 38.60/38.73 ** KEPT (pick-wt=13): 190 [] 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).
% 38.60/38.73 ** KEPT (pick-wt=13): 192 [copy,191,flip.1] c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(A,B))=B| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(A)),B)).
% 38.60/38.73 ** KEPT (pick-wt=18): 193 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(A)),c_Lambda_OdB_OAbs(B)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),B)).
% 38.60/38.73 ** KEPT (pick-wt=15): 194 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),c_Lambda_Osko__Lambda__Xbeta__cases__2__1(A,B)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(A)),B)).
% 38.60/38.73 ** KEPT (pick-wt=12): 195 [] c_Lambda_Oliftn(A,c_Lambda_OdB_OVar(B),C)=c_Lambda_OdB_OVar(B)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=26): 196 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),D),C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,B),D)).
% 38.60/38.73 ** KEPT (pick-wt=28): 197 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),hAPP(hAPP(hAPP(c_Lambda_Osubst,D),B),C)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),D)).
% 38.60/38.73 ** KEPT (pick-wt=28): 198 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),D),C)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),B),D)).
% 38.60/38.73 ** KEPT (pick-wt=13): 199 [] 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.
% 38.60/38.73 ** KEPT (pick-wt=18): 200 [] 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.
% 38.60/38.73 ** KEPT (pick-wt=18): 201 [] 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.
% 38.60/38.73 ** KEPT (pick-wt=16): 202 [] c_Type_Otyping(A,B,c_Type_Osko__Type__Xtyping__elims__2__1(C,A,D,B))| -c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,D),B),C).
% 38.60/38.73 ** KEPT (pick-wt=16): 203 [] c_Type_Otyping(A,B,C)| -c_Type_Otyping(A,D,C)| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),D),B)).
% 38.60/38.73 ** KEPT (pick-wt=24): 204 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,A),B)),hAPP(hAPP(c_Lambda_Olift,C),B)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),C)).
% 38.60/38.73 ** KEPT (pick-wt=37): 205 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xvar__app__types__1__1(C,D,A,B))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(E),F,tc_Lambda_OdB,tc_Lambda_OdB),D)| -c_Type_Otypings(A,F,G)| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(E),F,tc_Lambda_OdB,tc_Lambda_OdB),B,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 38.60/38.73 ** KEPT (pick-wt=18): 206 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xvar__app__typesE__1__1(C,A,D,B))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(D),B,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 38.60/38.73 ** KEPT (pick-wt=22): 207 [] c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,B,C,tc_Lambda_OdB,tc_Lambda_OdB),D)| -c_Type_Otypings(A,C,E)| -c_Type_Otyping(A,B,c_List_Ofoldr(c_Type_Otype_OFun,E,D,tc_Type_Otype,tc_Type_Otype)).
% 38.60/38.73 ** KEPT (pick-wt=20): 208 [] c_Type_Otyping(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(B,A,C),tc_Type_Otype),C,c_Type_Osko__Type__Xtyping__elims__3__2(B,A,C))| -c_Type_Otyping(A,c_Lambda_OdB_OAbs(C),B).
% 38.60/38.73 ** KEPT (pick-wt=18): 209 [] c_Type_Otyping(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(A,B),tc_Type_Otype),B,c_Type_Osko__Type__Xabs__typeE__1__2(A,B))| -c_Type_Otyping(A,c_Lambda_OdB_OAbs(B),C).
% 38.60/38.73 ** KEPT (pick-wt=14): 210 [] 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).
% 38.60/38.73 ** KEPT (pick-wt=15): 211 [] 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).
% 38.60/38.73 ** KEPT (pick-wt=23): 212 [] 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).
% 38.60/38.73 ** KEPT (pick-wt=20): 213 [] c_Type_Otyping(A,B,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(C,A,B,D)),C))| -c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),D),C).
% 38.60/38.73 ** KEPT (pick-wt=14): 214 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=14): 215 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A).
% 38.60/38.73 ** KEPT (pick-wt=34): 216 [] 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))).
% 38.60/38.73 ** KEPT (pick-wt=18): 217 [] 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).
% 38.60/38.73 ** KEPT (pick-wt=8): 218 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 38.60/38.73 ** KEPT (pick-wt=14): 219 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(A)),c_Lambda_OdB_OAbs(B)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),B)).
% 38.60/38.73 ** KEPT (pick-wt=13): 220 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,A),c_Lambda_OdB_OVar(B))))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 38.60/38.73 ** KEPT (pick-wt=20): 221 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,A),B)),hAPP(hAPP(c_Lambda_Olift,C),B)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),C)).
% 38.60/38.73 ** KEPT (pick-wt=13): 222 [] 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).
% 38.60/38.73 ** KEPT (pick-wt=21): 223 [] 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).
% 38.60/38.73 ** KEPT (pick-wt=20): 224 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),hAPP(hAPP(c_Lambda_OdB_OApp,C),B)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),C)).
% 38.60/38.73 ** KEPT (pick-wt=20): 225 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),hAPP(hAPP(c_Lambda_OdB_OApp,A),C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,B),C)).
% 38.60/38.73 ** KEPT (pick-wt=5): 226 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 38.60/38.73 Following clause subsumed by 226 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=14): 227 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_HOL_Oord__class_Oless(D,C,A).
% 38.60/38.73 ** KEPT (pick-wt=14): 228 [] -class_Orderings_Opreorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(D,C,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 38.60/38.73 ** KEPT (pick-wt=5): 229 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 38.60/38.73 ** KEPT (pick-wt=8): 230 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OAbs(B)|A=B.
% 38.60/38.73 ** KEPT (pick-wt=8): 231 [] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 38.60/38.73 ** KEPT (pick-wt=4): 232 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 38.60/38.73 Following clause subsumed by 232 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=6): 233 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 38.60/38.73 ** KEPT (pick-wt=6): 234 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 38.60/38.73 ** KEPT (pick-wt=6): 235 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 38.60/38.73 ** KEPT (pick-wt=13): 236 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)|C=B.
% 38.60/38.73 ** KEPT (pick-wt=13): 237 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(C,B,A)|c_HOL_Oord__class_Oless(B,C,A).
% 38.60/38.73 Following clause subsumed by 237 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)|C=B.
% 38.60/38.73 Following clause subsumed by 237 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|C=B|c_HOL_Oord__class_Oless(C,B,A).
% 38.60/38.73 Following clause subsumed by 237 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).
% 38.60/38.73 ** KEPT (pick-wt=14): 238 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|B=D.
% 38.60/38.73 ** KEPT (pick-wt=14): 239 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|A=C.
% 38.60/38.73 ** KEPT (pick-wt=20): 240 [] c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),D)| -c_Type_Otyping(A,C,E)| -c_Type_Otyping(A,B,hAPP(hAPP(c_Type_Otype_OFun,E),D)).
% 38.60/38.73 ** KEPT (pick-wt=7): 241 [] -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(A)),B)).
% 38.60/38.73 Following clause subsumed by 232 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).
% 38.60/38.73 ** KEPT (pick-wt=15): 242 [] 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).
% 38.60/38.73 ** KEPT (pick-wt=14): 243 [] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=hAPP(hAPP(c_Type_Otype_OFun,C),D)|B=D.
% 38.60/38.73 ** KEPT (pick-wt=14): 244 [] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=hAPP(hAPP(c_Type_Otype_OFun,C),D)|A=C.
% 38.60/38.73 ** KEPT (pick-wt=8): 245 [] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 38.60/38.73 ** KEPT (pick-wt=8): 246 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OVar(B)|A=B.
% 38.60/38.73 ** KEPT (pick-wt=8): 247 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 38.60/38.73 ** KEPT (pick-wt=5): 248 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 38.60/38.73 ** KEPT (pick-wt=10): 249 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 38.60/38.73 ** KEPT (pick-wt=10): 250 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 38.60/38.73 ** KEPT (pick-wt=10): 251 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 38.60/38.73 Following clause subsumed by 251 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 38.60/38.73 ** KEPT (pick-wt=16): 252 [] 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).
% 38.60/38.73 ** KEPT (pick-wt=14): 253 [] c_Type_Otyping(A,B,C)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,D),B))| -c_Type_Otyping(A,D,C).
% 38.60/38.73 ** KEPT (pick-wt=15): 254 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),c_Lambda_OdB_OVar(B)),C)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 38.60/38.73 ** KEPT (pick-wt=15): 255 [] hAPP(c_Type_Oshift(A,B,C,D),E)=hAPP(A,E)| -c_HOL_Oord__class_Oless(E,B,tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=12): 256 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,A),B)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 38.60/38.73 ** KEPT (pick-wt=37): 258 [copy,257,flip.1] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=v_T____|hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,C),D),E)))| -c_Type_Otyping(F,D,B)| -hBOOL(hAPP(c_InductTermi_OIT,D))| -c_Type_Otyping(c_Type_Oshift(F,E,B,tc_Type_Otype),C,G)| -hBOOL(hAPP(c_InductTermi_OIT,C)).
% 38.60/38.73 ** KEPT (pick-wt=37): 260 [copy,259,flip.1] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=v_T____|hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,C),D),E)))| -c_Type_Otyping(F,D,A)| -hBOOL(hAPP(c_InductTermi_OIT,D))| -c_Type_Otyping(c_Type_Oshift(F,E,A,tc_Type_Otype),C,G)| -hBOOL(hAPP(c_InductTermi_OIT,C)).
% 38.60/38.73 ** KEPT (pick-wt=18): 261 [] c_Type_Otyping(A,c_Lambda_OdB_OAbs(B),hAPP(hAPP(c_Type_Otype_OFun,C),D))| -c_Type_Otyping(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),C,tc_Type_Otype),B,D).
% 38.60/38.73 ** KEPT (pick-wt=10): 262 [] hAPP(A,B)=C| -c_Type_Otyping(A,c_Lambda_OdB_OVar(B),C).
% 38.60/38.73 ** KEPT (pick-wt=24): 263 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),hAPP(hAPP(hAPP(c_Lambda_Osubst,D),B),C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),D)).
% 38.60/38.73 ** KEPT (pick-wt=32): 264 [] 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).
% 38.60/38.73 ** KEPT (pick-wt=9): 265 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(A)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 38.60/38.73 ** KEPT (pick-wt=22): 266 [] -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).
% 38.60/38.73 ** KEPT (pick-wt=10): 267 [] -hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_t____),v_u),v_i))).
% 38.60/38.73 ** KEPT (pick-wt=6): 268 [] class_Orderings_Opreorder(tc_fun(A,B))| -class_Orderings_Opreorder(B).
% 38.60/38.73 ** KEPT (pick-wt=6): 269 [] class_Orderings_Oorder(tc_fun(A,B))| -class_Orderings_Oorder(B).
% 38.60/38.73 ** KEPT (pick-wt=7): 270 [] A=B| -c_fe_qual(A,B,C).
% 38.60/38.73 ** KEPT (pick-wt=14): 289 [copy,210,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).
% 38.60/38.73 ** KEPT (pick-wt=15): 290 [copy,211,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).
% 38.60/38.73 Following clause subsumed by 231 during input processing: 0 [copy,218,flip.1] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 38.60/38.73 Following clause subsumed by 248 during input processing: 0 [copy,229,flip.1] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 38.60/38.73 Following clause subsumed by 218 during input processing: 0 [copy,231,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 38.60/38.73 Following clause subsumed by 247 during input processing: 0 [copy,245,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 38.60/38.73 Following clause subsumed by 245 during input processing: 0 [copy,247,flip.1] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 38.60/38.73 Following clause subsumed by 229 during input processing: 0 [copy,248,flip.1] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 38.60/38.73 Following clause subsumed by 210 during input processing: 0 [copy,289,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).
% 38.60/38.73 Following clause subsumed by 211 during input processing: 0 [copy,290,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).
% 38.60/38.73
% 38.60/38.73 ------------> process sos:
% 38.60/38.73 ** KEPT (pick-wt=3): 296 [] A=A.
% 38.60/38.73 ** KEPT (pick-wt=17): 298 [copy,297,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).
% 38.60/38.73 ---> New Demodulator: 299 [new_demod,298] 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).
% 38.60/38.73 ** KEPT (pick-wt=17): 300 [] 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).
% 38.60/38.73 ** KEPT (pick-wt=13): 302 [copy,301,flip.1] 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)).
% 38.60/38.73 ---> New Demodulator: 303 [new_demod,302] 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)).
% 38.60/38.73 ** KEPT (pick-wt=22): 305 [copy,304,flip.1] c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=11): 306 [] c_HOL_Ominus__class_Ominus(c_Suc(A),c_Suc(B),tc_nat)=c_HOL_Ominus__class_Ominus(A,B,tc_nat).
% 38.60/38.73 ---> New Demodulator: 307 [new_demod,306] c_HOL_Ominus__class_Ominus(c_Suc(A),c_Suc(B),tc_nat)=c_HOL_Ominus__class_Ominus(A,B,tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=6): 309 [copy,308,flip.1] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(tc_nat).
% 38.60/38.73 ---> New Demodulator: 310 [new_demod,309] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=14): 311 [] c_Lambda_Oliftn(c_Suc(A),B,C)=hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(A,B,C)),C).
% 38.60/38.73 ** KEPT (pick-wt=7): 312 [] c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 38.60/38.73 ---> New Demodulator: 313 [new_demod,312] c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 38.60/38.73 ** KEPT (pick-wt=7): 314 [] c_HOL_Ominus__class_Ominus(A,A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=13): 315 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 38.60/38.73 ** KEPT (pick-wt=17): 317 [copy,316,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).
% 38.60/38.73 ---> New Demodulator: 318 [new_demod,317] 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).
% 38.60/38.73 ** KEPT (pick-wt=8): 319 [] c_HOL_Ominus__class_Ominus(c_Suc(A),c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 38.60/38.73 ---> New Demodulator: 320 [new_demod,319] c_HOL_Ominus__class_Ominus(c_Suc(A),c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 38.60/38.73 ** KEPT (pick-wt=10): 321 [] c_HOL_Oord__class_Oless(A,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=10): 322 [] c_HOL_Oord__class_Oless(A,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A)),tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=5): 323 [] c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 38.60/38.73 Following clause subsumed by 323 during input processing: 0 [] c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=8): 324 [] c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 38.60/38.73 ---> New Demodulator: 325 [new_demod,324] c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=7): 326 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 38.60/38.73 ---> New Demodulator: 327 [new_demod,326] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 38.60/38.73 ** KEPT (pick-wt=11): 329 [copy,328,demod,310,310] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))=c_HOL_Oone__class_Oone(tc_nat).
% 38.60/38.73 ---> New Demodulator: 330 [new_demod,329] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))=c_HOL_Oone__class_Oone(tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=15): 331 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ominus__class_Ominus(B,A,tc_nat))=B|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=21): 333 [copy,332,demod,310] c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),c_Lambda_OdB_OdB__size(B))),c_HOL_Oone__class_Oone(tc_nat)).
% 38.60/38.73 ---> New Demodulator: 334 [new_demod,333] c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),c_Lambda_OdB_OdB__size(B))),c_HOL_Oone__class_Oone(tc_nat)).
% 38.60/38.73 ** KEPT (pick-wt=19): 336 [copy,335,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).
% 38.60/38.73 ---> New Demodulator: 337 [new_demod,336] 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).
% 38.60/38.73 ** KEPT (pick-wt=12): 339 [copy,338,demod,310] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(A))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),c_HOL_Oone__class_Oone(tc_nat)).
% 38.60/38.73 ---> New Demodulator: 340 [new_demod,339] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(A))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),c_HOL_Oone__class_Oone(tc_nat)).
% 38.60/38.73 ** KEPT (pick-wt=11): 342 [copy,341,unit_del,232] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.60/38.73 ---> New Demodulator: 343 [new_demod,342] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 38.60/38.73 ** KEPT (pick-wt=19): 344 [] 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).
% 38.60/38.73 ** KEPT (pick-wt=6): 346 [copy,345,demod,325] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=6): 347 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat).
% 38.60/38.73 Following clause subsumed by 347 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat).
% 38.60/38.73 Following clause subsumed by 346 during input processing: 0 [demod,310] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 38.60/38.73 Following clause subsumed by 321 during input processing: 0 [] c_HOL_Oord__class_Oless(A,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=15): 349 [copy,348,flip.1] c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B).
% 38.60/38.73 ---> New Demodulator: 350 [new_demod,349] c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B).
% 38.60/38.73 ** KEPT (pick-wt=15): 352 [copy,351,demod,350] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B).
% 38.60/38.73 Following clause subsumed by 296 during input processing: 0 [demod,325,310] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=8): 353 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),C)).
% 38.60/38.73 Following clause subsumed by 353 during input processing: 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),C)).
% 38.60/38.73 ** KEPT (pick-wt=11): 355 [copy,354,demod,310,310] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(tc_nat).
% 38.60/38.73 ---> New Demodulator: 356 [new_demod,355] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=10): 357 [] c_Suc(A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A).
% 38.60/38.73 ---> New Demodulator: 358 [new_demod,357] c_Suc(A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A).
% 38.60/38.73 Following clause subsumed by 315 during input processing: 0 [demod,358] 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)).
% 38.60/38.73 ** KEPT (pick-wt=16): 360 [copy,359,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).
% 38.60/38.73 ---> New Demodulator: 361 [new_demod,360] 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).
% 38.60/38.73 ** KEPT (pick-wt=11): 362 [] 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).
% 38.60/38.73 ---> New Demodulator: 363 [new_demod,362] 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).
% 38.60/38.73 ** KEPT (pick-wt=13): 365 [copy,364,demod,358] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A),tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=23): 366 [] 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)).
% 38.60/38.73 ** KEPT (pick-wt=23): 367 [] 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)).
% 38.60/38.73 ---> New Demodulator: 368 [new_demod,367] 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)).
% 38.60/38.73 Following clause subsumed by 296 during input processing: 0 [demod,358,356,358,356,330] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=12): 369 [] c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=17): 370 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat).
% 38.60/38.73 Following clause subsumed by 366 during input processing: 0 [demod,358,368,358] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))=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)).
% 38.60/38.73 ** KEPT (pick-wt=8): 371 [] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.73 ---> New Demodulator: 372 [new_demod,371] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=19): 373 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat)=c_HOL_Ominus__class_Ominus(A,C,tc_nat).
% 38.60/38.73 ---> New Demodulator: 374 [new_demod,373] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat)=c_HOL_Ominus__class_Ominus(A,C,tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=19): 375 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat)=c_HOL_Ominus__class_Ominus(B,C,tc_nat).
% 38.60/38.73 ---> New Demodulator: 376 [new_demod,375] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat)=c_HOL_Ominus__class_Ominus(B,C,tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=24): 378 [copy,377,demod,358,356,368,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(B,tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat)))=c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),tc_Lambda_OdB).
% 38.60/38.73 ---> New Demodulator: 379 [new_demod,378] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(B,tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat)))=c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),tc_Lambda_OdB).
% 38.60/38.73 ** KEPT (pick-wt=15): 380 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,C,tc_nat),B,tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=27): 382 [copy,381,demod,358,358] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A),B,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),C),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat).
% 38.60/38.73 ---> New Demodulator: 383 [new_demod,382] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A),B,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),C),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=19): 385 [copy,384,demod,358] c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),B),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),B,tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=14): 387 [copy,386,demod,358,356] c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(A),tc_Lambda_OdB)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat)).
% 38.60/38.73 ---> New Demodulator: 388 [new_demod,387] c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(A),tc_Lambda_OdB)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat)).
% 38.60/38.73 ** KEPT (pick-wt=8): 390 [copy,389,demod,358,356,358,356] c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 38.60/38.73 ---> New Demodulator: 391 [new_demod,390] c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 38.60/38.73 Following clause subsumed by 296 during input processing: 0 [demod,358,356,391,358,356] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=20): 393 [copy,392,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).
% 38.60/38.73 ---> New Demodulator: 394 [new_demod,393] 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).
% 38.60/38.73 ** KEPT (pick-wt=10): 396 [copy,395,demod,358,unit_del,232] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A),tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=14): 398 [copy,397,demod,358] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),B),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=9): 399 [] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(A,B),B)=c_Transitive__Closure_Ortranclp(A,B).
% 38.60/38.73 ---> New Demodulator: 400 [new_demod,399] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(A,B),B)=c_Transitive__Closure_Ortranclp(A,B).
% 38.60/38.73 ** KEPT (pick-wt=9): 402 [copy,401,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 38.60/38.73 ---> New Demodulator: 403 [new_demod,402] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 38.60/38.73 ** KEPT (pick-wt=9): 404 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 38.60/38.73 ---> New Demodulator: 405 [new_demod,404] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 38.60/38.73 Following clause subsumed by 296 during input processing: 0 [demod,403] A=A.
% 38.60/38.73 ** KEPT (pick-wt=20): 407 [copy,406,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).
% 38.60/38.73 ---> New Demodulator: 408 [new_demod,407] 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).
% 38.60/38.73 ** KEPT (pick-wt=11): 409 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat)=A.
% 38.60/38.73 ---> New Demodulator: 410 [new_demod,409] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat)=A.
% 38.60/38.73 ** KEPT (pick-wt=11): 411 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat)=B.
% 38.60/38.73 ---> New Demodulator: 412 [new_demod,411] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat)=B.
% 38.60/38.73 ** KEPT (pick-wt=14): 414 [copy,413,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)).
% 38.60/38.73 ---> New Demodulator: 415 [new_demod,414] 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)).
% 38.60/38.73 ** KEPT (pick-wt=6): 416 [] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(A))=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.73 ---> New Demodulator: 417 [new_demod,416] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(A))=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=7): 418 [] c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(A),tc_Lambda_OdB)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.73 ---> New Demodulator: 419 [new_demod,418] c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(A),tc_Lambda_OdB)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=15): 420 [] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,C)=c_Lambda_OdB_OVar(A)|A=C|c_HOL_Oord__class_Oless(C,A,tc_nat).
% 38.60/38.73 ** KEPT (pick-wt=28): 422 [copy,421,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).
% 38.60/38.74 ---> New Demodulator: 423 [new_demod,422] 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).
% 38.60/38.74 ** KEPT (pick-wt=27): 425 [copy,424,demod,358] 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),c_HOL_Oone__class_Oone(tc_nat)),B),C,D).
% 38.60/38.74 ** KEPT (pick-wt=30): 426 [] 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).
% 38.60/38.74 ---> New Demodulator: 427 [new_demod,426] 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).
% 38.60/38.74 ** KEPT (pick-wt=41): 428 [] 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).
% 38.60/38.74 ** KEPT (pick-wt=10): 430 [copy,429,unit_del,232] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),A)=B.
% 38.60/38.74 ---> New Demodulator: 431 [new_demod,430] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),A)=B.
% 38.60/38.74 ** KEPT (pick-wt=14): 432 [] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 38.60/38.74 ** KEPT (pick-wt=18): 433 [] 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).
% 38.60/38.74 ** KEPT (pick-wt=23): 434 [] 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)).
% 38.60/38.74 ** KEPT (pick-wt=15): 436 [copy,435,demod,415] hBOOL(hAPP(hAPP(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)))).
% 38.60/38.74 ** KEPT (pick-wt=11): 437 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 38.60/38.74 Following clause subsumed by 437 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).
% 38.60/38.74 Following clause subsumed by 437 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 38.60/38.74 ** KEPT (pick-wt=9): 438 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=29): 439 [] 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)).
% 38.60/38.74 Following clause subsumed by 296 during input processing: 0 [demod,431] B=B.
% 38.60/38.74 ** KEPT (pick-wt=9): 440 [] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 38.60/38.74 ---> New Demodulator: 441 [new_demod,440] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 38.60/38.74 ** KEPT (pick-wt=5): 442 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(A))).
% 38.60/38.74 ** KEPT (pick-wt=7): 443 [] c_Type_Otyping(A,c_Lambda_OdB_OVar(B),hAPP(A,B)).
% 38.60/38.74 ** KEPT (pick-wt=13): 444 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),B)),C),B)=A.
% 38.60/38.74 ---> New Demodulator: 445 [new_demod,444] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),B)),C),B)=A.
% 38.60/38.74 ** KEPT (pick-wt=4): 446 [] hBOOL(hAPP(c_InductTermi_OIT,v_t____)).
% 38.60/38.74 ** KEPT (pick-wt=8): 447 [] c_Type_Otyping(c_Type_Oshift(v_e,v_i,v_T____,tc_Type_Otype),v_t____,v_T_H).
% 38.60/38.74 ** KEPT (pick-wt=4): 448 [] hBOOL(hAPP(c_InductTermi_OIT,v_u)).
% 38.60/38.74 ** KEPT (pick-wt=4): 449 [] c_Type_Otyping(v_e,v_u,v_T____).
% 38.60/38.74 ** KEPT (pick-wt=2): 450 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 451 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 452 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 453 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 454 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 455 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 456 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 457 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 458 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 459 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 460 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 461 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 462 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 463 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 464 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 465 [] class_OrderedGroup_Omonoid__mult(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 466 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 467 [] class_Nat_Osemiring__char__0(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 468 [] class_Orderings_Opreorder(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 469 [] class_Orderings_Olinorder(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 470 [] class_Orderings_Oorder(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 471 [] class_Power_Opower(tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=2): 472 [] class_Orderings_Opreorder(tc_bool).
% 38.60/38.74 ** KEPT (pick-wt=2): 473 [] class_Orderings_Oorder(tc_bool).
% 38.60/38.74 ** KEPT (pick-wt=4): 474 [] c_fe_qual(A,A,B).
% 38.60/38.74 Following clause subsumed by 296 during input processing: 0 [copy,296,flip.1] A=A.
% 38.60/38.74 296 back subsumes 293.
% 38.60/38.74 296 back subsumes 292.
% 38.60/38.74 296 back subsumes 291.
% 38.60/38.74 296 back subsumes 271.
% 38.60/38.74 >>>> Starting back demodulation with 299.
% 38.60/38.74 >>>> Starting back demodulation with 303.
% 38.60/38.74 >>>> Starting back demodulation with 307.
% 38.60/38.74 >>>> Starting back demodulation with 310.
% 38.60/38.74 >> back demodulating 302 with 310.
% 38.60/38.74 >> back demodulating 281 with 310.
% 38.60/38.74 >> back demodulating 280 with 310.
% 38.60/38.74 >> back demodulating 273 with 310.
% 38.60/38.74 >> back demodulating 272 with 310.
% 38.60/38.74 >> back demodulating 158 with 310.
% 38.60/38.74 >> back demodulating 157 with 310.
% 38.60/38.74 >> back demodulating 141 with 310.
% 38.60/38.74 >> back demodulating 140 with 310.
% 38.60/38.74 >> back demodulating 117 with 310.
% 38.60/38.74 >> back demodulating 81 with 310.
% 38.60/38.74 >> back demodulating 80 with 310.
% 38.60/38.74 >> back demodulating 75 with 310.
% 38.60/38.74 >> back demodulating 59 with 310.
% 38.60/38.74 >> back demodulating 11 with 310.
% 38.60/38.74 >> back demodulating 10 with 310.
% 38.60/38.74 ** KEPT (pick-wt=19): 484 [copy,311,flip.1,demod,358] hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(A,B,C)),C)=c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A),B,C).
% 38.60/38.74 >>>> Starting back demodulation with 313.
% 38.60/38.74 ** KEPT (pick-wt=7): 485 [copy,314,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ominus__class_Ominus(A,A,tc_nat).
% 38.60/38.74 Following clause subsumed by 315 during input processing: 0 [copy,315,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 38.60/38.74 >>>> Starting back demodulation with 318.
% 38.60/38.74 >>>> Starting back demodulation with 320.
% 38.60/38.74 >>>> Starting back demodulation with 325.
% 38.60/38.74 >> back demodulating 276 with 325.
% 38.60/38.74 >>>> Starting back demodulation with 327.
% 38.60/38.74 >>>> Starting back demodulation with 330.
% 38.60/38.74 >>>> Starting back demodulation with 334.
% 38.60/38.74 >>>> Starting back demodulation with 337.
% 38.60/38.74 >>>> Starting back demodulation with 340.
% 38.60/38.74 >>>> Starting back demodulation with 343.
% 38.60/38.74 >>>> Starting back demodulation with 350.
% 38.60/38.74 >> back demodulating 322 with 350.
% 38.60/38.74 >> back demodulating 321 with 350.
% 38.60/38.74 >> back demodulating 305 with 350.
% 38.60/38.74 Following clause subsumed by 366 during input processing: 0 [copy,352,flip.1,demod,358,368,358] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))=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)).
% 38.60/38.74 >>>> Starting back demodulation with 356.
% 38.60/38.74 >>>> Starting back demodulation with 358.
% 38.60/38.74 >> back demodulating 352 with 358.
% 38.60/38.74 >> back demodulating 349 with 358.
% 38.60/38.74 >> back demodulating 347 with 358.
% 38.60/38.74 >> back demodulating 323 with 358.
% 38.60/38.74 >> back demodulating 319 with 358.
% 38.60/38.74 >> back demodulating 311 with 358.
% 38.60/38.74 >> back demodulating 309 with 358.
% 38.60/38.74 >> back demodulating 306 with 358.
% 38.60/38.74 >> back demodulating 174 with 358.
% 38.60/38.74 >> back demodulating 173 with 358.
% 38.60/38.74 >> back demodulating 162 with 358.
% 38.60/38.74 >> back demodulating 161 with 358.
% 38.60/38.74 >> back demodulating 155 with 358.
% 38.60/38.74 >> back demodulating 148 with 358.
% 38.60/38.74 >> back demodulating 142 with 358.
% 38.60/38.74 >> back demodulating 126 with 358.
% 38.60/38.74 >> back demodulating 120 with 358.
% 38.60/38.74 >> back demodulating 79 with 358.
% 38.60/38.74 >> back demodulating 74 with 358.
% 38.60/38.74 >> back demodulating 73 with 358.
% 38.60/38.74 >> back demodulating 62 with 358.
% 38.60/38.74 >> back demodulating 44 with 358.
% 38.60/38.74 >> back demodulating 43 with 358.
% 38.60/38.74 >> back demodulating 41 with 358.
% 38.60/38.74 >> back demodulating 16 with 358.
% 38.60/38.74 >> back demodulating 6 with 358.
% 38.60/38.74 >> back demodulating 5 with 358.
% 38.60/38.74 >> back demodulating 2 with 358.
% 38.60/38.74 >>>> Starting back demodulation with 361.
% 38.60/38.74 >>>> Starting back demodulation with 363.
% 38.60/38.74 Following clause subsumed by 366 during input processing: 0 [copy,366,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)).
% 38.60/38.74 >>>> Starting back demodulation with 368.
% 38.60/38.74 >> back demodulating 333 with 368.
% 38.60/38.74 ** KEPT (pick-wt=12): 509 [copy,369,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat).
% 38.60/38.74 ** KEPT (pick-wt=17): 510 [copy,370,flip.1] c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat).
% 38.60/38.74 >>>> Starting back demodulation with 372.
% 38.60/38.74 >>>> Starting back demodulation with 374.
% 38.60/38.74 >>>> Starting back demodulation with 376.
% 38.60/38.74 >>>> Starting back demodulation with 379.
% 38.60/38.74 Following clause subsumed by 380 during input processing: 0 [copy,380,flip.1] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,C,tc_nat),B,tc_nat).
% 38.60/38.74 >>>> Starting back demodulation with 383.
% 38.60/38.74 Following clause subsumed by 370 during input processing: 0 [copy,385,flip.1] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),B,tc_nat)=c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),B),tc_nat).
% 38.60/38.74 >>>> Starting back demodulation with 388.
% 38.60/38.74 >>>> Starting back demodulation with 391.
% 38.60/38.74 >>>> Starting back demodulation with 394.
% 38.60/38.74 >>>> Starting back demodulation with 400.
% 38.60/38.74 >>>> Starting back demodulation with 403.
% 38.60/38.74 >> back demodulating 362 with 403.
% 38.60/38.74 >> back demodulating 355 with 403.
% 38.60/38.74 >>>> Starting back demodulation with 405.
% 38.60/38.74 >> back demodulating 329 with 405.
% 38.60/38.74 >>>> Starting back demodulation with 408.
% 38.60/38.74 >>>> Starting back demodulation with 410.
% 38.60/38.74 >>>> Starting back demodulation with 412.
% 38.60/38.74 >> back demodulating 124 with 412.
% 38.60/38.74 >>>> Starting back demodulation with 415.
% 38.60/38.74 >> back demodulating 216 with 415.
% 38.60/38.74 >>>> Starting back demodulation with 417.
% 38.60/38.74 >>>> Starting back demodulation with 419.
% 38.60/38.74 >>>> Starting back demodulation with 423.
% 38.60/38.74 ** KEPT (pick-wt=27): 512 [copy,425,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),c_HOL_Oone__class_Oone(tc_nat)),D),E,C)=c_Type_Oshift(c_Type_Oshift(A,D,E,C),c_HOL_Ozero__class_Ozero(tc_nat),B,C).
% 38.60/38.74 >>>> Starting back demodulation with 427.
% 38.60/38.74 ** KEPT (pick-wt=41): 513 [copy,428,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).
% 38.60/38.74 >>>> Starting back demodulation with 431.
% 38.60/38.74 ** KEPT (pick-wt=14): 514 [copy,432,flip.1] hAPP(hAPP(A,B),C)=hAPP(c_COMBC(A,C,D,E,F),B).
% 38.60/38.74 ** KEPT (pick-wt=23): 515 [copy,434,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).
% 38.60/38.74 ** KEPT (pick-wt=29): 516 [copy,439,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).
% 38.60/38.74 >>>> Starting back demodulation with 441.
% 38.60/38.74 >>>> Starting back demodulation with 445.
% 38.60/38.74 Following clause subsumed by 491 during input processing: 0 [copy,484,flip.1] c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A),B,C)=hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(A,B,C)),C).
% 38.60/38.74 Following clause subsumed by 314 during input processing: 0 [copy,485,flip.1] c_HOL_Ominus__class_Ominus(A,A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.74 Following clause subsumed by 484 during input processing: 0 [copy,491,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),c_HOL_Oone__class_Oone(tc_nat)),A),B,C).
% 38.60/38.74 ** KEPT (pick-wt=10): 517 [copy,504,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A).
% 38.60/38.74 >>>> Starting back demodulation with 508.
% 38.60/38.74 Following clause subsumed by 369 during input processing: 0 [copy,509,flip.1] c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.74 Following clause subsumed by 370 during input processing: 0 [copy,510,flip.1] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat).
% 38.60/38.74 510 back subsumes 385.
% 38.60/38.74 Following clause subsumed by 425 during input processing: 0 [copy,512,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),c_HOL_Oone__class_Oone(tc_nat)),B),C,D).
% 38.60/38.74 Following clause subsumed by 428 during input processing: 0 [copy,513,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).
% 38.60/38.74 Following clause subsumed by 432 during input processing: 0 [copy,514,flip.1] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 38.60/38.74 Following clause subsumed by 434 during input processing: 0 [copy,515,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)).
% 38.60/38.74 Following clause subsumed by 439 during input processing: 0 [copy,516,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)).
% 38.60/38.74 Following clause subsumed by 504 during input processing: 0 [copy,517,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 38.60/38.74
% 38.60/38.74 ======= end of input processing =======
% 38.60/38.74
% 38.60/38.74 =========== start of search ===========
% 38.60/38.74
% 38.60/38.74
% 38.60/38.74 Resetting weight limit to 2.
% 38.60/38.74
% 38.60/38.74
% 38.60/38.74 Resetting weight limit to 2.
% 39.40/39.54
% 39.40/39.54 sos_size=130
% 39.40/39.54
% 39.40/39.54 Search stopped because sos empty.
% 39.40/39.54
% 39.40/39.54
% 39.40/39.54 Search stopped because sos empty.
% 39.40/39.54
% 39.40/39.54 ============ end of search ============
% 39.40/39.54
% 39.40/39.54 -------------- statistics -------------
% 39.40/39.54 clauses given 131
% 39.40/39.54 clauses generated 78505
% 39.40/39.54 clauses kept 429
% 39.40/39.54 clauses forward subsumed 100
% 39.40/39.54 clauses back subsumed 5
% 39.40/39.54 Kbytes malloced 8789
% 39.40/39.54
% 39.40/39.54 ----------- times (seconds) -----------
% 39.40/39.54 user CPU time 0.85 (0 hr, 0 min, 0 sec)
% 39.40/39.54 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 39.40/39.54 wall-clock time 39 (0 hr, 0 min, 39 sec)
% 39.40/39.54
% 39.40/39.54 Process 4018 finished Wed Jul 27 09:19:03 2022
% 39.40/39.54 Otter interrupted
% 39.40/39.54 PROOF NOT FOUND
%------------------------------------------------------------------------------