TSTP Solution File: LCL794-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL794-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:05:26 EDT 2022
% Result : Unknown 51.84s 51.99s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL794-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Jul 27 09:22:08 EDT 2022
% 0.14/0.35 % CPUTime :
% 51.54/51.66 ----- Otter 3.3f, August 2004 -----
% 51.54/51.66 The process was started by sandbox on n021.cluster.edu,
% 51.54/51.66 Wed Jul 27 09:22:08 2022
% 51.54/51.66 The command was "./otter". The process ID is 8417.
% 51.54/51.66
% 51.54/51.66 set(prolog_style_variables).
% 51.54/51.66 set(auto).
% 51.54/51.66 dependent: set(auto1).
% 51.54/51.66 dependent: set(process_input).
% 51.54/51.66 dependent: clear(print_kept).
% 51.54/51.66 dependent: clear(print_new_demod).
% 51.54/51.66 dependent: clear(print_back_demod).
% 51.54/51.66 dependent: clear(print_back_sub).
% 51.54/51.66 dependent: set(control_memory).
% 51.54/51.66 dependent: assign(max_mem, 12000).
% 51.54/51.66 dependent: assign(pick_given_ratio, 4).
% 51.54/51.66 dependent: assign(stats_level, 1).
% 51.54/51.66 dependent: assign(max_seconds, 10800).
% 51.54/51.66 clear(print_given).
% 51.54/51.66
% 51.54/51.66 list(usable).
% 51.54/51.66 0 [] A=A.
% 51.54/51.66 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.
% 51.54/51.66 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.
% 51.54/51.66 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.
% 51.54/51.66 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.
% 51.54/51.66 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.
% 51.54/51.66 0 [] c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a)=c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a).
% 51.54/51.66 0 [] c_List_Olist_OCons(V_x,c_List_Oappend(V_xs1,V_zs,T_a),T_a)=c_List_Oappend(c_List_Olist_OCons(V_x,V_xs1,T_a),V_zs,T_a).
% 51.54/51.66 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)!=c_Lambda_OdB_OAbs(V_r)|V_ss=c_List_Olist_ONil(tc_Lambda_OdB).
% 51.54/51.66 0 [] c_List_Olist_OCons(V_x,V_xa,T_a)!=c_List_Olist_ONil(T_a).
% 51.54/51.66 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.
% 51.54/51.66 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.
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat)|c_Suc(V_m)=V_n| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 51.54/51.66 0 [] c_List_Oappend(c_List_Olist_OCons(V_x,V_xs,T_a),V_ys,T_a)=c_List_Olist_OCons(V_x,c_List_Oappend(V_xs,V_ys,T_a),T_a).
% 51.54/51.66 0 [] c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a)=c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a).
% 51.54/51.66 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).
% 51.54/51.66 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.
% 51.54/51.66 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Olistsum(c_List_Olist_ONil(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 51.54/51.66 0 [] c_Lambda_OdB_OAbs(V_r)=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 51.54/51.66 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_y,V_z,T_a)| -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a).
% 51.54/51.66 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_z,T_a)| -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a).
% 51.54/51.66 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)| -c_HOL_Oord__class_Oless(V_z,V_y,T_a).
% 51.54/51.66 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)| -c_HOL_Oord__class_Oless(V_z,V_x,T_a).
% 51.54/51.66 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_x,V_b,T_a).
% 51.54/51.66 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_x,V_a,T_a).
% 51.54/51.66 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))).
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat).
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat).
% 51.54/51.66 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)).
% 51.54/51.66 0 [] c_List_Ofoldl(V_f,V_a,c_List_Olist_OCons(V_x,V_xs,T_b),T_a,T_b)=c_List_Ofoldl(V_f,hAPP(hAPP(V_f,V_a),V_x),V_xs,T_a,T_b).
% 51.54/51.66 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)).
% 51.54/51.66 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).
% 51.54/51.66 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))).
% 51.54/51.66 0 [] hBOOL(hAPP(V_P,V_T))| -hBOOL(hAPP(V_P,c_Type_Osko__Type__Xtype__induct__1__1(V_P))).
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)|c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x)=V_s.
% 51.54/51.66 0 [] c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeE__1__1(V_T,V_e,V_t,V_ts))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 51.54/51.66 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.
% 51.54/51.66 0 [] c_List_Oreplicate(c_Suc(V_n),V_x,T_a)=c_List_Olist_OCons(V_x,c_List_Oreplicate(V_n,V_x,T_a),T_a).
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat).
% 51.54/51.66 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)).
% 51.54/51.66 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)).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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)).
% 51.54/51.66 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)).
% 51.54/51.66 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)).
% 51.54/51.66 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)).
% 51.54/51.66 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)).
% 51.54/51.66 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)).
% 51.54/51.66 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).
% 51.54/51.66 0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_z,V_x,T_a)| -c_HOL_Oord__class_Oless(V_z,V_y,T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 51.54/51.66 0 [] -class_Orderings_Opreorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_z,T_a)| -c_HOL_Oord__class_Oless(V_y,V_z,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 51.54/51.66 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Olistsum(V_xs,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).
% 51.54/51.66 0 [] c_Lambda_Osubstn(V_t,V_s,V_n)=c_Lambda_Osubst(V_t,c_Lambda_Oliftn(V_n,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),V_n).
% 51.54/51.66 0 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(V_i),V_s,V_k)=c_Lambda_OdB_OVar(V_i)|V_i=V_k|c_HOL_Oord__class_Oless(V_k,V_i,tc_nat).
% 51.54/51.66 0 [] V_n=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 51.54/51.66 0 [] c_Orderings_Oord__class_Omax(c_Suc(V_m),c_Suc(V_n),tc_nat)=c_Suc(c_Orderings_Oord__class_Omax(V_m,V_n,tc_nat)).
% 51.54/51.66 0 [] c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a)=hAPP(V_f3,V_dB).
% 51.54/51.66 0 [] c_Lambda_Obeta(c_Lambda_Osubst(V_r,V_t,V_i),c_Lambda_Osubst(V_s,V_t,V_i))| -c_Lambda_Obeta(V_r,V_s).
% 51.54/51.66 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)).
% 51.54/51.66 0 [] c_List_Oreplicate(V_m,V_x,T_a)!=c_List_Oreplicate(V_n,V_y,T_a)|V_m=V_n.
% 51.54/51.66 0 [] c_List_Oappend(V_ys,V_xs,T_a)!=c_List_Oappend(V_zs,V_xs,T_a)|V_ys=V_zs.
% 51.54/51.66 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Oappend(V_xs,V_zs,T_a)|V_ys=V_zs.
% 51.54/51.66 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)| -c_HOL_Oord__class_Oless(V_y,V_z,T_a)| -c_HOL_Oord__class_Oless(V_x,V_z,T_a).
% 51.54/51.66 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).
% 51.54/51.66 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)).
% 51.54/51.66 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)).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 0 [] c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a)=V_xs.
% 51.54/51.66 0 [] V_x=c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a).
% 51.54/51.66 0 [] V_xs=c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a).
% 51.54/51.66 0 [] c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a)=V_ys.
% 51.54/51.66 0 [] V_ys=c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a).
% 51.54/51.66 0 [] c_Type_Otype_OAtom(V_nat)!=c_Type_Otype_OAtom(V_nat_H)|V_nat=V_nat_H.
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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)).
% 51.54/51.66 0 [] -class_Nat_Osemiring__char__0(T_a)|c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)!=c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)|V_m=V_n.
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_pwr,V_x),V_p)),hAPP(hAPP(V_pwr,V_x),V_q))=hAPP(hAPP(V_pwr,V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_p),V_q))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] c_Lambda_Oliftn(c_Suc(V_n),V_t,V_k)=c_Lambda_Olift(c_Lambda_Oliftn(V_n,V_t,V_k),V_k).
% 51.54/51.66 0 [] c_Suc(V_x)!=c_Suc(V_y)|V_x=V_y.
% 51.54/51.66 0 [] c_Suc(V_nat)!=c_Suc(V_nat_H)|V_nat=V_nat_H.
% 51.54/51.66 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).
% 51.54/51.66 0 [] v_n____=v_i____.
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 51.54/51.66 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).
% 51.54/51.66 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 51.54/51.66 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 51.54/51.66 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).
% 51.54/51.66 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)).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_z,V_y,T_a)|c_HOL_Oord__class_Oless(V_z,V_x,T_a)| -c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a).
% 51.54/51.66 0 [] 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))| -c_InductTermi_OIT(V_s)| -c_InductTermi_OIT(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(V_r,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)).
% 51.54/51.66 0 [] c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b)=V_a.
% 51.54/51.66 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).
% 51.54/51.66 0 [] c_List_Olist_ONil(T_a)!=c_List_Oappend(V_xs,V_ys,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 51.54/51.66 0 [] c_List_Olist_ONil(T_a)!=c_List_Oappend(V_xs,V_ys,T_a)|V_ys=c_List_Olist_ONil(T_a).
% 51.54/51.66 0 [] c_Lambda_OdB_OAbs(V_dB)!=c_Lambda_OdB_OAbs(V_dB_H)|V_dB=V_dB_H.
% 51.54/51.66 0 [] c_List_Olist_OCons(V_a_H,V_list_H,T_a)!=c_List_Olist_ONil(T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_pwr,hAPP(hAPP(V_mul,V_x),V_y)),V_q)=hAPP(hAPP(V_mul,hAPP(hAPP(V_pwr,V_x),V_q)),hAPP(hAPP(V_pwr,V_y),V_q))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_add,V_y),V_z))=hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_x),V_y)),hAPP(hAPP(V_mul,V_x),V_z))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,V_x),V_y)=hAPP(hAPP(V_mul,V_y),V_x)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_mul,V_y),V_z))=hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_x),V_y)),V_z)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,V_r1),V_x)=V_x| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,V_r0),V_x)=V_r0| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_add,V_x),V_y)=hAPP(hAPP(V_add,V_y),V_x)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_add,V_x),hAPP(hAPP(V_add,V_y),V_z))=hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_x),V_y)),V_z)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_add,V_r0),V_x)=V_x| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_add,V_a),hAPP(hAPP(V_add,V_c),V_d))=hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_c)),V_d)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_add,V_a),V_c)=hAPP(hAPP(V_add,V_c),V_a)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_b)),V_c)=hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_c)),V_b)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_add,V_a),hAPP(hAPP(V_add,V_c),V_d))=hAPP(hAPP(V_add,V_c),hAPP(hAPP(V_add,V_a),V_d))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_b)),V_c)=hAPP(hAPP(V_add,V_a),hAPP(hAPP(V_add,V_b),V_c))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_b)),hAPP(hAPP(V_add,V_c),V_d))=hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_c)),hAPP(hAPP(V_add,V_b),V_d))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_rx),V_ry))=hAPP(hAPP(V_mul,V_rx),hAPP(hAPP(V_mul,V_lx),V_ry))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_rx),V_ry))=hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_rx)),V_ry)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),V_rx)=hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_ly),V_rx))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),V_rx)=hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_rx)),V_ly)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),hAPP(hAPP(V_mul,V_rx),V_ry))=hAPP(hAPP(V_mul,V_rx),hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),V_ry))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),hAPP(hAPP(V_mul,V_rx),V_ry))=hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_ly),hAPP(hAPP(V_mul,V_rx),V_ry)))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),hAPP(hAPP(V_mul,V_rx),V_ry))=hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_rx)),hAPP(hAPP(V_mul,V_ly),V_ry))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,V_a),V_r1)=V_a| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,V_r1),V_a)=V_a| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,V_a),V_r0)=V_r0| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,V_r0),V_a)=V_r0| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_b)),V_c)=hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_a),V_c)),hAPP(hAPP(V_mul,V_b),V_c))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,V_a),V_b)=hAPP(hAPP(V_mul,V_b),V_a)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_add,V_a),V_r0)=V_a| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_add,V_r0),V_a)=V_a| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_add,V_m),V_m)=hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_r1),V_r1)),V_m)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_add,V_m),hAPP(hAPP(V_mul,V_a),V_m))=hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_r1)),V_m)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_a),V_m)),V_m)=hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_r1)),V_m)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_a),V_m)),hAPP(hAPP(V_mul,V_b),V_m))=hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_b)),V_m)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] -hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_xc),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f1,V_xc))).
% 51.54/51.66 0 [] -hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f1,V_nat))).
% 51.54/51.66 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).
% 51.54/51.66 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)).
% 51.54/51.66 0 [] c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))| -c_InductTermi_OIT(V_r).
% 51.54/51.66 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)).
% 51.54/51.66 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))).
% 51.54/51.66 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 51.54/51.66 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(V_x,V_y,T_a)=c_Orderings_Oord__class_Omax(V_y,V_x,T_a).
% 51.54/51.66 0 [] c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k)=c_Lambda_OdB_OVar(V_i)| -c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 51.54/51.66 0 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a)=c_List_Olist_ONil(T_a).
% 51.54/51.66 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OAbs(V_r).
% 51.54/51.66 0 [] c_List_Olist_OCons(V_x,V_t,T_a)!=V_t.
% 51.54/51.66 0 [] V_xs!=c_List_Olist_OCons(V_x,V_xs,T_a).
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)|c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_x),V_s,V_x)=c_Lambda_Oliftn(V_x,V_s,c_HOL_Ozero__class_Ozero(tc_nat)).
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)|c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat).
% 51.54/51.66 0 [] -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat).
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 51.54/51.66 0 [] c_List_Olist_OCons(V_x,V_xs,T_a)=c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a).
% 51.54/51.66 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Orderings_Oord__class_Omax(V_x,V_y,T_a)),V_z)=c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z),T_a).
% 51.54/51.66 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)=c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a).
% 51.54/51.66 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a)=c_Orderings_Oord__class_Omax(V_y,c_Orderings_Oord__class_Omax(V_x,V_z,T_a),T_a).
% 51.54/51.66 0 [] c_List_Olist_ONil(T_a)=c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a).
% 51.54/51.66 0 [] c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t))| -c_Lambda_Obeta(V_s,V_t).
% 51.54/51.66 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)=c_Orderings_Oord__class_Omax(V_x,V_y,T_a).
% 51.54/51.66 0 [] c_List_Oappend(c_List_Oreplicate(V_i,V_x,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a)=c_List_Olist_OCons(V_x,c_List_Oreplicate(V_i,V_x,T_a),T_a).
% 51.54/51.66 0 [] c_List_Ofoldl(V_f,V_a,c_List_Oappend(V_xs,V_ys,T_b),T_a,T_b)=c_List_Ofoldl(V_f,c_List_Ofoldl(V_f,V_a,V_xs,T_a,T_b),V_ys,T_a,T_b).
% 51.54/51.66 0 [] c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),T_a)=hAPP(V_f1,V_nat).
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_n,tc_nat).
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat).
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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.
% 51.54/51.66 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.
% 51.54/51.66 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)).
% 51.54/51.66 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.
% 51.54/51.66 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.
% 51.54/51.66 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.
% 51.54/51.66 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.
% 51.54/51.66 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.
% 51.54/51.66 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 51.54/51.66 0 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k)=V_t.
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.66 0 [] c_Suc(V_m)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.66 0 [] c_Suc(V_nat_H)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_m).
% 51.54/51.66 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_nat_H).
% 51.54/51.66 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).
% 51.54/51.66 0 [] -c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 51.54/51.66 0 [] -c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 51.54/51.66 0 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a).
% 51.54/51.66 0 [] c_Orderings_Oord__class_Omax(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=V_n.
% 51.54/51.66 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_a).
% 51.54/51.66 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Olist_ONil(T_a)|V_ys=c_List_Olist_ONil(T_a).
% 51.54/51.66 0 [] V_m=V_n|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat).
% 51.54/51.66 0 [] V_m=V_n| -c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)|c_HOL_Oord__class_Oless(V_n,V_m,tc_nat).
% 51.54/51.66 0 [] V_n=V_m| -c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)|c_HOL_Oord__class_Oless(V_n,V_m,tc_nat).
% 51.54/51.66 0 [] c_Lambda_OdB_OAbs(V_r)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_ss=c_List_Olist_ONil(tc_Lambda_OdB).
% 51.54/51.66 0 [] c_Type_Otype_Otype__rec(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),T_a)=hAPP(V_f1,V_nat).
% 51.54/51.66 0 [] c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB))| -c_Lambda_Obeta(V_r,V_s).
% 51.54/51.66 0 [] c_List_Olist_ONil(T_a)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a).
% 51.54/51.66 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)).
% 51.54/51.66 0 [] -c_HOL_Oord__class_Oless(V_x,V_x,tc_nat).
% 51.54/51.66 0 [] -c_HOL_Oord__class_Oless(V_n,V_n,tc_nat).
% 51.54/51.66 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 51.54/51.66 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 51.54/51.66 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 51.54/51.66 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).
% 51.54/51.66 0 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t),c_Lambda_Osubst(V_s,V_t,c_HOL_Ozero__class_Ozero(tc_nat))).
% 51.54/51.66 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).
% 51.54/51.66 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Olistsum(c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Olistsum(V_xs,T_a)).
% 51.54/51.66 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|V_x=V_y.
% 51.54/51.66 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)|V_m=V_n.
% 51.54/51.66 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).
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(V_y,V_x,tc_nat)|c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)|V_x=V_y.
% 51.54/51.66 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|V_x=V_y.
% 51.54/51.66 0 [] c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_k,V_x,T_a),T_a)=c_List_Oappend(c_List_Oreplicate(V_k,V_x,T_a),c_List_Oreplicate(V_n,V_x,T_a),T_a).
% 51.54/51.66 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 51.54/51.66 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 51.54/51.66 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(V_x,V_x,T_a)=V_x.
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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.
% 51.54/51.66 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.
% 51.54/51.66 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).
% 51.54/51.66 0 [] c_List_Olist_ONil(T_a)!=c_List_Olist_OCons(V_a_H,V_list_H,T_a).
% 51.54/51.66 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 51.54/51.66 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat).
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat).
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 51.54/51.66 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)|hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s)=V_t.
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_pwr,V_x),V_q))=hAPP(hAPP(V_pwr,V_x),c_Suc(V_q))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_pwr,V_x),V_q)),V_x)=hAPP(hAPP(V_pwr,V_x),c_Suc(V_q))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_pwr,V_x),c_Suc(V_q))=hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_pwr,V_x),V_q))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] hAPP(hAPP(V_pwr,V_x),c_Suc(V_n))=hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_pwr,V_x),V_n))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_x,T_a)=c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_m,V_x,T_a),T_a).
% 51.54/51.66 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 51.54/51.66 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 51.54/51.66 0 [] c_List_Oreplicate(V_n,V_x,T_a)!=c_List_Olist_ONil(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.66 0 [] c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a)=hAPP(hAPP(V_f3,V_dB),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB,T_a)).
% 51.54/51.66 0 [] c_List_Olist_ONil(T_a)!=c_List_Oreplicate(V_n,V_x,T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.66 0 [] c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 51.54/51.66 0 [] c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubst(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)).
% 51.54/51.66 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).
% 51.54/51.66 0 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(V_j),V_u,V_i)=c_Lambda_OdB_OVar(V_j)| -c_HOL_Oord__class_Oless(V_j,V_i,tc_nat).
% 51.54/51.66 0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f3,V_dB))).
% 51.54/51.66 0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_xa),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f3,V_xa))).
% 51.54/51.66 0 [] c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j))| -c_InductTermi_OIT(V_r).
% 51.54/51.66 0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat).
% 51.54/51.66 0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat).
% 51.54/51.66 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=V_xs|V_ys=c_List_Olist_ONil(T_a).
% 51.54/51.66 0 [] V_xs!=c_List_Oappend(V_xs,V_ys,T_a)|V_ys=c_List_Olist_ONil(T_a).
% 51.54/51.66 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=V_ys|V_xs=c_List_Olist_ONil(T_a).
% 51.54/51.66 0 [] V_ys!=c_List_Oappend(V_xs,V_ys,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 51.54/51.66 0 [] c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olist_OCons(V_x,V_xs,T_a).
% 51.54/51.66 0 [] c_Suc(V_n)!=V_n.
% 51.54/51.66 0 [] V_n!=c_Suc(V_n).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 0 [] c_List_Olist_OCons(V_a,V_list,T_a)!=c_List_Olist_OCons(V_a_H,V_list_H,T_a)|V_a=V_a_H.
% 51.54/51.66 0 [] c_List_Olist_OCons(V_a,V_list,T_a)!=c_List_Olist_OCons(V_a_H,V_list_H,T_a)|V_list=V_list_H.
% 51.54/51.66 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)).
% 51.54/51.66 0 [] c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olist_OCons(V_x,c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),V_xs,T_a),T_a).
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat).
% 51.54/51.66 0 [] c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 51.54/51.66 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)).
% 51.54/51.66 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Olistsum(c_List_Oappend(V_xs,V_ys,T_a),T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_List_Olistsum(V_xs,T_a)),c_List_Olistsum(V_ys,T_a)).
% 51.54/51.66 0 [] c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a)!=c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a)|V_xs=V_ys.
% 51.54/51.66 0 [] c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a)!=c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a)|V_x=V_y.
% 51.54/51.66 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 51.54/51.66 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)).
% 51.54/51.66 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).
% 51.54/51.66 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))).
% 51.54/51.66 0 [] c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 51.54/51.66 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))).
% 51.54/51.66 0 [] c_List_Oappend(c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a)=c_List_Oappend(V_xs,c_List_Oappend(V_ys,V_zs,T_a),T_a).
% 51.54/51.66 0 [] c_List_Oappend(V_xs,c_List_Oappend(V_xs1,V_us,T_a),T_a)=c_List_Oappend(c_List_Oappend(V_xs,V_xs1,T_a),V_us,T_a).
% 51.54/51.66 0 [] c_List_Oappend(c_List_Oappend(V_zs,V_x,T_a),V_ys,T_a)=c_List_Oappend(V_zs,c_List_Oappend(V_x,V_ys,T_a),T_a).
% 51.54/51.66 0 [] c_List_Oappend(V_xs,c_List_Oappend(V_x,V_ts,T_a),T_a)=c_List_Oappend(c_List_Oappend(V_xs,V_x,T_a),V_ts,T_a).
% 51.54/51.66 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a).
% 51.54/51.66 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 51.54/51.66 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 51.54/51.66 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 51.54/51.66 0 [] c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=V_n.
% 51.54/51.66 0 [] c_List_Oreplicate(V_m,V_x,T_a)!=c_List_Oreplicate(V_n,V_y,T_a)|V_x=V_y|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.66 0 [] V_x=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)).
% 51.54/51.66 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)=V_n.
% 51.54/51.66 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat))=V_m.
% 51.54/51.66 0 [] hAPP(hAPP(V_pwr,V_x),c_HOL_Ozero__class_Ozero(tc_nat))=V_r1| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 51.54/51.66 0 [] c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(V_t,V_s,V_k)),c_Lambda_Osubst(V_u,V_s,V_k)).
% 51.54/51.66 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=c_Lambda_OdB_OAbs(V_dB_H).
% 51.54/51.66 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2).
% 51.54/51.66 0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_xb),V_xc),t_a)))|hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_xb),V_xc))).
% 51.54/51.66 0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),t_a)))|hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_dB1),V_dB2))).
% 51.54/51.66 0 [] c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a)=hAPP(hAPP(V_f2,V_dB1),V_dB2).
% 51.54/51.66 0 [] c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a)=hAPP(hAPP(hAPP(hAPP(V_f2,V_dB1),V_dB2),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB1,T_a)),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB2,T_a)).
% 51.54/51.66 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.
% 51.54/51.66 0 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_s),hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_t))| -c_Lambda_Obeta(V_s,V_t).
% 51.54/51.66 0 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_u),hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u))| -c_Lambda_Obeta(V_s,V_t).
% 51.54/51.66 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)).
% 51.54/51.66 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)).
% 51.54/51.66 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).
% 51.54/51.66 0 [] c_Lambda_OdB_OVar(V_m)=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 51.54/51.66 0 [] c_Lambda_OdB_OVar(V_m)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_ss=c_List_Olist_ONil(tc_Lambda_OdB).
% 51.54/51.66 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).
% 51.54/51.66 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Olistsum(V_xs,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).
% 51.54/51.66 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).
% 51.54/51.66 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)).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=c_Lambda_OdB_OVar(V_nat).
% 51.54/51.66 0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_xd),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f1,V_xd))).
% 51.54/51.66 0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f1,V_nat))).
% 51.54/51.66 0 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k)=V_u.
% 51.54/51.66 0 [] -c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t).
% 51.54/51.66 0 [] c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a)=hAPP(V_f1,V_nat).
% 51.54/51.66 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OAbs(V_dB_H).
% 51.54/51.66 0 [] c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)).
% 51.54/51.66 0 [] c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a)=hAPP(V_f1,V_nat).
% 51.54/51.66 0 [] c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____).
% 51.54/51.66 0 [] c_Type_Otyping(V_e,V_t_H,V_T)| -c_Lambda_Obeta(V_t,V_t_H)| -c_Type_Otyping(V_e,V_t,V_T).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 0 [] hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H)!=c_Type_Otype_OAtom(V_nat).
% 51.54/51.66 0 [] c_Type_Osko__Type__Xtype__induct__1__1(V_P)!=hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2)|hBOOL(hAPP(V_P,V_T))|hBOOL(hAPP(V_P,V_T2)).
% 51.54/51.66 0 [] c_Type_Osko__Type__Xtype__induct__1__1(V_P)!=hAPP(hAPP(c_Type_Otype_OFun,V_T1a),V_x)|hBOOL(hAPP(V_P,V_T))|hBOOL(hAPP(V_P,V_T1a)).
% 51.54/51.66 0 [] c_Type_Otype_Otype__rec(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),T_a)=hAPP(hAPP(hAPP(hAPP(V_f2,V_type1),V_type2),c_Type_Otype_Otype__rec(V_f1,V_f2,V_type1,T_a)),c_Type_Otype_Otype__rec(V_f1,V_f2,V_type2,T_a)).
% 51.54/51.66 0 [] c_Type_Otype_Otype__case(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),T_a)=hAPP(hAPP(V_f2,V_type1),V_type2).
% 51.54/51.66 0 [] -hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_xa),V_xb),t_a)))|hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_xa),V_xb))).
% 51.54/51.66 0 [] -hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),t_a)))|hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_type1),V_type2))).
% 51.54/51.66 0 [] c_Type_Otype_OAtom(V_nat)!=hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H).
% 51.54/51.66 0 [] c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a)=hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a)).
% 51.54/51.66 0 [] c_List_Ofoldr(V_f,c_List_Oappend(V_xs,V_ys,T_b),V_a,T_b,T_a)=c_List_Ofoldr(V_f,V_xs,c_List_Ofoldr(V_f,V_ys,V_a,T_b,T_a),T_b,T_a).
% 51.54/51.66 0 [] c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a)=V_a.
% 51.54/51.66 0 [] c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))| -c_InductTermi_OIT(V_t).
% 51.54/51.66 0 [] c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k)=V_t.
% 51.54/51.66 0 [] c_Lambda_Obeta(c_Lambda_Olift(V_r,V_i),c_Lambda_Olift(V_s,V_i))| -c_Lambda_Obeta(V_r,V_s).
% 51.54/51.66 0 [] v_T____!=hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2)|c_InductTermi_OIT(c_Lambda_Osubst(V_t,V_u,V_i))| -c_Type_Otyping(V_e,V_u,V_T2)| -c_InductTermi_OIT(V_u)| -c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_T2,tc_Type_Otype),V_t,V_Ta)| -c_InductTermi_OIT(V_t).
% 51.54/51.66 0 [] v_T____!=hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2)|c_InductTermi_OIT(c_Lambda_Osubst(V_t,V_u,V_i))| -c_Type_Otyping(V_e,V_u,V_T1)| -c_InductTermi_OIT(V_u)| -c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_T1,tc_Type_Otype),V_t,V_Ta)| -c_InductTermi_OIT(V_t).
% 51.54/51.66 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).
% 51.54/51.66 0 [] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____).
% 51.54/51.66 0 [] c_InductTermi_OIT(v_u____).
% 51.54/51.66 0 [] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 51.54/51.66 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).
% 51.54/51.66 0 [] c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(V_nat),tc_Lambda_OdB)=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.66 0 [] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(V_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.66 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.
% 51.54/51.66 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.
% 51.54/51.66 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.
% 51.54/51.66 0 [] c_InductTermi_OIT(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),c_Lambda_OdB_OVar(V_i)))| -c_InductTermi_OIT(V_t).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 0 [] c_Lambda_Olift(c_Lambda_OdB_OVar(V_i),V_k)=c_Lambda_OdB_OVar(V_i)| -c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 51.54/51.66 0 [] c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 51.54/51.66 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)).
% 51.54/51.66 0 [] c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 51.54/51.66 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,c_Lambda_Osubst(V_t,V_u,V_i),V_T).
% 51.54/51.66 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).
% 51.54/51.66 0 [] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)).
% 51.54/51.66 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).
% 51.54/51.66 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).
% 51.54/51.66 0 [] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))).
% 51.54/51.66 0 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 51.54/51.66 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).
% 51.54/51.66 0 [] v_T____=hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)).
% 51.54/51.66 0 [] c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),c_Lambda_Olift(V_t,V_i),V_T)| -c_Type_Otyping(V_e,V_t,V_T).
% 51.54/51.66 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OVar(V_nat_H)|V_nat=V_nat_H.
% 51.54/51.66 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.
% 51.54/51.66 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.
% 51.54/51.66 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)).
% 51.54/51.66 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.
% 51.54/51.66 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.
% 51.54/51.66 0 [] c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))).
% 51.54/51.66 0 [] c_Lambda_OdB_OVar(V_nat)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H).
% 51.54/51.66 0 [] hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x)=V_T.
% 51.54/51.66 0 [] hAPP(V_e,V_i)=V_T| -c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T).
% 51.54/51.66 0 [] c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(V_s,V_k)),c_Lambda_Olift(V_t,V_k)).
% 51.54/51.66 0 [] c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)).
% 51.54/51.66 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)!=c_Lambda_OdB_OVar(V_nat).
% 51.54/51.66 0 [] -c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)).
% 51.54/51.66 0 [] class_Orderings_Opreorder(tc_fun(T_2,T_1))| -class_Orderings_Opreorder(T_1).
% 51.54/51.66 0 [] class_Orderings_Oorder(tc_fun(T_2,T_1))| -class_Orderings_Oorder(T_1).
% 51.54/51.66 0 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 51.54/51.66 0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 51.54/51.66 0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 51.54/51.66 0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 51.54/51.66 0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 51.54/51.66 0 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 51.54/51.66 0 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 51.54/51.66 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 51.54/51.66 0 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 51.54/51.66 0 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 51.54/51.66 0 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 51.54/51.66 0 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 51.54/51.66 0 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 51.54/51.66 0 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 51.54/51.66 0 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 51.54/51.66 0 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 51.54/51.66 0 [] class_Nat_Osemiring__char__0(tc_nat).
% 51.54/51.66 0 [] class_Orderings_Opreorder(tc_nat).
% 51.54/51.66 0 [] class_Orderings_Olinorder(tc_nat).
% 51.54/51.66 0 [] class_Orderings_Oorder(tc_nat).
% 51.54/51.66 0 [] class_Power_Opower(tc_nat).
% 51.54/51.67 0 [] c_fe_qual(V_x,V_x,T_a).
% 51.54/51.67 0 [] V_X=V_Y| -c_fe_qual(V_X,V_Y,T_a).
% 51.54/51.67 end_of_list.
% 51.54/51.67
% 51.54/51.67 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 51.54/51.67
% 51.54/51.67 This ia a non-Horn set with equality. The strategy will be
% 51.54/51.67 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 51.54/51.67 deletion, with positive clauses in sos and nonpositive
% 51.54/51.67 clauses in usable.
% 51.54/51.67
% 51.54/51.67 dependent: set(knuth_bendix).
% 51.54/51.67 dependent: set(anl_eq).
% 51.54/51.67 dependent: set(para_from).
% 51.54/51.67 dependent: set(para_into).
% 51.54/51.67 dependent: clear(para_from_right).
% 51.54/51.67 dependent: clear(para_into_right).
% 51.54/51.67 dependent: set(para_from_vars).
% 51.54/51.67 dependent: set(eq_units_both_ways).
% 51.54/51.67 dependent: set(dynamic_demod_all).
% 51.54/51.67 dependent: set(dynamic_demod).
% 51.54/51.67 dependent: set(order_eq).
% 51.54/51.67 dependent: set(back_demod).
% 51.54/51.67 dependent: set(lrpo).
% 51.54/51.67 dependent: set(hyper_res).
% 51.54/51.67 dependent: set(unit_deletion).
% 51.54/51.67 dependent: set(factor).
% 51.54/51.67
% 51.54/51.67 ------------> process usable:
% 51.54/51.67 ** KEPT (pick-wt=16): 1 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)|B=C.
% 51.54/51.67 ** KEPT (pick-wt=20): 2 [] -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.
% 51.54/51.67 ** KEPT (pick-wt=18): 3 [] -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.
% 51.54/51.67 ** KEPT (pick-wt=18): 4 [] -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.
% 51.54/51.67 ** KEPT (pick-wt=18): 5 [] -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.
% 51.54/51.67 ** KEPT (pick-wt=13): 6 [] c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_Lambda_OdB_OAbs(C)|B=c_List_Olist_ONil(tc_Lambda_OdB).
% 51.54/51.67 ** KEPT (pick-wt=7): 7 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 51.54/51.67 ** KEPT (pick-wt=16): 8 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B)|A=C.
% 51.54/51.67 Following clause subsumed by 1 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.
% 51.54/51.67 ** KEPT (pick-wt=13): 9 [] c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat)|c_Suc(A)=B| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=22): 10 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=13): 11 [] 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.
% 51.54/51.67 ** KEPT (pick-wt=9): 12 [] -class_OrderedGroup_Omonoid__add(A)|c_List_Olistsum(c_List_Olist_ONil(A),A)=c_HOL_Ozero__class_Ozero(A).
% 51.54/51.67 ** KEPT (pick-wt=13): 13 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(D,B,A),C,A).
% 51.54/51.67 ** KEPT (pick-wt=13): 14 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(B,D,A),C,A).
% 51.54/51.67 ** KEPT (pick-wt=13): 15 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_HOL_Oord__class_Oless(B,D,A).
% 51.54/51.67 ** KEPT (pick-wt=13): 16 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_HOL_Oord__class_Oless(B,C,A).
% 51.54/51.67 Following clause subsumed by 15 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_HOL_Oord__class_Oless(B,D,A).
% 51.54/51.67 Following clause subsumed by 16 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_HOL_Oord__class_Oless(B,C,A).
% 51.54/51.67 ** KEPT (pick-wt=19): 17 [] 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)).
% 51.54/51.67 ** KEPT (pick-wt=19): 18 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=9): 19 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_Type_Osko__Type__Xtype__induct__1__1(A))).
% 51.54/51.67 ** KEPT (pick-wt=17): 20 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xlist__app__typeE__1__1(C,A,D,B))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,D,B,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 51.54/51.67 ** KEPT (pick-wt=28): 21 [] -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.
% 51.54/51.67 ** KEPT (pick-wt=20): 22 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=25): 23 [] -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)).
% 51.54/51.67 ** KEPT (pick-wt=25): 24 [] -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)).
% 51.54/51.67 ** KEPT (pick-wt=25): 25 [] -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).
% 51.54/51.67 Following clause subsumed by 23 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)).
% 51.54/51.67 ** KEPT (pick-wt=25): 26 [] -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)).
% 51.54/51.67 ** KEPT (pick-wt=25): 27 [] -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)).
% 51.54/51.67 ** KEPT (pick-wt=25): 28 [] -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)).
% 51.54/51.67 ** KEPT (pick-wt=25): 29 [] -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)).
% 51.54/51.67 Following clause subsumed by 23 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)).
% 51.54/51.67 ** KEPT (pick-wt=14): 30 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=14): 31 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=14): 32 [] -class_OrderedGroup_Omonoid__add(A)|c_List_Olistsum(B,A)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),B,A,A).
% 51.54/51.67 ** KEPT (pick-wt=10): 33 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=12): 34 [] c_Lambda_Obeta(c_Lambda_Osubst(A,B,C),c_Lambda_Osubst(D,B,C))| -c_Lambda_Obeta(A,D).
% 51.54/51.67 ** KEPT (pick-wt=12): 35 [] c_List_Oreplicate(A,B,C)!=c_List_Oreplicate(D,E,C)|A=D.
% 51.54/51.67 ** KEPT (pick-wt=12): 36 [] c_List_Oappend(A,B,C)!=c_List_Oappend(D,B,C)|A=D.
% 51.54/51.67 ** KEPT (pick-wt=12): 37 [] c_List_Oappend(A,B,C)!=c_List_Oappend(A,D,C)|B=D.
% 51.54/51.67 ** KEPT (pick-wt=17): 38 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(B,C,A),D,A)| -c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 51.54/51.67 ** KEPT (pick-wt=13): 39 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=8): 40 [] c_Type_Otype_OAtom(A)!=c_Type_Otype_OAtom(B)|A=B.
% 51.54/51.67 ** KEPT (pick-wt=13): 41 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=13): 42 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=13): 43 [] 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).
% 51.54/51.67 Following clause subsumed by 41 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).
% 51.54/51.67 Following clause subsumed by 42 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).
% 51.54/51.67 ** KEPT (pick-wt=15): 44 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=15): 45 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=21): 46 [] 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).
% 51.54/51.67 Following clause subsumed by 44 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).
% 51.54/51.67 ** KEPT (pick-wt=27): 48 [copy,47,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).
% 51.54/51.67 ** KEPT (pick-wt=12): 49 [] -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.
% 51.54/51.67 ** KEPT (pick-wt=31): 50 [] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,C),E))=hAPP(hAPP(B,C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),E))| -c_Groebner__Basis_Ogb__semiring(F,A,B,G,H,I).
% 51.54/51.67 ** KEPT (pick-wt=8): 51 [] c_Suc(A)!=c_Suc(B)|A=B.
% 51.54/51.67 Following clause subsumed by 51 during input processing: 0 [] c_Suc(A)!=c_Suc(B)|A=B.
% 51.54/51.67 ** KEPT (pick-wt=17): 52 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=17): 53 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=17): 54 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=17): 55 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=17): 56 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=20): 57 [] 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)).
% 51.54/51.67 ** KEPT (pick-wt=18): 58 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=23): 59 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=15): 60 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=17): 61 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(B,D,A)| -c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(D,C,A),A).
% 51.54/51.67 ** KEPT (pick-wt=25): 62 [] 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))| -c_InductTermi_OIT(B)| -c_InductTermi_OIT(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_Lambda_OdB,tc_Lambda_OdB)).
% 51.54/51.67 ** KEPT (pick-wt=11): 63 [] c_List_Olist_ONil(A)!=c_List_Oappend(B,C,A)|B=c_List_Olist_ONil(A).
% 51.54/51.67 ** KEPT (pick-wt=11): 64 [] c_List_Olist_ONil(A)!=c_List_Oappend(B,C,A)|C=c_List_Olist_ONil(A).
% 51.54/51.67 ** KEPT (pick-wt=8): 65 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OAbs(B)|A=B.
% 51.54/51.67 Following clause subsumed by 7 during input processing: 0 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 51.54/51.67 ** KEPT (pick-wt=30): 66 [] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E)=hAPP(hAPP(B,hAPP(hAPP(A,C),E)),hAPP(hAPP(A,D),E))| -c_Groebner__Basis_Ogb__semiring(F,B,A,G,H,I).
% 51.54/51.67 ** KEPT (pick-wt=30): 68 [copy,67,flip.1] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,C),E))=hAPP(hAPP(B,C),hAPP(hAPP(A,D),E))| -c_Groebner__Basis_Ogb__semiring(A,B,F,G,H,I).
% 51.54/51.67 ** KEPT (pick-wt=18): 69 [] hAPP(hAPP(A,B),C)=hAPP(hAPP(A,C),B)| -c_Groebner__Basis_Ogb__semiring(D,A,E,F,G,H).
% 51.54/51.67 ** KEPT (pick-wt=26): 71 [copy,70,flip.1] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(E,A,F,G,H,I).
% 51.54/51.67 ** KEPT (pick-wt=14): 72 [] hAPP(hAPP(A,B),C)=C| -c_Groebner__Basis_Ogb__semiring(D,A,E,F,B,G).
% 51.54/51.67 ** KEPT (pick-wt=14): 73 [] hAPP(hAPP(A,B),C)=B| -c_Groebner__Basis_Ogb__semiring(D,A,E,B,F,G).
% 51.54/51.67 ** KEPT (pick-wt=18): 74 [] hAPP(hAPP(A,B),C)=hAPP(hAPP(A,C),B)| -c_Groebner__Basis_Ogb__semiring(A,D,E,F,G,H).
% 51.54/51.67 ** KEPT (pick-wt=26): 76 [copy,75,flip.1] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(A,E,F,G,H,I).
% 51.54/51.67 ** KEPT (pick-wt=14): 77 [] hAPP(hAPP(A,B),C)=C| -c_Groebner__Basis_Ogb__semiring(A,D,E,B,F,G).
% 51.54/51.67 Following clause subsumed by 76 during input processing: 0 [flip.1] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(A,E,F,G,H,I).
% 51.54/51.67 Following clause subsumed by 74 during input processing: 0 [] hAPP(hAPP(A,B),C)=hAPP(hAPP(A,C),B)| -c_Groebner__Basis_Ogb__semiring(A,D,E,F,G,H).
% 51.54/51.67 ** KEPT (pick-wt=26): 78 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,hAPP(hAPP(A,B),D)),C)| -c_Groebner__Basis_Ogb__semiring(A,E,F,G,H,I).
% 51.54/51.67 ** KEPT (pick-wt=26): 79 [] hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))=hAPP(hAPP(A,C),hAPP(hAPP(A,B),D))| -c_Groebner__Basis_Ogb__semiring(A,E,F,G,H,I).
% 51.54/51.67 Following clause subsumed by 76 during input processing: 0 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(A,E,F,G,H,I).
% 51.54/51.67 ** KEPT (pick-wt=34): 80 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E))=hAPP(hAPP(A,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,C),E))| -c_Groebner__Basis_Ogb__semiring(A,F,G,H,I,J).
% 51.54/51.67 ** KEPT (pick-wt=26): 81 [] hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))=hAPP(hAPP(A,C),hAPP(hAPP(A,B),D))| -c_Groebner__Basis_Ogb__semiring(E,A,F,G,H,I).
% 51.54/51.67 Following clause subsumed by 71 during input processing: 0 [flip.1] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(E,A,F,G,H,I).
% 51.54/51.67 Following clause subsumed by 71 during input processing: 0 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(E,A,F,G,H,I).
% 51.54/51.67 ** KEPT (pick-wt=26): 82 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,hAPP(hAPP(A,B),D)),C)| -c_Groebner__Basis_Ogb__semiring(E,A,F,G,H,I).
% 51.54/51.67 Following clause subsumed by 81 during input processing: 0 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E))=hAPP(hAPP(A,D),hAPP(hAPP(A,hAPP(hAPP(A,B),C)),E))| -c_Groebner__Basis_Ogb__semiring(F,A,G,H,I,J).
% 51.54/51.67 Following clause subsumed by 71 during input processing: 0 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E))=hAPP(hAPP(A,B),hAPP(hAPP(A,C),hAPP(hAPP(A,D),E)))| -c_Groebner__Basis_Ogb__semiring(F,A,G,H,I,J).
% 51.54/51.67 ** KEPT (pick-wt=34): 83 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E))=hAPP(hAPP(A,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,C),E))| -c_Groebner__Basis_Ogb__semiring(F,A,G,H,I,J).
% 51.54/51.67 ** KEPT (pick-wt=14): 84 [] hAPP(hAPP(A,B),C)=B| -c_Groebner__Basis_Ogb__semiring(D,A,E,F,C,G).
% 51.54/51.67 Following clause subsumed by 72 during input processing: 0 [] hAPP(hAPP(A,B),C)=C| -c_Groebner__Basis_Ogb__semiring(D,A,E,F,B,G).
% 51.54/51.67 ** KEPT (pick-wt=14): 85 [] hAPP(hAPP(A,B),C)=C| -c_Groebner__Basis_Ogb__semiring(D,A,E,C,F,G).
% 51.54/51.67 Following clause subsumed by 73 during input processing: 0 [] hAPP(hAPP(A,B),C)=B| -c_Groebner__Basis_Ogb__semiring(D,A,E,B,F,G).
% 51.54/51.67 ** KEPT (pick-wt=30): 86 [] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E)=hAPP(hAPP(B,hAPP(hAPP(A,C),E)),hAPP(hAPP(A,D),E))| -c_Groebner__Basis_Ogb__semiring(B,A,F,G,H,I).
% 51.54/51.67 Following clause subsumed by 69 during input processing: 0 [] hAPP(hAPP(A,B),C)=hAPP(hAPP(A,C),B)| -c_Groebner__Basis_Ogb__semiring(D,A,E,F,G,H).
% 51.54/51.67 ** KEPT (pick-wt=14): 87 [] hAPP(hAPP(A,B),C)=B| -c_Groebner__Basis_Ogb__semiring(A,D,E,C,F,G).
% 51.54/51.67 Following clause subsumed by 77 during input processing: 0 [] hAPP(hAPP(A,B),C)=C| -c_Groebner__Basis_Ogb__semiring(A,D,E,B,F,G).
% 51.54/51.67 ** KEPT (pick-wt=22): 88 [] hAPP(hAPP(A,B),B)=hAPP(hAPP(C,hAPP(hAPP(A,D),D)),B)| -c_Groebner__Basis_Ogb__semiring(A,C,E,F,D,G).
% 51.54/51.67 ** KEPT (pick-wt=26): 89 [] hAPP(hAPP(A,B),hAPP(hAPP(C,D),B))=hAPP(hAPP(C,hAPP(hAPP(A,D),E)),B)| -c_Groebner__Basis_Ogb__semiring(A,C,F,G,E,H).
% 51.54/51.67 ** KEPT (pick-wt=26): 90 [] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),D)=hAPP(hAPP(B,hAPP(hAPP(A,C),E)),D)| -c_Groebner__Basis_Ogb__semiring(A,B,F,G,E,H).
% 51.54/51.67 ** KEPT (pick-wt=30): 91 [] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,E),D))=hAPP(hAPP(B,hAPP(hAPP(A,C),E)),D)| -c_Groebner__Basis_Ogb__semiring(A,B,F,G,H,I).
% 51.54/51.67 ** KEPT (pick-wt=15): 92 [] -hBOOL(hAPP(A,c_Type_Otype_Otype__case(B,C,c_Type_Otype_OAtom(D),t_a)))|hBOOL(hAPP(A,hAPP(B,D))).
% 51.54/51.67 Following clause subsumed by 92 during input processing: 0 [] -hBOOL(hAPP(A,c_Type_Otype_Otype__case(B,C,c_Type_Otype_OAtom(D),t_a)))|hBOOL(hAPP(A,hAPP(B,D))).
% 51.54/51.67 ** KEPT (pick-wt=19): 93 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=19): 94 [] 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)).
% 51.54/51.67 ** KEPT (pick-wt=5): 95 [] c_InductTermi_OIT(c_Lambda_OdB_OAbs(A))| -c_InductTermi_OIT(A).
% 51.54/51.67 ** KEPT (pick-wt=35): 96 [] -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)).
% 51.54/51.67 ** KEPT (pick-wt=9): 97 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=11): 98 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(B,C,A)=c_Orderings_Oord__class_Omax(C,B,A).
% 51.54/51.67 ** KEPT (pick-wt=12): 99 [] c_Lambda_Oliftn(A,c_Lambda_OdB_OVar(B),C)=c_Lambda_OdB_OVar(B)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=6): 100 [] c_List_Olist_OCons(A,B,C)!=B.
% 51.54/51.67 Following clause subsumed by 100 during input processing: 0 [flip.1] c_List_Olist_OCons(B,A,C)!=A.
% 51.54/51.67 ** KEPT (pick-wt=9): 101 [] -c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=26): 102 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Orderings_Oord__class_Omax(B,C,A)),D)=c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A).
% 51.54/51.67 ** KEPT (pick-wt=17): 103 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(B,C,A),D,A)=c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(C,D,A),A).
% 51.54/51.67 ** KEPT (pick-wt=17): 104 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(C,D,A),A)=c_Orderings_Oord__class_Omax(C,c_Orderings_Oord__class_Omax(B,D,A),A).
% 51.54/51.67 ** KEPT (pick-wt=8): 105 [] c_Lambda_Obeta(c_Lambda_OdB_OAbs(A),c_Lambda_OdB_OAbs(B))| -c_Lambda_Obeta(A,B).
% 51.54/51.67 ** KEPT (pick-wt=14): 106 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(B,C,A),A)=c_Orderings_Oord__class_Omax(B,C,A).
% 51.54/51.67 ** KEPT (pick-wt=10): 107 [] c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=10): 108 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat).
% 51.54/51.67 Following clause subsumed by 107 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).
% 51.54/51.67 Following clause subsumed by 42 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).
% 51.54/51.67 Following clause subsumed by 41 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).
% 51.54/51.67 ** KEPT (pick-wt=17): 109 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=17): 110 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=18): 112 [copy,111,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).
% 51.54/51.67 ** KEPT (pick-wt=19): 113 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=13): 114 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=15): 115 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=16): 117 [copy,116,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).
% 51.54/51.67 ** KEPT (pick-wt=13): 118 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=11): 119 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 51.54/51.67 ** KEPT (pick-wt=11): 120 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 51.54/51.67 ** KEPT (pick-wt=13): 122 [copy,121,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.
% 51.54/51.67 ** KEPT (pick-wt=11): 123 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 51.54/51.67 ** KEPT (pick-wt=11): 124 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 51.54/51.67 ** KEPT (pick-wt=11): 125 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 51.54/51.67 ** KEPT (pick-wt=11): 126 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 51.54/51.67 Following clause subsumed by 119 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.
% 51.54/51.67 ** KEPT (pick-wt=6): 127 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=5): 128 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.67 Following clause subsumed by 128 during input processing: 0 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=13): 129 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=13): 130 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=12): 132 [copy,131,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.67 Following clause subsumed by 132 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.67 Following clause subsumed by 128 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.67 Following clause subsumed by 128 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=5): 133 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 51.54/51.67 Following clause subsumed by 133 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=11): 134 [] c_List_Oappend(A,B,C)!=c_List_Olist_ONil(C)|A=c_List_Olist_ONil(C).
% 51.54/51.67 ** KEPT (pick-wt=11): 135 [] c_List_Oappend(A,B,C)!=c_List_Olist_ONil(C)|B=c_List_Olist_ONil(C).
% 51.54/51.67 ** KEPT (pick-wt=12): 136 [] A=B|c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=12): 137 [] A=B| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 51.54/51.67 Following clause subsumed by 136 during input processing: 0 [] A=B| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)|c_HOL_Oord__class_Oless(A,B,tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=13): 138 [] c_Lambda_OdB_OAbs(A)!=c_List_Ofoldl(c_Lambda_OdB_OApp,B,C,tc_Lambda_OdB,tc_Lambda_OdB)|C=c_List_Olist_ONil(tc_Lambda_OdB).
% 51.54/51.67 ** KEPT (pick-wt=16): 139 [] c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,C,B,tc_Lambda_OdB,tc_Lambda_OdB))| -c_Lambda_Obeta(A,C).
% 51.54/51.67 ** KEPT (pick-wt=4): 140 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 51.54/51.67 Following clause subsumed by 140 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=6): 141 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 51.54/51.67 ** KEPT (pick-wt=6): 142 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 51.54/51.67 ** KEPT (pick-wt=6): 143 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 51.54/51.67 ** KEPT (pick-wt=22): 144 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=17): 146 [copy,145,flip.2] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Olistsum(C,A))=c_List_Olistsum(c_List_Olist_OCons(B,C,A),A).
% 51.54/51.67 ** KEPT (pick-wt=13): 147 [] -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.
% 51.54/51.67 ** KEPT (pick-wt=13): 148 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(C,B,A)|c_HOL_Oord__class_Oless(B,C,A).
% 51.54/51.67 Following clause subsumed by 148 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.
% 51.54/51.67 Following clause subsumed by 148 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).
% 51.54/51.67 Following clause subsumed by 148 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).
% 51.54/51.67 ** KEPT (pick-wt=8): 149 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(B,B,A)=B.
% 51.54/51.67 ** KEPT (pick-wt=24): 150 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=22): 151 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=18): 152 [] 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.
% 51.54/51.67 ** KEPT (pick-wt=18): 153 [] 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.
% 51.54/51.67 ** KEPT (pick-wt=13): 154 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=7): 155 [] c_List_Olist_ONil(A)!=c_List_Olist_OCons(B,C,A).
% 51.54/51.67 ** KEPT (pick-wt=14): 156 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=14): 157 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=13): 158 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=20): 159 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_List_Ofoldl(c_Lambda_OdB_OApp,C,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)|hAPP(hAPP(c_Lambda_OdB_OApp,A),B)=C.
% 51.54/51.67 ** KEPT (pick-wt=23): 160 [] hAPP(hAPP(A,B),hAPP(hAPP(C,B),D))=hAPP(hAPP(C,B),c_Suc(D))| -c_Groebner__Basis_Ogb__semiring(E,A,C,F,G,H).
% 51.54/51.67 ** KEPT (pick-wt=23): 161 [] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),C)=hAPP(hAPP(B,C),c_Suc(D))| -c_Groebner__Basis_Ogb__semiring(E,A,B,F,G,H).
% 51.54/51.67 ** KEPT (pick-wt=23): 162 [] hAPP(hAPP(A,B),c_Suc(C))=hAPP(hAPP(D,B),hAPP(hAPP(A,B),C))| -c_Groebner__Basis_Ogb__semiring(E,D,A,F,G,H).
% 51.54/51.67 Following clause subsumed by 162 during input processing: 0 [] hAPP(hAPP(A,B),c_Suc(C))=hAPP(hAPP(D,B),hAPP(hAPP(A,B),C))| -c_Groebner__Basis_Ogb__semiring(E,D,A,F,G,H).
% 51.54/51.67 ** KEPT (pick-wt=14): 163 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=14): 164 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=11): 165 [] c_List_Oreplicate(A,B,C)!=c_List_Olist_ONil(C)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=11): 166 [] c_List_Olist_ONil(A)!=c_List_Oreplicate(B,C,A)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=17): 167 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xlist__app__typeD__1__1(C,A,D,B))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,D,B,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 51.54/51.67 ** KEPT (pick-wt=20): 168 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=12): 169 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,C)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=16): 170 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OAbs(E),t_a)))|hBOOL(hAPP(A,hAPP(D,E))).
% 51.54/51.67 Following clause subsumed by 170 during input processing: 0 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OAbs(E),t_a)))|hBOOL(hAPP(A,hAPP(D,E))).
% 51.54/51.67 ** KEPT (pick-wt=8): 171 [] c_InductTermi_OIT(c_Lambda_Osubst(A,c_Lambda_OdB_OVar(B),C))| -c_InductTermi_OIT(A).
% 51.54/51.67 ** KEPT (pick-wt=9): 172 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=9): 173 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=10): 174 [] c_List_Oappend(A,B,C)!=A|B=c_List_Olist_ONil(C).
% 51.54/51.67 Following clause subsumed by 174 during input processing: 0 [flip.1] c_List_Oappend(A,B,C)!=A|B=c_List_Olist_ONil(C).
% 51.54/51.67 ** KEPT (pick-wt=10): 175 [] c_List_Oappend(A,B,C)!=B|A=c_List_Olist_ONil(C).
% 51.54/51.67 Following clause subsumed by 175 during input processing: 0 [flip.1] c_List_Oappend(B,A,C)!=A|B=c_List_Olist_ONil(C).
% 51.54/51.67 ** KEPT (pick-wt=4): 176 [] c_Suc(A)!=A.
% 51.54/51.67 Following clause subsumed by 176 during input processing: 0 [flip.1] c_Suc(A)!=A.
% 51.54/51.67 ** KEPT (pick-wt=20): 177 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=20): 178 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=20): 179 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=20): 180 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=20): 181 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=20): 182 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=18): 183 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=18): 184 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=18): 185 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=12): 186 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_OCons(D,E,C)|A=D.
% 51.54/51.67 ** KEPT (pick-wt=12): 187 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_OCons(D,E,C)|B=E.
% 51.54/51.67 ** KEPT (pick-wt=9): 188 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=9): 189 [] c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=21): 190 [] -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)).
% 51.54/51.67 ** KEPT (pick-wt=19): 192 [copy,191,flip.2] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_List_Olistsum(B,A)),c_List_Olistsum(C,A))=c_List_Olistsum(c_List_Oappend(B,C,A),A).
% 51.54/51.67 ** KEPT (pick-wt=20): 193 [] c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C)!=c_List_Oappend(D,c_List_Olist_OCons(E,c_List_Olist_ONil(C),C),C)|A=D.
% 51.54/51.67 ** KEPT (pick-wt=20): 194 [] c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C)!=c_List_Oappend(D,c_List_Olist_OCons(E,c_List_Olist_ONil(C),C),C)|B=E.
% 51.54/51.67 ** KEPT (pick-wt=20): 195 [] 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)).
% 51.54/51.67 ** KEPT (pick-wt=18): 196 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=10): 197 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 51.54/51.67 ** KEPT (pick-wt=10): 198 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 51.54/51.67 ** KEPT (pick-wt=10): 199 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 51.54/51.67 Following clause subsumed by 199 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 51.54/51.67 ** KEPT (pick-wt=16): 200 [] c_List_Oreplicate(A,B,C)!=c_List_Oreplicate(D,E,C)|B=E|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=15): 201 [] hAPP(hAPP(A,B),c_HOL_Ozero__class_Ozero(tc_nat))=C| -c_Groebner__Basis_Ogb__semiring(D,E,A,F,C,G).
% 51.54/51.67 ** KEPT (pick-wt=8): 202 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 51.54/51.67 ** KEPT (pick-wt=8): 203 [] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 51.54/51.67 ** KEPT (pick-wt=21): 204 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,hAPP(hAPP(c_Lambda_OdB_OApp,E),F),t_a)))|hBOOL(hAPP(A,hAPP(hAPP(C,E),F))).
% 51.54/51.67 Following clause subsumed by 204 during input processing: 0 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,hAPP(hAPP(c_Lambda_OdB_OApp,E),F),t_a)))|hBOOL(hAPP(A,hAPP(hAPP(C,E),F))).
% 51.54/51.67 ** KEPT (pick-wt=16): 205 [] 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.
% 51.54/51.67 ** KEPT (pick-wt=14): 206 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),hAPP(hAPP(c_Lambda_OdB_OApp,A),C))| -c_Lambda_Obeta(B,C).
% 51.54/51.67 ** KEPT (pick-wt=14): 207 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),hAPP(hAPP(c_Lambda_OdB_OApp,C),B))| -c_Lambda_Obeta(A,C).
% 51.54/51.67 ** KEPT (pick-wt=15): 208 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=13): 209 [] c_Lambda_OdB_OVar(A)!=c_List_Ofoldl(c_Lambda_OdB_OApp,B,C,tc_Lambda_OdB,tc_Lambda_OdB)|C=c_List_Olist_ONil(tc_Lambda_OdB).
% 51.54/51.67 ** 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).
% 51.54/51.67 ** KEPT (pick-wt=14): 211 [] -class_OrderedGroup_Omonoid__add(A)|c_List_Olistsum(B,A)=c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,c_HOL_Ozero__class_Ozero(A),A,A).
% 51.54/51.67 ** KEPT (pick-wt=19): 213 [copy,212,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).
% 51.54/51.67 ** KEPT (pick-wt=23): 215 [copy,214,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).
% 51.54/51.67 ** KEPT (pick-wt=18): 216 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=37): 217 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=5): 218 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 51.54/51.67 ** KEPT (pick-wt=16): 219 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OVar(E),t_a)))|hBOOL(hAPP(A,hAPP(B,E))).
% 51.54/51.67 Following clause subsumed by 219 during input processing: 0 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OVar(E),t_a)))|hBOOL(hAPP(A,hAPP(B,E))).
% 51.54/51.67 ** KEPT (pick-wt=4): 220 [] -c_Lambda_Obeta(c_Lambda_OdB_OVar(A),B).
% 51.54/51.67 ** KEPT (pick-wt=5): 221 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 51.54/51.67 ** KEPT (pick-wt=11): 222 [] c_Type_Otyping(A,B,C)| -c_Lambda_Obeta(D,B)| -c_Type_Otyping(A,D,C).
% 51.54/51.67 ** KEPT (pick-wt=18): 223 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=20): 224 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=8): 225 [] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=c_Type_Otype_OAtom(C).
% 51.54/51.67 ** KEPT (pick-wt=12): 227 [copy,226,factor_simp] c_Type_Osko__Type__Xtype__induct__1__1(A)!=hAPP(hAPP(c_Type_Otype_OFun,B),C)|hBOOL(hAPP(A,C)).
% 51.54/51.67 ** KEPT (pick-wt=12): 229 [copy,228,factor_simp] c_Type_Osko__Type__Xtype__induct__1__1(A)!=hAPP(hAPP(c_Type_Otype_OFun,B),C)|hBOOL(hAPP(A,B)).
% 51.54/51.67 ** KEPT (pick-wt=20): 230 [] -hBOOL(hAPP(A,c_Type_Otype_Otype__case(B,C,hAPP(hAPP(c_Type_Otype_OFun,D),E),t_a)))|hBOOL(hAPP(A,hAPP(hAPP(C,D),E))).
% 51.54/51.67 Following clause subsumed by 230 during input processing: 0 [] -hBOOL(hAPP(A,c_Type_Otype_Otype__case(B,C,hAPP(hAPP(c_Type_Otype_OFun,D),E),t_a)))|hBOOL(hAPP(A,hAPP(hAPP(C,D),E))).
% 51.54/51.67 ** KEPT (pick-wt=8): 231 [] c_Type_Otype_OAtom(A)!=hAPP(hAPP(c_Type_Otype_OFun,B),C).
% 51.54/51.67 ** KEPT (pick-wt=6): 232 [] c_InductTermi_OIT(c_Lambda_Olift(A,B))| -c_InductTermi_OIT(A).
% 51.54/51.67 ** KEPT (pick-wt=10): 233 [] c_Lambda_Obeta(c_Lambda_Olift(A,B),c_Lambda_Olift(C,B))| -c_Lambda_Obeta(A,C).
% 51.54/51.67 ** KEPT (pick-wt=28): 235 [copy,234,flip.1] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=v_T____|c_InductTermi_OIT(c_Lambda_Osubst(C,D,E))| -c_Type_Otyping(F,D,B)| -c_InductTermi_OIT(D)| -c_Type_Otyping(c_Type_Oshift(F,E,B,tc_Type_Otype),C,G)| -c_InductTermi_OIT(C).
% 51.54/51.67 ** KEPT (pick-wt=28): 237 [copy,236,flip.1] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=v_T____|c_InductTermi_OIT(c_Lambda_Osubst(C,D,E))| -c_Type_Otyping(F,D,A)| -c_InductTermi_OIT(D)| -c_Type_Otyping(c_Type_Oshift(F,E,A,tc_Type_Otype),C,G)| -c_InductTermi_OIT(C).
% 51.54/51.67 ** KEPT (pick-wt=15): 238 [] hAPP(c_Type_Oshift(A,B,C,D),E)=hAPP(A,E)| -c_HOL_Oord__class_Oless(E,B,tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=20): 239 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=16): 240 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=16): 241 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=9): 242 [] -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).
% 51.54/51.67 ** KEPT (pick-wt=41): 244 [copy,243,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).
% 51.54/51.67 ** KEPT (pick-wt=18): 245 [] 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.
% 51.54/51.67 ** KEPT (pick-wt=18): 246 [] 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.
% 51.54/51.67 ** KEPT (pick-wt=13): 247 [] 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.
% 51.54/51.67 ** KEPT (pick-wt=9): 248 [] c_InductTermi_OIT(hAPP(hAPP(c_Lambda_OdB_OApp,A),c_Lambda_OdB_OVar(B)))| -c_InductTermi_OIT(A).
% 51.54/51.67 ** KEPT (pick-wt=16): 249 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=11): 250 [] c_Lambda_Olift(c_Lambda_OdB_OVar(A),B)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=22): 251 [] c_Type_Otyping(A,B,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(C,A,B,D),C,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,B,D,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 51.54/51.67 ** KEPT (pick-wt=22): 252 [] 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)).
% 51.54/51.67 ** KEPT (pick-wt=22): 253 [] c_Type_Otyping(A,B,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(C,A,B,D),C,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,B,D,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 51.54/51.67 ** KEPT (pick-wt=19): 254 [] -c_Type_Otyping(A,B,C)| -c_Type_Otyping(c_Type_Oshift(A,D,C,tc_Type_Otype),E,F)|c_Type_Otyping(A,c_Lambda_Osubst(E,B,D),F).
% 51.54/51.67 ** KEPT (pick-wt=24): 255 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=23): 256 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=20): 257 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=18): 258 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=14): 259 [] c_Type_Otyping(c_Type_Oshift(A,B,C,tc_Type_Otype),c_Lambda_Olift(D,B),E)| -c_Type_Otyping(A,D,E).
% 51.54/51.67 ** KEPT (pick-wt=8): 260 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OVar(B)|A=B.
% 51.54/51.67 ** KEPT (pick-wt=14): 261 [] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=hAPP(hAPP(c_Type_Otype_OFun,C),D)|A=C.
% 51.54/51.67 ** KEPT (pick-wt=14): 262 [] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=hAPP(hAPP(c_Type_Otype_OFun,C),D)|B=D.
% 51.54/51.67 ** KEPT (pick-wt=20): 263 [] 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)).
% 51.54/51.67 ** KEPT (pick-wt=14): 264 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|A=C.
% 51.54/51.67 ** KEPT (pick-wt=14): 265 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|B=D.
% 51.54/51.67 ** KEPT (pick-wt=8): 266 [] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 51.54/51.67 ** KEPT (pick-wt=10): 267 [] hAPP(A,B)=C| -c_Type_Otyping(A,c_Lambda_OdB_OVar(B),C).
% 51.54/51.67 ** KEPT (pick-wt=8): 268 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 51.54/51.67 ** KEPT (pick-wt=23): 269 [] -c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)).
% 51.54/51.67 ** KEPT (pick-wt=6): 270 [] class_Orderings_Opreorder(tc_fun(A,B))| -class_Orderings_Opreorder(B).
% 51.54/51.67 ** KEPT (pick-wt=6): 271 [] class_Orderings_Oorder(tc_fun(A,B))| -class_Orderings_Oorder(B).
% 51.54/51.67 ** KEPT (pick-wt=7): 272 [] A=B| -c_fe_qual(A,B,C).
% 51.54/51.67 Following clause subsumed by 155 during input processing: 0 [copy,7,flip.1] c_List_Olist_ONil(A)!=c_List_Olist_OCons(B,C,A).
% 51.54/51.67 133 back subsumes 127.
% 51.54/51.67 Following clause subsumed by 7 during input processing: 0 [copy,155,flip.1] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 51.54/51.67 Following clause subsumed by 203 during input processing: 0 [copy,202,flip.1] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 51.54/51.67 Following clause subsumed by 202 during input processing: 0 [copy,203,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 51.54/51.67 ** KEPT (pick-wt=15): 288 [copy,208,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).
% 51.54/51.67 ** 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).
% 51.54/51.67 Following clause subsumed by 221 during input processing: 0 [copy,218,flip.1] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 51.54/51.67 Following clause subsumed by 218 during input processing: 0 [copy,221,flip.1] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 51.54/51.67 Following clause subsumed by 231 during input processing: 0 [copy,225,flip.1] c_Type_Otype_OAtom(A)!=hAPP(hAPP(c_Type_Otype_OFun,B),C).
% 51.54/51.67 Following clause subsumed by 225 during input processing: 0 [copy,231,flip.1] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=c_Type_Otype_OAtom(C).
% 51.54/51.67 Following clause subsumed by 268 during input processing: 0 [copy,266,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 51.54/51.67 Following clause subsumed by 266 during input processing: 0 [copy,268,flip.1] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 51.54/51.67 Following clause subsumed by 208 during input processing: 0 [copy,288,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).
% 51.54/51.67 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).
% 51.54/51.67
% 51.54/51.67 ------------> process sos:
% 51.54/51.67 ** KEPT (pick-wt=3): 293 [] A=A.
% 51.54/51.67 ** KEPT (pick-wt=15): 294 [] c_List_Olist_OCons(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 51.54/51.67 ---> New Demodulator: 295 [new_demod,294] c_List_Olist_OCons(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,295] c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,295] c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C)=c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C).
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,295] c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C)=c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C).
% 51.54/51.67 ** KEPT (pick-wt=11): 297 [copy,296,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OAbs(A).
% 51.54/51.67 ---> New Demodulator: 298 [new_demod,297] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OAbs(A).
% 51.54/51.67 ** KEPT (pick-wt=25): 300 [copy,299,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(B,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),tc_Lambda_OdB).
% 51.54/51.67 ---> New Demodulator: 301 [new_demod,300] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(B,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),tc_Lambda_OdB).
% 51.54/51.67 ** KEPT (pick-wt=6): 302 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat).
% 51.54/51.67 Following clause subsumed by 302 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=15): 303 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)).
% 51.54/51.67 ** KEPT (pick-wt=20): 304 [] c_List_Ofoldl(A,B,c_List_Olist_OCons(C,D,E),F,E)=c_List_Ofoldl(A,hAPP(hAPP(A,B),C),D,F,E).
% 51.54/51.67 ** KEPT (pick-wt=13): 306 [copy,305,flip.1] 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)).
% 51.54/51.67 ---> New Demodulator: 307 [new_demod,306] 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)).
% 51.54/51.67 ** KEPT (pick-wt=7): 309 [copy,308,unit_del,140] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,A)=B.
% 51.54/51.67 ---> New Demodulator: 310 [new_demod,309] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,A)=B.
% 51.54/51.67 ** KEPT (pick-wt=13): 311 [] c_List_Oreplicate(c_Suc(A),B,C)=c_List_Olist_OCons(B,c_List_Oreplicate(A,B,C),C).
% 51.54/51.67 ---> New Demodulator: 312 [new_demod,311] c_List_Oreplicate(c_Suc(A),B,C)=c_List_Olist_OCons(B,c_List_Oreplicate(A,B,C),C).
% 51.54/51.67 ** KEPT (pick-wt=23): 313 [] 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)).
% 51.54/51.67 ---> New Demodulator: 314 [new_demod,313] 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)).
% 51.54/51.67 ** KEPT (pick-wt=23): 315 [] 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)).
% 51.54/51.67 ** KEPT (pick-wt=13): 316 [] c_Lambda_Osubstn(A,B,C)=c_Lambda_Osubst(A,c_Lambda_Oliftn(C,B,c_HOL_Ozero__class_Ozero(tc_nat)),C).
% 51.54/51.67 ** KEPT (pick-wt=15): 317 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=12): 319 [copy,318,flip.1] c_Suc(c_Orderings_Oord__class_Omax(A,B,tc_nat))=c_Orderings_Oord__class_Omax(c_Suc(A),c_Suc(B),tc_nat).
% 51.54/51.67 ---> New Demodulator: 320 [new_demod,319] c_Suc(c_Orderings_Oord__class_Omax(A,B,tc_nat))=c_Orderings_Oord__class_Omax(c_Suc(A),c_Suc(B),tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=11): 321 [] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(C,D).
% 51.54/51.67 ** KEPT (pick-wt=13): 322 [] 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)).
% 51.54/51.67 ---> New Demodulator: 323 [new_demod,322] 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)).
% 51.54/51.67 ** KEPT (pick-wt=15): 325 [copy,324,flip.1] c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)).
% 51.54/51.67 ---> New Demodulator: 326 [new_demod,325] c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)).
% 51.54/51.67 Following clause subsumed by 303 during input processing: 0 [demod,326] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)).
% 51.54/51.67 ** KEPT (pick-wt=10): 328 [copy,327,demod,326] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)),tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=10): 330 [copy,329,demod,326] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_Suc(A)),tc_nat).
% 51.54/51.67 Following clause subsumed by 328 during input processing: 0 [demod,326] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)),tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=7): 331 [] c_List_Oappend(A,c_List_Olist_ONil(B),B)=A.
% 51.54/51.67 ---> New Demodulator: 332 [new_demod,331] c_List_Oappend(A,c_List_Olist_ONil(B),B)=A.
% 51.54/51.67 ** KEPT (pick-wt=7): 334 [copy,333,flip.1] c_List_Oappend(c_List_Olist_ONil(A),B,A)=B.
% 51.54/51.67 ---> New Demodulator: 335 [new_demod,334] c_List_Oappend(c_List_Olist_ONil(A),B,A)=B.
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,332] A=A.
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,335] B=B.
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,335] A=A.
% 51.54/51.67 ** KEPT (pick-wt=13): 336 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 51.54/51.67 ** KEPT (pick-wt=12): 337 [] c_Lambda_Oliftn(c_Suc(A),B,C)=c_Lambda_Olift(c_Lambda_Oliftn(A,B,C),C).
% 51.54/51.67 ** KEPT (pick-wt=3): 338 [] v_n____=v_i____.
% 51.54/51.67 ---> New Demodulator: 339 [new_demod,338] v_n____=v_i____.
% 51.54/51.67 Following clause subsumed by 302 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=9): 340 [] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 51.54/51.67 ---> New Demodulator: 341 [new_demod,340] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 51.54/51.67 ** KEPT (pick-wt=15): 342 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=15): 343 [] 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_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 51.54/51.67 ** KEPT (pick-wt=8): 344 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Olist_ONil(B).
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,341] c_Lambda_OdB_OAbs(A)=c_Lambda_OdB_OAbs(A).
% 51.54/51.67 ** KEPT (pick-wt=11): 346 [copy,345,unit_del,140] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 51.54/51.67 ---> New Demodulator: 347 [new_demod,346] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 51.54/51.67 ** KEPT (pick-wt=5): 349 [copy,348,unit_del,140] c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=9): 350 [] c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,335] c_List_Olist_OCons(A,B,C)=c_List_Olist_OCons(A,B,C).
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,332] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 51.54/51.67 ** KEPT (pick-wt=19): 351 [] c_List_Oappend(c_List_Oreplicate(A,B,C),c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C)=c_List_Olist_OCons(B,c_List_Oreplicate(A,B,C),C).
% 51.54/51.67 ** KEPT (pick-wt=21): 352 [] c_List_Ofoldl(A,B,c_List_Oappend(C,D,E),F,E)=c_List_Ofoldl(A,c_List_Ofoldl(A,B,C,F,E),D,F,E).
% 51.54/51.67 ** KEPT (pick-wt=10): 353 [] c_Type_Otype_Otype__case(A,B,c_Type_Otype_OAtom(C),D)=hAPP(A,C).
% 51.54/51.67 ** KEPT (pick-wt=7): 354 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 51.54/51.67 ---> New Demodulator: 355 [new_demod,354] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 51.54/51.67 ** KEPT (pick-wt=9): 356 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=11): 357 [] 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).
% 51.54/51.67 ---> New Demodulator: 358 [new_demod,357] 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).
% 51.54/51.67 ** KEPT (pick-wt=11): 359 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),C,B).
% 51.54/51.67 ** KEPT (pick-wt=7): 360 [] c_Orderings_Oord__class_Omax(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 51.54/51.67 ---> New Demodulator: 361 [new_demod,360] c_Orderings_Oord__class_Omax(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 51.54/51.67 ** KEPT (pick-wt=10): 362 [] c_Type_Otype_Otype__rec(A,B,c_Type_Otype_OAtom(C),D)=hAPP(A,C).
% 51.54/51.67 ** KEPT (pick-wt=8): 363 [] c_List_Olist_ONil(A)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),B,A).
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,323] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 51.54/51.67 ** KEPT (pick-wt=17): 364 [] 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).
% 51.54/51.67 ** KEPT (pick-wt=12): 365 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B),c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat))).
% 51.54/51.67 ** KEPT (pick-wt=11): 366 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 51.54/51.67 Following clause subsumed by 366 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).
% 51.54/51.67 Following clause subsumed by 366 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 51.54/51.67 ** KEPT (pick-wt=21): 367 [] c_List_Oappend(c_List_Oreplicate(A,B,C),c_List_Oreplicate(D,B,C),C)=c_List_Oappend(c_List_Oreplicate(D,B,C),c_List_Oreplicate(A,B,C),C).
% 51.54/51.67 Following clause subsumed by 349 during input processing: 0 [] c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 51.54/51.67 Following clause subsumed by 349 during input processing: 0 [] c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 51.54/51.67 ** KEPT (pick-wt=20): 368 [] c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,D)=c_List_Oappend(c_List_Oreplicate(A,C,D),c_List_Oreplicate(B,C,D),D).
% 51.54/51.67 ---> New Demodulator: 369 [new_demod,368] c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,D)=c_List_Oappend(c_List_Oreplicate(A,C,D),c_List_Oreplicate(B,C,D),D).
% 51.54/51.67 ** KEPT (pick-wt=18): 370 [] c_Lambda_OdB_OdB__rec(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(hAPP(C,D),c_Lambda_OdB_OdB__rec(A,B,C,D,E)).
% 51.54/51.67 ** KEPT (pick-wt=11): 371 [] c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 51.54/51.67 ---> New Demodulator: 372 [new_demod,371] c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,335] c_List_Olist_OCons(B,C,A)=c_List_Olist_OCons(B,C,A).
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,307] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 51.54/51.67 ** KEPT (pick-wt=21): 374 [copy,373,demod,295] c_List_Oappend(c_List_Oreplicate(A,B,C),c_List_Olist_OCons(B,D,C),C)=c_List_Oappend(c_List_Olist_OCons(B,c_List_Oreplicate(A,B,C),C),D,C).
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,341] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)=hAPP(hAPP(c_Lambda_OdB_OApp,A),B).
% 51.54/51.67 ** KEPT (pick-wt=22): 376 [copy,375,demod,314] c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(B)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))).
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,332] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 51.54/51.67 ** KEPT (pick-wt=13): 377 [] 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_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 51.54/51.67 ** KEPT (pick-wt=15): 378 [] c_List_Oappend(c_List_Oappend(A,B,C),D,C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 51.54/51.67 ---> New Demodulator: 379 [new_demod,378] c_List_Oappend(c_List_Oappend(A,B,C),D,C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,379] c_List_Oappend(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(A,c_List_Oappend(B,C,D),D).
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,379] c_List_Oappend(A,c_List_Oappend(B,D,C),C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,379] c_List_Oappend(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(A,c_List_Oappend(B,C,D),D).
% 51.54/51.67 ** KEPT (pick-wt=7): 380 [] c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=A.
% 51.54/51.67 ---> New Demodulator: 381 [new_demod,380] c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=A.
% 51.54/51.67 ** KEPT (pick-wt=9): 383 [copy,382,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 51.54/51.67 ---> New Demodulator: 384 [new_demod,383] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 51.54/51.67 ** KEPT (pick-wt=9): 385 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 51.54/51.67 ---> New Demodulator: 386 [new_demod,385] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,384] A=A.
% 51.54/51.67 ** KEPT (pick-wt=20): 388 [copy,387,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(A,B,C)),c_Lambda_Osubst(D,B,C))=c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,A),D),B,C).
% 51.54/51.67 ---> New Demodulator: 389 [new_demod,388] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(A,B,C)),c_Lambda_Osubst(D,B,C))=c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,A),D),B,C).
% 51.54/51.67 ** KEPT (pick-wt=16): 390 [] c_Lambda_OdB_OdB__case(A,B,C,hAPP(hAPP(c_Lambda_OdB_OApp,D),E),F)=hAPP(hAPP(B,D),E).
% 51.54/51.67 ** KEPT (pick-wt=30): 392 [copy,391,flip.1] hAPP(hAPP(hAPP(hAPP(A,B),C),c_Lambda_OdB_OdB__rec(D,A,E,B,F)),c_Lambda_OdB_OdB__rec(D,A,E,C,F))=c_Lambda_OdB_OdB__rec(D,A,E,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),F).
% 51.54/51.67 ---> New Demodulator: 393 [new_demod,392] hAPP(hAPP(hAPP(hAPP(A,B),C),c_Lambda_OdB_OdB__rec(D,A,E,B,F)),c_Lambda_OdB_OdB__rec(D,A,E,C,F))=c_Lambda_OdB_OdB__rec(D,A,E,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),F).
% 51.54/51.67 ** KEPT (pick-wt=20): 395 [copy,394,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).
% 51.54/51.67 ---> New Demodulator: 396 [new_demod,395] 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).
% 51.54/51.67 ** KEPT (pick-wt=20): 398 [copy,397,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).
% 51.54/51.67 ---> New Demodulator: 399 [new_demod,398] 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).
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,341] c_Lambda_OdB_OVar(A)=c_Lambda_OdB_OVar(A).
% 51.54/51.67 Following clause subsumed by 293 during input processing: 0 [demod,310] B=B.
% 51.54/51.67 ** KEPT (pick-wt=11): 400 [] c_Lambda_OdB_OdB__rec(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 51.54/51.67 ** KEPT (pick-wt=3): 401 [] c_InductTermi_OIT(c_Lambda_OdB_OVar(A)).
% 51.54/51.67 ** KEPT (pick-wt=11): 402 [] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 51.54/51.67 ** KEPT (pick-wt=8): 403 [] c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____).
% 51.54/51.67 ** KEPT (pick-wt=27): 405 [copy,404,flip.1] hAPP(hAPP(hAPP(hAPP(A,B),C),c_Type_Otype_Otype__rec(D,A,B,E)),c_Type_Otype_Otype__rec(D,A,C,E))=c_Type_Otype_Otype__rec(D,A,hAPP(hAPP(c_Type_Otype_OFun,B),C),E).
% 51.54/51.67 ---> New Demodulator: 406 [new_demod,405] hAPP(hAPP(hAPP(hAPP(A,B),C),c_Type_Otype_Otype__rec(D,A,B,E)),c_Type_Otype_Otype__rec(D,A,C,E))=c_Type_Otype_Otype__rec(D,A,hAPP(hAPP(c_Type_Otype_OFun,B),C),E).
% 51.54/51.68 ** KEPT (pick-wt=15): 407 [] c_Type_Otype_Otype__case(A,B,hAPP(hAPP(c_Type_Otype_OFun,C),D),E)=hAPP(hAPP(B,C),D).
% 51.54/51.68 ** KEPT (pick-wt=20): 409 [copy,408,flip.1] hAPP(hAPP(A,B),c_List_Ofoldr(A,C,D,E,F))=c_List_Ofoldr(A,c_List_Olist_OCons(B,C,E),D,E,F).
% 51.54/51.68 ---> New Demodulator: 410 [new_demod,409] hAPP(hAPP(A,B),c_List_Ofoldr(A,C,D,E,F))=c_List_Ofoldr(A,c_List_Olist_OCons(B,C,E),D,E,F).
% 51.54/51.68 ** KEPT (pick-wt=21): 411 [] c_List_Ofoldr(A,c_List_Oappend(B,C,D),E,D,F)=c_List_Ofoldr(A,B,c_List_Ofoldr(A,C,E,D,F),D,F).
% 51.54/51.68 ---> New Demodulator: 412 [new_demod,411] c_List_Ofoldr(A,c_List_Oappend(B,C,D),E,D,F)=c_List_Ofoldr(A,B,c_List_Ofoldr(A,C,E,D,F),D,F).
% 51.54/51.68 ** KEPT (pick-wt=9): 413 [] c_List_Ofoldr(A,c_List_Olist_ONil(B),C,B,D)=C.
% 51.54/51.68 ---> New Demodulator: 414 [new_demod,413] c_List_Ofoldr(A,c_List_Olist_ONil(B),C,B,D)=C.
% 51.54/51.68 ** KEPT (pick-wt=8): 415 [] c_Lambda_Osubst(c_Lambda_Olift(A,B),C,B)=A.
% 51.54/51.68 ---> New Demodulator: 416 [new_demod,415] c_Lambda_Osubst(c_Lambda_Olift(A,B),C,B)=A.
% 51.54/51.68 ** KEPT (pick-wt=14): 418 [copy,417,demod,339] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____).
% 51.54/51.68 ** KEPT (pick-wt=2): 419 [] c_InductTermi_OIT(v_u____).
% 51.54/51.68 ** KEPT (pick-wt=8): 420 [] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____).
% 51.54/51.68 ** KEPT (pick-wt=7): 421 [] c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(A),tc_Lambda_OdB)=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.68 ---> New Demodulator: 422 [new_demod,421] c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(A),tc_Lambda_OdB)=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=6): 423 [] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(A))=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.68 ---> New Demodulator: 424 [new_demod,423] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(A))=c_HOL_Ozero__class_Ozero(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=22): 425 [] 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),c_Suc(B),C,D).
% 51.54/51.68 ** KEPT (pick-wt=18): 427 [copy,426,demod,339] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)).
% 51.54/51.68 ** KEPT (pick-wt=17): 429 [copy,428,demod,339,410] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype)).
% 51.54/51.68 ** KEPT (pick-wt=4): 430 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 51.54/51.68 ** KEPT (pick-wt=11): 432 [copy,431,demod,410,flip.1] c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype)=v_T____.
% 51.54/51.68 ---> New Demodulator: 433 [new_demod,432] c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype)=v_T____.
% 51.54/51.68 Following clause subsumed by 430 during input processing: 0 [demod,410,433] c_Type_Otyping(v_e____,v_u____,v_T____).
% 51.54/51.68 ** KEPT (pick-wt=9): 434 [] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 51.54/51.68 ---> New Demodulator: 435 [new_demod,434] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 51.54/51.68 ** KEPT (pick-wt=17): 437 [copy,436,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(A,B)),c_Lambda_Olift(C,B))=c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,A),C),B).
% 51.54/51.68 ---> New Demodulator: 438 [new_demod,437] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(A,B)),c_Lambda_Olift(C,B))=c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,A),C),B).
% 51.54/51.68 ** KEPT (pick-wt=7): 439 [] c_Type_Otyping(A,c_Lambda_OdB_OVar(B),hAPP(A,B)).
% 51.54/51.68 ** KEPT (pick-wt=2): 440 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 441 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 442 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 443 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 444 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 445 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 446 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 447 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 448 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 449 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 450 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 451 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 452 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 453 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 454 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 455 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 456 [] class_Nat_Osemiring__char__0(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 457 [] class_Orderings_Opreorder(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 458 [] class_Orderings_Olinorder(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 459 [] class_Orderings_Oorder(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=2): 460 [] class_Power_Opower(tc_nat).
% 51.54/51.68 ** KEPT (pick-wt=4): 461 [] c_fe_qual(A,A,B).
% 51.54/51.68 Following clause subsumed by 293 during input processing: 0 [copy,293,flip.1] A=A.
% 51.54/51.68 293 back subsumes 292.
% 51.54/51.68 293 back subsumes 281.
% 51.54/51.68 293 back subsumes 280.
% 51.54/51.68 >>>> Starting back demodulation with 295.
% 51.54/51.68 >>>> Starting back demodulation with 298.
% 51.54/51.68 >>>> Starting back demodulation with 301.
% 51.54/51.68 ** KEPT (pick-wt=15): 462 [copy,303,flip.1] 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).
% 51.54/51.68 ** KEPT (pick-wt=20): 463 [copy,304,flip.1] c_List_Ofoldl(A,hAPP(hAPP(A,B),C),D,E,F)=c_List_Ofoldl(A,B,c_List_Olist_OCons(C,D,F),E,F).
% 51.54/51.68 >>>> Starting back demodulation with 307.
% 51.54/51.68 >>>> Starting back demodulation with 310.
% 51.54/51.68 >>>> Starting back demodulation with 312.
% 51.54/51.68 >>>> Starting back demodulation with 314.
% 51.54/51.68 >> back demodulating 300 with 314.
% 51.54/51.68 Following clause subsumed by 315 during input processing: 0 [copy,315,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)).
% 51.54/51.68 ** KEPT (pick-wt=13): 466 [copy,316,flip.1] c_Lambda_Osubst(A,c_Lambda_Oliftn(B,C,c_HOL_Ozero__class_Ozero(tc_nat)),B)=c_Lambda_Osubstn(A,C,B).
% 51.54/51.68 >>>> Starting back demodulation with 320.
% 51.54/51.68 ** KEPT (pick-wt=11): 467 [copy,321,flip.1] hAPP(A,B)=c_Lambda_OdB_OdB__case(C,D,A,c_Lambda_OdB_OAbs(B),E).
% 51.54/51.68 >>>> Starting back demodulation with 323.
% 51.54/51.68 >>>> Starting back demodulation with 326.
% 51.54/51.68 >>>> Starting back demodulation with 332.
% 51.54/51.68 >>>> Starting back demodulation with 335.
% 51.54/51.68 Following clause subsumed by 336 during input processing: 0 [copy,336,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 51.54/51.68 ** KEPT (pick-wt=12): 468 [copy,337,flip.1] c_Lambda_Olift(c_Lambda_Oliftn(A,B,C),C)=c_Lambda_Oliftn(c_Suc(A),B,C).
% 51.54/51.68 >>>> Starting back demodulation with 339.
% 51.54/51.68 >>>> Starting back demodulation with 341.
% 51.54/51.68 >> back demodulating 297 with 341.
% 51.54/51.68 >> back demodulating 159 with 341.
% 51.54/51.68 ** KEPT (pick-wt=15): 469 [copy,343,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(A),tc_Lambda_OdB).
% 51.54/51.68 Following clause subsumed by 363 during input processing: 0 [copy,344,flip.1] c_List_Olist_ONil(A)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),B,A).
% 51.54/51.68 >>>> Starting back demodulation with 347.
% 51.54/51.68 ** KEPT (pick-wt=19): 470 [copy,351,flip.1] c_List_Olist_OCons(A,c_List_Oreplicate(B,A,C),C)=c_List_Oappend(c_List_Oreplicate(B,A,C),c_List_Olist_OCons(A,c_List_Olist_ONil(C),C),C).
% 51.54/51.68 ** KEPT (pick-wt=21): 471 [copy,352,flip.1] c_List_Ofoldl(A,c_List_Ofoldl(A,B,C,D,E),F,D,E)=c_List_Ofoldl(A,B,c_List_Oappend(C,F,E),D,E).
% 51.54/51.68 ** KEPT (pick-wt=10): 472 [copy,353,flip.1] hAPP(A,B)=c_Type_Otype_Otype__case(A,C,c_Type_Otype_OAtom(B),D).
% 51.54/51.68 >>>> Starting back demodulation with 355.
% 51.54/51.68 >>>> Starting back demodulation with 358.
% 51.54/51.68 Following clause subsumed by 359 during input processing: 0 [copy,359,flip.1] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),C,B).
% 51.54/51.68 >>>> Starting back demodulation with 361.
% 51.54/51.68 ** KEPT (pick-wt=10): 473 [copy,362,flip.1] hAPP(A,B)=c_Type_Otype_Otype__rec(A,C,c_Type_Otype_OAtom(B),D).
% 51.54/51.68 Following clause subsumed by 344 during input processing: 0 [copy,363,flip.1] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Olist_ONil(B).
% 51.54/51.68 Following clause subsumed by 367 during input processing: 0 [copy,367,flip.1] c_List_Oappend(c_List_Oreplicate(A,B,C),c_List_Oreplicate(D,B,C),C)=c_List_Oappend(c_List_Oreplicate(D,B,C),c_List_Oreplicate(A,B,C),C).
% 51.54/51.68 >>>> Starting back demodulation with 369.
% 51.54/51.68 ** KEPT (pick-wt=18): 474 [copy,370,flip.1] hAPP(hAPP(A,B),c_Lambda_OdB_OdB__rec(C,D,A,B,E))=c_Lambda_OdB_OdB__rec(C,D,A,c_Lambda_OdB_OAbs(B),E).
% 51.54/51.68 >>>> Starting back demodulation with 372.
% 51.54/51.68 ** KEPT (pick-wt=21): 475 [copy,374,flip.1] c_List_Oappend(c_List_Olist_OCons(A,c_List_Oreplicate(B,A,C),C),D,C)=c_List_Oappend(c_List_Oreplicate(B,A,C),c_List_Olist_OCons(A,D,C),C).
% 51.54/51.68 ** KEPT (pick-wt=22): 476 [copy,376,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(B)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))=c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,A),B)).
% 51.54/51.68 ** KEPT (pick-wt=13): 477 [copy,377,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(A)).
% 51.54/51.68 >>>> Starting back demodulation with 379.
% 51.54/51.68 >>>> Starting back demodulation with 381.
% 51.54/51.68 >>>> Starting back demodulation with 384.
% 51.54/51.68 >> back demodulating 357 with 384.
% 51.54/51.68 >> back demodulating 322 with 384.
% 51.54/51.68 >>>> Starting back demodulation with 386.
% 51.54/51.68 >> back demodulating 306 with 386.
% 51.54/51.68 >>>> Starting back demodulation with 389.
% 51.54/51.68 ** KEPT (pick-wt=16): 478 [copy,390,flip.1] hAPP(hAPP(A,B),C)=c_Lambda_OdB_OdB__case(D,A,E,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),F).
% 51.54/51.68 >>>> Starting back demodulation with 393.
% 51.54/51.68 >>>> Starting back demodulation with 396.
% 51.54/51.68 >>>> Starting back demodulation with 399.
% 51.54/51.68 ** KEPT (pick-wt=11): 479 [copy,400,flip.1] hAPP(A,B)=c_Lambda_OdB_OdB__rec(A,C,D,c_Lambda_OdB_OVar(B),E).
% 51.54/51.68 ** KEPT (pick-wt=11): 480 [copy,402,flip.1] hAPP(A,B)=c_Lambda_OdB_OdB__case(A,C,D,c_Lambda_OdB_OVar(B),E).
% 51.54/51.68 >>>> Starting back demodulation with 406.
% 51.54/51.68 ** KEPT (pick-wt=15): 481 [copy,407,flip.1] hAPP(hAPP(A,B),C)=c_Type_Otype_Otype__case(D,A,hAPP(hAPP(c_Type_Otype_OFun,B),C),E).
% 51.54/51.68 >>>> Starting back demodulation with 410.
% 51.54/51.68 >> back demodulating 215 with 410.
% 51.54/51.68 >>>> Starting back demodulation with 412.
% 51.54/51.68 >>>> Starting back demodulation with 414.
% 51.54/51.68 >>>> Starting back demodulation with 416.
% 51.54/51.68 >>>> Starting back demodulation with 422.
% 51.54/51.68 >>>> Starting back demodulation with 424.
% 51.54/51.68 ** KEPT (pick-wt=22): 483 [copy,425,flip.1] c_Type_Oshift(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),B,C),c_Suc(D),E,C)=c_Type_Oshift(c_Type_Oshift(A,D,E,C),c_HOL_Ozero__class_Ozero(tc_nat),B,C).
% 51.54/51.68 >>>> Starting back demodulation with 433.
% 51.54/51.68 >> back demodulating 429 with 433.
% 51.54/51.68 >>>> Starting back demodulation with 435.
% 51.54/51.68 >>>> Starting back demodulation with 438.
% 51.54/51.68 Following clause subsumed by 303 during input processing: 0 [copy,462,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)).
% 51.54/51.68 Following clause subsumed by 304 during input processing: 0 [copy,463,flip.1] c_List_Ofoldl(A,B,c_List_Olist_OCons(C,D,E),F,E)=c_List_Ofoldl(A,hAPP(hAPP(A,B),C),D,F,E).
% 51.54/51.68 >>>> Starting back demodulation with 465.
% 51.54/51.68 Following clause subsumed by 316 during input processing: 0 [copy,466,flip.1] c_Lambda_Osubstn(A,B,C)=c_Lambda_Osubst(A,c_Lambda_Oliftn(C,B,c_HOL_Ozero__class_Ozero(tc_nat)),C).
% 51.54/51.68 Following clause subsumed by 321 during input processing: 0 [copy,467,flip.1] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(C,D).
% 51.54/51.68 Following clause subsumed by 337 during input processing: 0 [copy,468,flip.1] c_Lambda_Oliftn(c_Suc(A),B,C)=c_Lambda_Olift(c_Lambda_Oliftn(A,B,C),C).
% 51.84/51.99 Following clause subsumed by 343 during input processing: 0 [copy,469,flip.1] 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_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 51.84/51.99 Following clause subsumed by 351 during input processing: 0 [copy,470,flip.1] c_List_Oappend(c_List_Oreplicate(A,B,C),c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C)=c_List_Olist_OCons(B,c_List_Oreplicate(A,B,C),C).
% 51.84/51.99 Following clause subsumed by 352 during input processing: 0 [copy,471,flip.1] c_List_Ofoldl(A,B,c_List_Oappend(C,D,E),F,E)=c_List_Ofoldl(A,c_List_Ofoldl(A,B,C,F,E),D,F,E).
% 51.84/51.99 Following clause subsumed by 353 during input processing: 0 [copy,472,flip.1] c_Type_Otype_Otype__case(A,B,c_Type_Otype_OAtom(C),D)=hAPP(A,C).
% 51.84/51.99 Following clause subsumed by 362 during input processing: 0 [copy,473,flip.1] c_Type_Otype_Otype__rec(A,B,c_Type_Otype_OAtom(C),D)=hAPP(A,C).
% 51.84/51.99 Following clause subsumed by 370 during input processing: 0 [copy,474,flip.1] c_Lambda_OdB_OdB__rec(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(hAPP(C,D),c_Lambda_OdB_OdB__rec(A,B,C,D,E)).
% 51.84/51.99 Following clause subsumed by 374 during input processing: 0 [copy,475,flip.1] c_List_Oappend(c_List_Oreplicate(A,B,C),c_List_Olist_OCons(B,D,C),C)=c_List_Oappend(c_List_Olist_OCons(B,c_List_Oreplicate(A,B,C),C),D,C).
% 51.84/51.99 Following clause subsumed by 376 during input processing: 0 [copy,476,flip.1] c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(B)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))).
% 51.84/51.99 Following clause subsumed by 377 during input processing: 0 [copy,477,flip.1] 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_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 51.84/51.99 Following clause subsumed by 390 during input processing: 0 [copy,478,flip.1] c_Lambda_OdB_OdB__case(A,B,C,hAPP(hAPP(c_Lambda_OdB_OApp,D),E),F)=hAPP(hAPP(B,D),E).
% 51.84/51.99 Following clause subsumed by 400 during input processing: 0 [copy,479,flip.1] c_Lambda_OdB_OdB__rec(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 51.84/51.99 Following clause subsumed by 402 during input processing: 0 [copy,480,flip.1] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 51.84/51.99 Following clause subsumed by 407 during input processing: 0 [copy,481,flip.1] c_Type_Otype_Otype__case(A,B,hAPP(hAPP(c_Type_Otype_OFun,C),D),E)=hAPP(hAPP(B,C),D).
% 51.84/51.99 Following clause subsumed by 425 during input processing: 0 [copy,483,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),c_Suc(B),C,D).
% 51.84/51.99
% 51.84/51.99 ======= end of input processing =======
% 51.84/51.99
% 51.84/51.99 =========== start of search ===========
% 51.84/51.99
% 51.84/51.99
% 51.84/51.99 Resetting weight limit to 2.
% 51.84/51.99
% 51.84/51.99
% 51.84/51.99 Resetting weight limit to 2.
% 51.84/51.99
% 51.84/51.99 sos_size=121
% 51.84/51.99
% 51.84/51.99 Search stopped because sos empty.
% 51.84/51.99
% 51.84/51.99
% 51.84/51.99 Search stopped because sos empty.
% 51.84/51.99
% 51.84/51.99 ============ end of search ============
% 51.84/51.99
% 51.84/51.99 -------------- statistics -------------
% 51.84/51.99 clauses given 122
% 51.84/51.99 clauses generated 47487
% 51.84/51.99 clauses kept 403
% 51.84/51.99 clauses forward subsumed 122
% 51.84/51.99 clauses back subsumed 4
% 51.84/51.99 Kbytes malloced 8789
% 51.84/51.99
% 51.84/51.99 ----------- times (seconds) -----------
% 51.84/51.99 user CPU time 0.33 (0 hr, 0 min, 0 sec)
% 51.84/51.99 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 51.84/51.99 wall-clock time 51 (0 hr, 0 min, 51 sec)
% 51.84/51.99
% 51.84/51.99 Process 8417 finished Wed Jul 27 09:22:59 2022
% 51.84/51.99 Otter interrupted
% 51.84/51.99 PROOF NOT FOUND
%------------------------------------------------------------------------------