TSTP Solution File: LCL812-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL812-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 13:05:30 EDT 2022
% Result : Unknown 181.29s 181.39s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL812-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jul 27 09:23:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 180.18/180.26 ----- Otter 3.3f, August 2004 -----
% 180.18/180.26 The process was started by sandbox2 on n008.cluster.edu,
% 180.18/180.26 Wed Jul 27 09:23:53 2022
% 180.18/180.26 The command was "./otter". The process ID is 29114.
% 180.18/180.26
% 180.18/180.26 set(prolog_style_variables).
% 180.18/180.26 set(auto).
% 180.18/180.26 dependent: set(auto1).
% 180.18/180.26 dependent: set(process_input).
% 180.18/180.26 dependent: clear(print_kept).
% 180.18/180.26 dependent: clear(print_new_demod).
% 180.18/180.26 dependent: clear(print_back_demod).
% 180.18/180.26 dependent: clear(print_back_sub).
% 180.18/180.26 dependent: set(control_memory).
% 180.18/180.26 dependent: assign(max_mem, 12000).
% 180.18/180.26 dependent: assign(pick_given_ratio, 4).
% 180.18/180.26 dependent: assign(stats_level, 1).
% 180.18/180.26 dependent: assign(max_seconds, 10800).
% 180.18/180.26 clear(print_given).
% 180.18/180.26
% 180.18/180.26 list(usable).
% 180.18/180.26 0 [] A=A.
% 180.18/180.26 0 [] -class_Orderings_Olinorder(T_a)| -class_Int_Onumber(T_a)|c_lesse_quals(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)|c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a).
% 180.18/180.26 0 [] c_Type_Otype_OFun(V_type1,V_type2)!=c_Type_Otype_OFun(V_type1_H,V_type2_H)|V_type2=V_type2_H.
% 180.18/180.26 0 [] c_Type_Otype_OFun(V_type1,V_type2)!=c_Type_Otype_OFun(V_type1_H,V_type2_H)|V_type1=V_type1_H.
% 180.18/180.26 0 [] c_Suc(V_n)!=V_n.
% 180.18/180.26 0 [] V_n!=c_Suc(V_n).
% 180.18/180.26 0 [] -class_Orderings_Oorder(T_a)|c_lesse_quals(V_z,V_x,T_a)| -c_lesse_quals(V_z,V_y,T_a)| -c_lesse_quals(V_y,V_x,T_a).
% 180.18/180.26 0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_z,V_x,T_a)| -c_lesse_quals(V_z,V_y,T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 180.18/180.26 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_lesse_quals(V_y,V_x,T_a).
% 180.18/180.26 0 [] -class_Orderings_Opreorder(T_a)|c_lesse_quals(V_x,V_z,T_a)| -c_lesse_quals(V_y,V_z,T_a)| -c_lesse_quals(V_x,V_y,T_a).
% 180.18/180.26 0 [] -class_Orderings_Oorder(T_a)|c_lesse_quals(V_x,V_x,T_a).
% 180.18/180.26 0 [] -class_Orderings_Opreorder(T_a)|c_lesse_quals(V_x,V_x,T_a).
% 180.18/180.26 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_lesse_quals(V_x,V_y,T_a).
% 180.18/180.26 0 [] -class_Orderings_Opreorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_z,T_a)| -c_lesse_quals(V_y,V_z,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)| -c_lesse_quals(V_c,V_d,T_a)| -c_lesse_quals(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))=V_n| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_y,T_a)!=c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)|c_lesse_quals(V_y_H,V_x_H,T_a)| -c_lesse_quals(V_y,V_x,T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_y,T_a)!=c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)|c_lesse_quals(V_y,V_x,T_a)| -c_lesse_quals(V_y_H,V_x_H,T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_y,T_a)!=c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)|c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_y,T_a)!=c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)| -c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a).
% 180.18/180.26 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_n,c_Suc(V_i),tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 180.18/180.26 0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|V_a=V_b| -c_lesse_quals(V_b,V_a,T_a).
% 180.18/180.26 0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_lesse_quals(V_b,V_a,T_a)|V_a=V_b.
% 180.18/180.26 0 [] -class_Orderings_Oorder(T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_x,V_y,T_a)| -c_lesse_quals(V_x,V_y,T_a).
% 180.18/180.26 0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|V_x=V_y| -c_lesse_quals(V_x,V_y,T_a).
% 180.18/180.26 0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)|V_a=V_b| -c_lesse_quals(V_a,V_b,T_a).
% 180.18/180.26 0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_lesse_quals(V_a,V_b,T_a)|V_a=V_b.
% 180.18/180.26 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y| -c_lesse_quals(V_x,V_y,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 180.18/180.26 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_x,V_y,T_a)| -c_lesse_quals(V_x,V_y,T_a).
% 180.18/180.26 0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_y,V_x,T_a)|c_lesse_quals(V_x,V_y,T_a).
% 180.18/180.26 0 [] c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat))=V_n| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 180.18/180.26 0 [] V_n=c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 180.18/180.26 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)=c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),V_n))|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),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).
% 180.18/180.26 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)| -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_lesse_quals(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)| -c_lesse_quals(V_b,V_c,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)| -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_lesse_quals(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)| -c_lesse_quals(V_b,V_a,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)!=c_HOL_Ozero__class_Ozero(T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)!=c_HOL_Ozero__class_Ozero(T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 180.18/180.26 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_lesse_quals(V_c,V_d,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 180.18/180.26 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_lesse_quals(V_a,V_b,T_a).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)| -c_lesse_quals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),T_a).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 180.18/180.26 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat).
% 180.18/180.26 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 180.18/180.26 0 [] hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat)))| -c_HOL_Oord__class_Oless(V_a,V_b,tc_nat)| -hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(V_a,V_b,tc_nat))).
% 180.18/180.26 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat).
% 180.18/180.26 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 180.18/180.26 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 180.18/180.26 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).
% 180.18/180.26 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)).
% 180.18/180.26 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).
% 180.18/180.26 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)).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_HOL_Ominus__class_Ominus(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.18/180.26 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))).
% 180.18/180.26 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)).
% 180.18/180.26 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)).
% 180.18/180.26 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).
% 180.18/180.26 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)).
% 180.18/180.26 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)).
% 180.18/180.26 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)).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat)| -c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat).
% 180.18/180.26 0 [] c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat).
% 180.18/180.26 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat))=V_m|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_lesse_quals(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 180.18/180.26 0 [] c_HOL_Oone__class_Oone(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 180.18/180.26 0 [] c_List_Otake(c_Int_Onumber__class_Onumber__of(V_v,tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olist_OCons(V_x,c_List_Otake(c_HOL_Ominus__class_Ominus(c_Int_Onumber__class_Onumber__of(V_v,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_xs,T_a),T_a)|c_Int_Onumber__class_Onumber__of(V_v,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.18/180.26 0 [] c_Suc(V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Oone__class_Oone(tc_nat)).
% 180.18/180.26 0 [] c_Suc(V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),V_n).
% 180.18/180.26 0 [] c_List_Otake(c_Suc(V_n),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olist_OCons(V_x,c_List_Otake(V_n,V_xs,T_a),T_a).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_List_Olist__update(c_List_Olist_OCons(V_x,V_xs,T_a),c_Suc(V_i),V_y,T_a)=c_List_Olist_OCons(V_x,c_List_Olist__update(V_xs,V_i,V_y,T_a),T_a).
% 180.18/180.26 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,c_Type_Otype_OFun(V_T,V_U)).
% 180.18/180.26 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).
% 180.18/180.26 0 [] -class_Orderings_Olinorder(T_a)| -class_Int_Onumber(T_a)| -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a)| -c_lesse_quals(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),c_Power_Opower__class_Opower(V_b,c_Suc(V_n),T_a),T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add(T_a)|c_lesse_quals(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_lesse_quals(V_a,V_b,T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add(T_a)|c_lesse_quals(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_lesse_quals(V_a,V_b,T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(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).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_lesse_quals(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_lesse_quals(V_a,V_b,T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(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).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_lesse_quals(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_lesse_quals(V_a,V_b,T_a).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat).
% 180.18/180.26 0 [] c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat).
% 180.18/180.26 0 [] -class_Orderings_Opreorder(T_a)|c_lesse_quals(V_x,V_y,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 180.18/180.26 0 [] -class_Orderings_Oorder(T_a)|c_lesse_quals(V_x,V_y,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 180.18/180.26 0 [] -class_Orderings_Oorder(T_a)|V_x=V_y| -c_lesse_quals(V_x,V_y,T_a)| -c_lesse_quals(V_y,V_x,T_a).
% 180.18/180.26 0 [] -class_Orderings_Oorder(T_a)|V_x=V_y| -c_lesse_quals(V_y,V_x,T_a)| -c_lesse_quals(V_x,V_y,T_a).
% 180.18/180.26 0 [] -class_Orderings_Oorder(T_a)|V_x=V_y| -c_lesse_quals(V_y,V_x,T_a)| -c_lesse_quals(V_x,V_y,T_a).
% 180.18/180.26 0 [] -class_Orderings_Opreorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|c_lesse_quals(V_y,V_x,T_a)| -c_lesse_quals(V_x,V_y,T_a).
% 180.18/180.26 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_j,V_k,tc_nat).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat)=c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat).
% 180.18/180.26 0 [] c_Suc(V_nat)!=c_Suc(V_nat_H)|V_nat=V_nat_H.
% 180.18/180.26 0 [] c_Suc(V_x)!=c_Suc(V_y)|V_x=V_y.
% 180.18/180.26 0 [] c_Lambda_Oliftn(c_Suc(V_n),V_t,V_k)=hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(V_n,V_t,V_k)),V_k).
% 180.18/180.26 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_l,tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 180.18/180.26 0 [] c_HOL_Ominus__class_Ominus(c_Suc(V_n),c_HOL_Oone__class_Oone(tc_nat),tc_nat)=V_n.
% 180.18/180.26 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)).
% 180.18/180.26 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)).
% 180.18/180.26 0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ominus__class_Ominus(V_a,V_b,T_a)),V_b)=V_a.
% 180.18/180.26 0 [] -hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_b),V_x),V_b,tc_nat)))|hBOOL(hAPP(V_P,V_x)).
% 180.18/180.26 0 [] -hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_b),V_d),V_b,tc_nat)))|hBOOL(hAPP(V_P,V_d)).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add(T_a)|c_lesse_quals(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_lesse_quals(V_c,V_d,T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 180.18/180.26 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_Suc(V_m),tc_nat).
% 180.18/180.26 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|c_lesse_quals(V_y,V_x,T_a).
% 180.18/180.26 0 [] -class_Orderings_Olinorder(T_a)| -c_lesse_quals(V_x,V_x,T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 180.18/180.26 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_x,T_a)|c_lesse_quals(V_x,V_x,T_a).
% 180.18/180.26 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a)| -c_lesse_quals(V_y,V_x,T_a).
% 180.18/180.26 0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 180.18/180.26 0 [] -class_Orderings_Olinorder(T_a)| -c_lesse_quals(V_x,V_y,T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 180.18/180.26 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_lesse_quals(V_x,V_y,T_a).
% 180.18/180.26 0 [] -class_Orderings_Opreorder(T_a)| -c_lesse_quals(V_y,V_x,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 180.18/180.26 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat__aux(V_inc,c_Suc(V_n),V_i,T_a)=c_Nat_Osemiring__1__class_Oof__nat__aux(V_inc,V_n,hAPP(V_inc,V_i),T_a).
% 180.18/180.26 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat)=c_HOL_Ominus__class_Ominus(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k),tc_nat).
% 180.18/180.26 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a)!=c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)|V_xa=V_y.
% 180.18/180.26 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)!=c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)|V_x_H=V_y_H.
% 180.18/180.26 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)).
% 180.18/180.26 0 [] -class_Int_Oring__char__0(T_a)| -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(V_x,T_a)!=c_Int_Onumber__class_Onumber__of(V_y,T_a)|V_x=V_y.
% 180.18/180.26 0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k),tc_nat)=c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat).
% 180.18/180.26 0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat)=c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat).
% 180.18/180.26 0 [] c_Int_Onumber__class_Onumber__of(V_v,tc_nat)=c_Suc(c_HOL_Ominus__class_Ominus(c_Int_Onumber__class_Onumber__of(V_v,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(V_v,tc_nat),tc_nat).
% 180.18/180.26 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_k,tc_nat),V_j,tc_nat).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat),c_Suc(V_k),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat).
% 180.18/180.26 0 [] c_HOL_Ominus__class_Ominus(V_m,c_Suc(V_n),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_n,tc_nat).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a)!=c_Power_Opower__class_Opower(V_b,c_Suc(V_n),T_a)|V_a=V_b| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 180.18/180.26 0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),V_n,tc_nat)=V_m.
% 180.18/180.26 0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_n,tc_nat)=V_m.
% 180.18/180.26 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_b,T_a)=V_a.
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=V_a.
% 180.18/180.26 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_y,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_x=V_y.
% 180.18/180.26 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=V_b.
% 180.18/180.26 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=V_b.
% 180.18/180.26 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat__aux(V_inc,c_HOL_Ozero__class_Ozero(tc_nat),V_i,T_a)=V_i.
% 180.18/180.26 0 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k)=V_t.
% 180.18/180.26 0 [] c_Suc(V_m)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.18/180.26 0 [] c_Suc(V_nat_H)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.18/180.26 0 [] c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=V_n.
% 180.18/180.26 0 [] c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=V_m.
% 180.18/180.26 0 [] c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.18/180.26 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_m).
% 180.18/180.26 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_nat_H).
% 180.18/180.26 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.18/180.26 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)).
% 180.18/180.26 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_lesse_quals(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).
% 180.18/180.26 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_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)| -class_OrderedGroup_Ocomm__monoid__add(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_lesse_quals(V_b,V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)| -class_OrderedGroup_Ocomm__monoid__add(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_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 180.18/180.26 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_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 180.18/180.26 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_lesse_quals(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).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 180.18/180.26 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_Suc(V_m),T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_Lambda_Oliftn(V_n,c_Lambda_OdB_OAbs(V_s),V_k)=c_Lambda_OdB_OAbs(c_Lambda_Oliftn(V_n,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))).
% 180.18/180.26 0 [] hAPP(c_Type_Oshift(V_e,V_i,V_T,T_a),V_j)=hAPP(V_e,c_HOL_Ominus__class_Ominus(V_j,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 180.18/180.26 0 [] c_Lambda_Osubstn(V_t,V_s,V_n)=hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),c_Lambda_Oliftn(V_n,V_s,c_HOL_Ozero__class_Ozero(tc_nat))),V_n).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),c_HOL_Oone__class_Oone(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 180.18/180.26 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a)=c_HOL_Oone__class_Oone(T_a).
% 180.18/180.26 0 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(V_i)),V_k)=c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)))|c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 180.18/180.26 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.
% 180.18/180.26 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).
% 180.18/180.26 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)).
% 180.18/180.26 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)).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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)).
% 180.18/180.26 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)).
% 180.18/180.26 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)).
% 180.18/180.26 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)).
% 180.18/180.26 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)).
% 180.18/180.26 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)).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a)!=c_List_Orev(V_xs,T_a)|V_xs=c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a).
% 180.18/180.26 0 [] -c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)|c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,V_x,T_a),c_List_Oappend(V_xs,V_x,T_a),T_a).
% 180.18/180.26 0 [] c_ListOrder_Ostep1(V_r,c_List_Oappend(V_x,V_vs,T_a),c_List_Oappend(V_x,V_us,T_a),T_a)| -c_ListOrder_Ostep1(V_r,V_vs,V_us,T_a).
% 180.18/180.26 0 [] c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a).
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(V_s)),c_Lambda_OdB_OAbs(V_s_H)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)).
% 180.18/180.26 0 [] c_List_Olistsp(V_A,V_xs,T_a)| -c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a).
% 180.18/180.26 0 [] c_List_Olistsp(V_A,V_ys,T_a)| -c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a).
% 180.18/180.26 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).
% 180.18/180.26 0 [] V_x=V_y|V_xs=V_ys| -c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a).
% 180.18/180.26 0 [] -hBOOL(hAPP(hAPP(V_r,V_y),V_xa))|c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_x,T_a),c_List_Olist_OCons(V_xa,V_x,T_a),T_a).
% 180.18/180.26 0 [] c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a).
% 180.18/180.26 0 [] c_List_Oappend(V_ys,V_xs,T_a)!=c_List_Oappend(V_zs,V_xs,T_a)|V_ys=V_zs.
% 180.18/180.26 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Oappend(V_xs,V_zs,T_a)|V_ys=V_zs.
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)).
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)).
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_z))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_z))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y)).
% 180.18/180.26 0 [] c_List_Otake(V_n,c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(V_a)))|V_a=c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 180.18/180.26 0 [] c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a)=V_xs.
% 180.18/180.26 0 [] V_x=c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a).
% 180.18/180.26 0 [] V_xs=c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a).
% 180.18/180.26 0 [] c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a)=V_ys.
% 180.18/180.26 0 [] V_ys=c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a).
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_r),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_i)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)).
% 180.18/180.26 0 [] V_xs=c_List_Orev(c_List_Orev(V_xs,T_a),T_a).
% 180.18/180.26 0 [] c_List_Orev(c_List_Orev(V_ys,T_a),T_a)=V_ys.
% 180.18/180.26 0 [] c_List_Orev(c_List_Orev(V_xs,T_a),T_a)=V_xs.
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_N,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(V_n,V_N,tc_nat).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_Lambda_Osubstn(c_Lambda_OdB_OAbs(V_t),V_s,V_k)=c_Lambda_OdB_OAbs(c_Lambda_Osubstn(V_t,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(V_r,V_y),V_x))|V_y=V_x| -c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a).
% 180.18/180.26 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.
% 180.18/180.26 0 [] c_List_Orev(V_xs,T_a)!=c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a)|V_xs=c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a).
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_t),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),V_i)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)).
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_r),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_i)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)).
% 180.18/180.26 0 [] hAPP(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_x)=hAPP(V_f,hAPP(V_g,V_x)).
% 180.18/180.26 0 [] hAPP(V_a,hAPP(V_b,V_v))=hAPP(c_Fun_Ocomp(V_a,V_b,T_c,T_b,T_a),V_v).
% 180.18/180.26 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(V_x,c_HOL_Oone__class_Oone(tc_nat),T_a)=V_x.
% 180.18/180.26 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a)=V_a.
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y))| -hBOOL(hAPP(hAPP(V_r,V_x),V_y)).
% 180.18/180.26 0 [] -c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a).
% 180.18/180.26 0 [] -c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] hBOOL(hAPP(V_P,V_t))| -hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(V_P)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(V_P),tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(V_P)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(V_P),tc_Lambda_OdB,tc_Lambda_OdB))).
% 180.18/180.26 0 [] -hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(V_P)),c_ListApplication_Osko__ListApplication__Xlem__1__4(V_P),tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(V_P)),c_ListApplication_Osko__ListApplication__Xlem__1__2(V_P),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(V_P,V_t)).
% 180.18/180.26 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_v),V_i)),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_v),V_j)),V_i)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i)),V_v),V_j)| -c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 180.18/180.26 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)=c_Nat_Osemiring__1__class_Oof__nat__aux(c_COMBC(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a),T_a,T_a,T_a),V_n,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 180.18/180.26 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))).
% 180.18/180.26 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))).
% 180.18/180.26 0 [] c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_i),V_s,V_k)=c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(V_i,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(V_k,V_i,tc_nat).
% 180.18/180.26 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)).
% 180.18/180.26 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))).
% 180.18/180.26 0 [] c_Type_Otyping(V_env,c_Lambda_OdB_OAbs(V_t),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).
% 180.18/180.26 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))).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)),c_Suc(V_k))=hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_i)| -c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 180.18/180.26 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_j)),V_u),V_i)=c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(V_j,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 180.18/180.26 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i)),V_s),V_k)=c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(V_i,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(V_k,V_i,tc_nat).
% 180.18/180.26 0 [] c_List_Otake(V_n,c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olist_OCons(V_x,c_List_Otake(c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_xs,T_a),T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.18/180.26 0 [] c_Int_Onumber__class_Onumber__of(V_v,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_List_Otake(c_Int_Onumber__class_Onumber__of(V_v,tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_Power_Opower__class_Opower(V_a,V_n,T_a)!=c_Power_Opower__class_Opower(V_b,V_n,T_a)|V_a=V_b| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 180.18/180.26 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),T_a)=c_HOL_Oone__class_Oone(T_a).
% 180.18/180.26 0 [] c_List_Orev(c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Oappend(c_List_Orev(V_xs,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a).
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(V_r,V_y),V_x))|c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)| -c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a).
% 180.18/180.26 0 [] c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a)=c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a).
% 180.18/180.26 0 [] c_List_Orev(V_xs,T_a)!=c_List_Olist_OCons(V_y,V_ys,T_a)|V_xs=c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 180.18/180.26 0 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_j)),V_i)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)))| -c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t_H)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)).
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s_H),V_t)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)).
% 180.18/180.26 0 [] c_List_Otake(V_n,V_xs,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.18/180.26 0 [] V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(V_a))),v_sko__InductTermi__XIT__Xcases__5(V_a)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)|V_a=c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 180.18/180.26 0 [] c_List_Olist__update(c_List_Olist_ONil(T_a),V_k,V_x,T_a)=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] c_List_Olist__update(c_List_Olist_ONil(T_a),V_i,V_y,T_a)=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] c_List_Olist__update(c_List_Olist_ONil(T_a),V_i,V_v,T_a)=c_List_Olist_ONil(T_a).
% 180.18/180.26 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.
% 180.18/180.26 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.
% 180.18/180.26 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.
% 180.18/180.26 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.
% 180.18/180.26 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.
% 180.18/180.26 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.
% 180.18/180.26 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.
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_List_Olist_OCons(V_x,V_xa,T_a)!=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] c_List_Olist_OCons(V_a_H,V_list_H,T_a)!=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] V_x=V_y|hBOOL(hAPP(hAPP(V_r,V_y),V_x))| -c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a).
% 180.18/180.26 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)).
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s_H),V_t_H)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)).
% 180.18/180.26 0 [] c_List_Orev(c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),T_a)=c_List_Olist_OCons(V_y,V_ys,T_a).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_Type_Otyping(V_e,V_t_H,V_T)| -c_Type_Otyping(V_e,V_t,V_T)| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)).
% 180.18/180.26 0 [] c_List_Orev(V_xs,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] c_List_Olist_OCons(V_x,V_t,T_a)!=V_t.
% 180.18/180.26 0 [] V_xs!=c_List_Olist_OCons(V_x,V_xs,T_a).
% 180.18/180.26 0 [] c_List_Olist__update(c_List_Olist_OCons(V_x,V_xs,T_a),c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a)=c_List_Olist_OCons(V_y,V_xs,T_a).
% 180.18/180.26 0 [] V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(V_a))),v_sko__InductTermi__XIT__Xcases__5(V_a)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))|V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 180.18/180.26 0 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_j)),V_i)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)),V_j)| -c_HOL_Oord__class_Oless(V_j,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a)=c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a).
% 180.18/180.26 0 [] -c_Type_Otyping(V_e_H,V_u,V_U)| -c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)|c_Type_Otyping(V_e_H,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),V_T).
% 180.18/180.26 0 [] V_ys=V_xs|c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)| -c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a)),T_a).
% 180.18/180.26 0 [] c_List_Olist_ONil(T_a)=c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a).
% 180.18/180.26 0 [] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a)=c_Transitive__Closure_Ortranclp(V_r,T_a).
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_s)),c_Lambda_OdB_OAbs(V_t)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)).
% 180.18/180.26 0 [] c_List_Orev(c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] c_List_Orev(c_List_Oappend(V_xs,V_ys,T_a),T_a)=c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Orev(V_xs,T_a),T_a).
% 180.18/180.26 0 [] hAPP(hAPP(V_plus,V_a),V_zero)=V_a| -c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a).
% 180.18/180.26 0 [] hAPP(hAPP(V_plus,V_zero),V_a)=V_a| -c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_List_Olist__update(V_xs,V_k,V_x,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(V_a)))|V_a=c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))|V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 180.18/180.26 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(V_a)),v_sko__InductTermi__XIT__Xcases__5(V_a)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 180.18/180.26 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(V_a)),v_sko__InductTermi__XIT__Xcases__5(V_a)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)))|V_a=c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))|V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)|c_HOL_Oone__class_Oone(T_a)!=c_HOL_Ozero__class_Ozero(T_a).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)|c_HOL_Ozero__class_Ozero(T_a)!=c_HOL_Oone__class_Oone(T_a).
% 180.18/180.26 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.
% 180.18/180.26 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.
% 180.18/180.26 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)).
% 180.18/180.26 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.
% 180.18/180.26 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.
% 180.18/180.26 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.
% 180.18/180.26 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.
% 180.18/180.26 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.
% 180.18/180.26 0 [] -class_Ring__and__Field_Osemiring__0(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Oone__class_Oone(T_a).
% 180.18/180.26 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] -c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 180.18/180.26 0 [] -c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 180.18/180.26 0 [] V_x=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)).
% 180.18/180.26 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)=V_n.
% 180.18/180.26 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat))=V_m.
% 180.18/180.26 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=c_Lambda_OdB_OAbs(V_dB_H).
% 180.18/180.26 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2).
% 180.18/180.26 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))).
% 180.18/180.26 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))).
% 180.18/180.26 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).
% 180.18/180.26 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)).
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_s)),hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_t)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)).
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_u)),hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)).
% 180.18/180.26 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)).
% 180.18/180.26 0 [] c_List_Omap(V_f,V_xs,T_b,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_b).
% 180.18/180.26 0 [] c_List_Omap(V_f,c_List_Oappend(V_xs,V_ys,T_b),T_b,T_a)=c_List_Oappend(c_List_Omap(V_f,V_xs,T_b,T_a),c_List_Omap(V_f,V_ys,T_b,T_a),T_a).
% 180.18/180.26 0 [] c_List_Olist_ONil(T_a)!=c_List_Omap(V_f,V_xs,T_b,T_a)|V_xs=c_List_Olist_ONil(T_b).
% 180.18/180.26 0 [] hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x)=V_T.
% 180.18/180.26 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).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 180.18/180.26 0 [] c_List_Olist_ONil(T_a)!=c_List_Oappend(V_xs,V_ys,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] c_List_Olist_ONil(T_a)!=c_List_Oappend(V_xs,V_ys,T_a)|V_ys=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] c_Lambda_OdB_OAbs(V_dB)!=c_Lambda_OdB_OAbs(V_dB_H)|V_dB=V_dB_H.
% 180.18/180.26 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Olist_ONil(T_a)|V_ys=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(V_a)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 180.18/180.26 0 [] -c_HOL_Oord__class_Oless(V_x,V_x,tc_nat).
% 180.18/180.26 0 [] -c_HOL_Oord__class_Oless(V_n,V_n,tc_nat).
% 180.18/180.26 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 180.18/180.26 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 180.18/180.26 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,V_r),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)|V_xs=V_ys| -c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a).
% 180.18/180.26 0 [] hAPP(hAPP(V_plus,hAPP(hAPP(V_plus,V_a),V_b)),V_c)=hAPP(hAPP(V_plus,V_a),hAPP(hAPP(V_plus,V_b),V_c))| -c_OrderedGroup_Osemigroup__add(V_plus,T_a).
% 180.18/180.26 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(V_a)),v_sko__InductTermi__XIT__Xcases__5(V_a)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)))|V_a=c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 180.18/180.26 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.
% 180.18/180.26 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).
% 180.18/180.26 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.
% 180.18/180.26 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).
% 180.18/180.26 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.
% 180.18/180.26 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.
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_List_Olist_ONil(T_a)!=c_List_Olist_OCons(V_a_H,V_list_H,T_a).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a).
% 180.18/180.26 0 [] V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(V_a))),v_sko__InductTermi__XIT__Xcases__5(V_a)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)|V_a=c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))|V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a)),T_a).
% 180.18/180.26 0 [] c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),V_xs,T_a)=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] c_List_Orev(V_xs,T_a)!=c_List_Orev(V_ys,T_a)|V_xs=V_ys.
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] V_ys=V_xs|V_y=V_x| -c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_Power_Opower__class_Opower(V_a,V_m,T_a)!=c_Power_Opower__class_Opower(V_a,V_n,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)|V_m=V_n.
% 180.18/180.26 0 [] c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Oone__class_Oone(T_a).
% 180.18/180.26 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Oone__class_Oone(T_a).
% 180.18/180.26 0 [] c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a)| -c_List_Olistsp(V_A,V_ys,T_a)| -c_List_Olistsp(V_A,V_xs,T_a).
% 180.18/180.26 0 [] c_Fun_Ocomp(V_f,c_Fun_Ocomp(V_g,V_h,T_d,T_c,T_a),T_c,T_b,T_a)=c_Fun_Ocomp(c_Fun_Ocomp(V_f,V_g,T_c,T_b,T_d),V_h,T_d,T_b,T_a).
% 180.18/180.26 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)).
% 180.18/180.26 0 [] -class_OrderedGroup_Osemigroup__add(T_a)|c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(T_a),T_a).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_List_Olist_ONil(T_a)!=c_List_Orev(V_xs,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 180.18/180.26 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).
% 180.18/180.26 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))).
% 180.18/180.26 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))).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_a,V_N,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(V_n,V_N,tc_nat).
% 180.18/180.26 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 180.18/180.26 0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat).
% 180.18/180.26 0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat).
% 180.18/180.26 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=V_xs|V_ys=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] V_xs!=c_List_Oappend(V_xs,V_ys,T_a)|V_ys=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=V_ys|V_xs=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] V_ys!=c_List_Oappend(V_xs,V_ys,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(V_a))),v_sko__InductTermi__XIT__Xcases__5(V_a)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 180.18/180.26 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.
% 180.18/180.26 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.
% 180.18/180.26 0 [] c_Type_Otyping(V_e,V_t_H,V_T)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H))| -c_Type_Otyping(V_e,V_t,V_T).
% 180.18/180.26 0 [] c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)|hBOOL(hAPP(hAPP(V_r,V_y),V_x))| -c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a).
% 180.18/180.26 0 [] c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_x,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)| -c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a).
% 180.18/180.26 0 [] c_List_Olist__update(c_List_Olist__update(V_xs,V_i,V_x,T_a),V_i_H,V_x_H,T_a)=c_List_Olist__update(c_List_Olist__update(V_xs,V_i_H,V_x_H,T_a),V_i,V_x,T_a)|V_i=V_i_H.
% 180.18/180.26 0 [] c_Fun_Ocomp(V_a,V_b,T_c,T_b,T_a)!=c_Fun_Ocomp(V_c,V_d,T_d,T_b,T_a)|hAPP(V_a,hAPP(V_b,V_v))=hAPP(V_c,hAPP(V_d,V_v)).
% 180.18/180.26 0 [] hAPP(V_f,hAPP(V_g,V_x))!=hAPP(V_f_H,hAPP(V_g_H,V_x_H))|hAPP(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_x)=hAPP(c_Fun_Ocomp(V_f_H,V_g_H,T_d,T_a,T_e),V_x_H).
% 180.18/180.26 0 [] c_List_Olist_ONil(T_a)=c_List_Orev(c_List_Olist_ONil(T_a),T_a).
% 180.18/180.26 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)).
% 180.18/180.26 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.
% 180.18/180.26 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.
% 180.18/180.26 0 [] c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(V_s)),V_k)=c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,V_s),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))).
% 180.18/180.26 0 [] c_List_Olist__update(c_List_Olist__update(V_xs,V_i,V_x,T_a),V_i,V_y,T_a)=c_List_Olist__update(V_xs,V_i,V_y,T_a).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,V_t),V_i),V_T)| -c_Type_Otyping(V_e,V_t,V_T).
% 180.18/180.26 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).
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_c))| -hBOOL(hAPP(hAPP(V_r,V_a),V_b)).
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c))| -hBOOL(hAPP(hAPP(V_r,V_b),V_c))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_b)).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 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).
% 180.18/180.26 0 [] c_List_Orev(c_List_Omap(V_f,V_xs,T_b,T_a),T_a)=c_List_Omap(V_f,c_List_Orev(V_xs,T_b),T_b,T_a).
% 180.18/180.26 0 [] hAPP(V_f,c_List_Osko__List__Xmap__ext__1__1(V_f,V_g,V_xs,T_a,T_b))!=hAPP(V_g,c_List_Osko__List__Xmap__ext__1__1(V_f,V_g,V_xs,T_a,T_b))|c_List_Omap(V_f,V_xs,T_a,T_b)=c_List_Omap(V_g,V_xs,T_a,T_b).
% 180.18/180.26 0 [] c_List_Otake(V_n,c_List_Omap(V_f,V_xs,T_b,T_a),T_a)=c_List_Omap(V_f,c_List_Otake(V_n,V_xs,T_b),T_b,T_a).
% 180.18/180.26 0 [] c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a)=c_List_Olist_ONil(T_a).
% 180.18/180.26 0 [] c_List_Omap(V_f,c_List_Omap(V_g,V_xs,T_c,T_b),T_b,T_a)=c_List_Omap(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_xs,T_c,T_a).
% 180.18/180.26 0 [] c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xa,T_b),T_b,T_a)=c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xa,T_b,T_a),T_a).
% 180.18/180.26 0 [] c_List_Olist_OCons(hAPP(V_f,V_xa),c_List_Omap(V_f,V_xb,T_b,T_a),T_a)=c_List_Omap(V_f,c_List_Olist_OCons(V_xa,V_xb,T_b),T_b,T_a).
% 180.18/180.26 0 [] c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a)=c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a).
% 180.18/180.26 0 [] hAPP(V_f,c_List_Osko__List__Xmap__cong__1__1(V_f,V_g,V_x,T_a,T_b))!=hAPP(V_g,c_List_Osko__List__Xmap__cong__1__1(V_f,V_g,V_x,T_a,T_b))|c_List_Omap(V_f,V_x,T_a,T_b)=c_List_Omap(V_g,V_x,T_a,T_b).
% 180.18/180.26 0 [] hAPP(V_f,c_List_Osko__List__Xmap__e_q__conv__1__1(V_f,V_g,V_xs,T_b,T_a))!=hAPP(V_g,c_List_Osko__List__Xmap__e_q__conv__1__1(V_f,V_g,V_xs,T_b,T_a))|c_List_Omap(V_f,V_xs,T_b,T_a)=c_List_Omap(V_g,V_xs,T_b,T_a).
% 180.18/180.26 0 [] c_List_Omap(V_f,c_List_Olist__update(V_xs,V_k,V_y,T_b),T_b,T_a)=c_List_Olist__update(c_List_Omap(V_f,V_xs,T_b,T_a),V_k,hAPP(V_f,V_y),T_a).
% 180.18/180.26 0 [] c_List_Olist_ONil(T_a)=c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a).
% 180.18/180.26 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)).
% 180.18/180.27 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)))| -c_ListOrder_Ostep1(c_Lambda_Obeta,V_rs,V_ss,tc_Lambda_OdB).
% 180.18/180.27 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).
% 180.18/180.27 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).
% 180.18/180.27 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)|V_r=c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_ListApplication_Osko__ListApplication__XApp__e_q__foldl__conv__1__1(V_r,V_s,V_t,V_ts),tc_Lambda_OdB,tc_Lambda_OdB)|V_ts=c_List_Olist_ONil(tc_Lambda_OdB).
% 180.18/180.27 0 [] V_t=c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(V_t),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(V_t),tc_Lambda_OdB,tc_Lambda_OdB).
% 180.18/180.27 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).
% 180.18/180.27 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).
% 180.18/180.27 0 [] c_List_Ofoldl(V_plus,hAPP(hAPP(V_plus,V_x),V_y),V_zs,T_a,T_a)=hAPP(hAPP(V_plus,V_x),c_List_Ofoldl(V_plus,V_y,V_zs,T_a,T_a))| -c_OrderedGroup_Osemigroup__add(V_plus,T_a).
% 180.18/180.27 0 [] c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b)=V_a.
% 180.18/180.27 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)).
% 180.18/180.27 0 [] hAPP(hAPP(V_plus,V_x),c_List_Ofoldl(V_plus,V_zero,V_zs,T_a,T_a))=c_List_Ofoldl(V_plus,V_x,V_zs,T_a,T_a)| -c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a).
% 180.18/180.27 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).
% 180.18/180.27 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).
% 180.18/180.27 0 [] hBOOL(hAPP(V_P,c_ListApplication_Osko__ListApplication__Xlem__1__3(V_P)))| -hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(V_P)),c_ListApplication_Osko__ListApplication__Xlem__1__2(V_P),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(V_P,V_t)).
% 180.18/180.27 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).
% 180.18/180.27 0 [] hBOOL(hAPP(V_P,V_t))|hBOOL(hAPP(V_P,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(V_P)))| -hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(V_P)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(V_P),tc_Lambda_OdB,tc_Lambda_OdB))).
% 180.18/180.27 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).
% 180.18/180.27 0 [] c_ListOrder_Ostep1(c_Lambda_Obeta,V_rs,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(V_n,V_rs,V_v),tc_Lambda_OdB)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_v)).
% 180.18/180.27 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(V_a)),v_sko__InductTermi__XIT__Xcases__5(V_a)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))|V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 180.18/180.27 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_t),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),V_i)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)).
% 180.18/180.27 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(V_a)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))|V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 180.18/180.27 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(V_t)),V_s),V_k)=c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_s),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))).
% 180.18/180.27 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=c_Lambda_OdB_OVar(V_nat).
% 180.18/180.27 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))).
% 180.18/180.27 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))).
% 180.18/180.27 0 [] -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)).
% 180.18/180.27 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).
% 180.18/180.27 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OAbs(V_dB_H).
% 180.18/180.27 0 [] hAPP(V_e,V_i)=V_T| -c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T).
% 180.18/180.27 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).
% 180.18/180.27 0 [] c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)).
% 180.18/180.27 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_ua______)).
% 180.18/180.27 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r)))| -hBOOL(hAPP(c_InductTermi_OIT,V_r)).
% 180.18/180.27 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,V_r),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)).
% 180.18/180.27 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),c_HOL_Ozero__class_Ozero(tc_nat)))).
% 180.18/180.27 0 [] v_n____=v_i____.
% 180.18/180.27 0 [] V_v=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(V_n,V_rs,V_v),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_v)).
% 180.18/180.27 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).
% 180.18/180.27 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).
% 180.18/180.27 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).
% 180.18/180.27 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).
% 180.18/180.27 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).
% 180.18/180.27 0 [] c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),c_HOL_Ozero__class_Ozero(tc_nat)).
% 180.18/180.27 0 [] c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(V_nat),tc_Lambda_OdB)=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.18/180.27 0 [] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(V_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.18/180.27 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).
% 180.18/180.27 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.
% 180.18/180.27 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).
% 180.18/180.27 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.
% 180.18/180.27 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.
% 180.18/180.27 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)).
% 180.18/180.27 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.
% 180.18/180.27 0 [] c_Type_Otypings(V_e,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts)| -c_Type_Otypings(c_Type_Oshift(V_e,V_i,V_T,tc_Type_Otype),V_ts,V_Ts)| -c_Type_Otyping(V_e,V_u,V_T).
% 180.18/180.27 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_j)),V_u),V_i)=c_Lambda_OdB_OVar(V_j)| -c_HOL_Oord__class_Oless(V_j,V_i,tc_nat).
% 180.18/180.27 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i)),V_s),V_k)=c_Lambda_OdB_OVar(V_i)|V_i=V_k|c_HOL_Oord__class_Oless(V_k,V_i,tc_nat).
% 180.18/180.27 0 [] c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)|hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_x)),V_s),V_x)=V_s.
% 180.18/180.27 0 [] c_Type_Otypings(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts)| -c_Type_Otypings(V_e,V_ts,V_Ts).
% 180.18/180.27 0 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(V_i)),V_k)=c_Lambda_OdB_OVar(V_i)| -c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 180.18/180.27 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).
% 180.18/180.27 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).
% 180.18/180.27 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).
% 180.18/180.27 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).
% 180.18/180.27 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).
% 180.18/180.27 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)))| -c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB).
% 180.18/180.27 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r)),V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(c_InductTermi_OIT,V_s))| -hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_s),c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))).
% 180.18/180.27 0 [] c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)| -c_List_Olistsp(c_InductTermi_OIT,V_ts,tc_Lambda_OdB).
% 180.18/180.27 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_s),V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_k)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_s),V_k)).
% 180.18/180.27 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OVar(V_nat_H)|V_nat=V_nat_H.
% 180.18/180.27 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.
% 180.18/180.27 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.
% 180.18/180.27 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k)=V_u.
% 180.18/180.27 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),c_Lambda_OdB_OVar(V_i)),V_j)))| -hBOOL(hAPP(c_InductTermi_OIT,V_r)).
% 180.18/180.27 0 [] hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_i)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_t),V_i),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 180.18/180.27 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.
% 180.18/180.27 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.
% 180.18/180.27 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.
% 180.18/180.27 0 [] c_Lambda_OdB_OVar(V_nat)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H).
% 180.18/180.27 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)))| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 180.18/180.27 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))).
% 180.18/180.27 0 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_s),V_k)),hAPP(hAPP(c_Lambda_Olift,V_t),V_k)).
% 180.18/180.27 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 180.18/180.27 0 [] hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R)=hAPP(hAPP(V_P,V_R),V_Q).
% 180.18/180.27 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.
% 180.18/180.27 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_u____)).
% 180.18/180.27 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k)=V_t.
% 180.18/180.27 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),c_Lambda_OdB_OVar(V_i))))| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 180.18/180.27 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)!=c_Lambda_OdB_OVar(V_nat).
% 180.18/180.27 0 [] c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB).
% 180.18/180.27 0 [] -hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))).
% 180.18/180.27 0 [] class_Orderings_Opreorder(tc_fun(T_2,T_1))| -class_Orderings_Opreorder(T_1).
% 180.18/180.27 0 [] class_Orderings_Oorder(tc_fun(T_2,T_1))| -class_Orderings_Oorder(T_1).
% 180.18/180.27 0 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 180.18/180.27 0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 180.18/180.27 0 [] class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat).
% 180.18/180.27 0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 180.18/180.27 0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 180.18/180.27 0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 180.18/180.27 0 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 180.18/180.27 0 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 180.18/180.27 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 180.18/180.27 0 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 180.18/180.27 0 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 180.18/180.27 0 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 180.18/180.27 0 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 180.18/180.27 0 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 180.18/180.27 0 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 180.18/180.27 0 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 180.18/180.27 0 [] class_OrderedGroup_Omonoid__mult(tc_nat).
% 180.18/180.27 0 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 180.18/180.27 0 [] class_Nat_Osemiring__char__0(tc_nat).
% 180.18/180.27 0 [] class_Orderings_Opreorder(tc_nat).
% 180.18/180.27 0 [] class_Orderings_Olinorder(tc_nat).
% 180.18/180.27 0 [] class_Orderings_Oorder(tc_nat).
% 180.18/180.27 0 [] class_Power_Opower(tc_nat).
% 180.18/180.27 0 [] class_Int_Onumber(tc_nat).
% 180.18/180.27 0 [] class_Orderings_Opreorder(tc_bool).
% 180.18/180.27 0 [] class_Orderings_Oorder(tc_bool).
% 180.18/180.27 0 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 180.18/180.27 0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 180.18/180.27 0 [] class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint).
% 180.18/180.27 0 [] class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint).
% 180.18/180.27 0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint).
% 180.18/180.27 0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 180.18/180.27 0 [] class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint).
% 180.18/180.27 0 [] class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint).
% 180.18/180.27 0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint).
% 180.18/180.27 0 [] class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint).
% 180.18/180.27 0 [] class_Ring__and__Field_Oordered__semidom(tc_Int_Oint).
% 180.18/180.27 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint).
% 180.18/180.27 0 [] class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint).
% 180.18/180.27 0 [] class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint).
% 180.18/180.27 0 [] class_Ring__and__Field_Ozero__ne_q__one(tc_Int_Oint).
% 180.18/180.27 0 [] class_Ring__and__Field_Oordered__idom(tc_Int_Oint).
% 180.18/180.27 0 [] class_OrderedGroup_Osemigroup__add(tc_Int_Oint).
% 180.18/180.27 0 [] class_Ring__and__Field_Osemiring__1(tc_Int_Oint).
% 180.18/180.27 0 [] class_Ring__and__Field_Osemiring__0(tc_Int_Oint).
% 180.18/180.27 0 [] class_OrderedGroup_Oab__group__add(tc_Int_Oint).
% 180.18/180.27 0 [] class_Ring__and__Field_Omult__zero(tc_Int_Oint).
% 180.18/180.27 0 [] class_OrderedGroup_Omonoid__mult(tc_Int_Oint).
% 180.18/180.27 0 [] class_OrderedGroup_Omonoid__add(tc_Int_Oint).
% 180.18/180.27 0 [] class_OrderedGroup_Ogroup__add(tc_Int_Oint).
% 180.18/180.27 0 [] class_Ring__and__Field_Oidom(tc_Int_Oint).
% 180.18/180.27 0 [] class_Nat_Osemiring__char__0(tc_Int_Oint).
% 180.18/180.27 0 [] class_Orderings_Opreorder(tc_Int_Oint).
% 180.18/180.27 0 [] class_Orderings_Olinorder(tc_Int_Oint).
% 180.18/180.27 0 [] class_Orderings_Oorder(tc_Int_Oint).
% 180.18/180.27 0 [] class_Int_Oring__char__0(tc_Int_Oint).
% 180.18/180.27 0 [] class_Int_Onumber__ring(tc_Int_Oint).
% 180.18/180.27 0 [] class_Power_Opower(tc_Int_Oint).
% 180.18/180.27 0 [] class_Int_Onumber(tc_Int_Oint).
% 180.18/180.27 0 [] hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R)=hAPP(hAPP(V_P,V_R),V_Q).
% 180.18/180.27 0 [] c_COMBB(V_P,V_Q,V_R,T_b,T_a,T_c)=hAPP(V_P,hAPP(V_Q,V_R)).
% 180.18/180.27 0 [] c_fe_qual(V_x,V_x,T_a).
% 180.18/180.27 0 [] V_X=V_Y| -c_fe_qual(V_X,V_Y,T_a).
% 180.18/180.27 end_of_list.
% 180.18/180.27
% 180.18/180.27 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 180.18/180.27
% 180.18/180.27 This ia a non-Horn set with equality. The strategy will be
% 180.18/180.27 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 180.18/180.27 deletion, with positive clauses in sos and nonpositive
% 180.18/180.27 clauses in usable.
% 180.18/180.27
% 180.18/180.27 dependent: set(knuth_bendix).
% 180.18/180.27 dependent: set(anl_eq).
% 180.18/180.27 dependent: set(para_from).
% 180.18/180.27 dependent: set(para_into).
% 180.18/180.27 dependent: clear(para_from_right).
% 180.18/180.27 dependent: clear(para_into_right).
% 180.18/180.27 dependent: set(para_from_vars).
% 180.18/180.27 dependent: set(eq_units_both_ways).
% 180.18/180.27 dependent: set(dynamic_demod_all).
% 180.18/180.27 dependent: set(dynamic_demod).
% 180.18/180.27 dependent: set(order_eq).
% 180.18/180.27 dependent: set(back_demod).
% 180.18/180.27 dependent: set(lrpo).
% 180.18/180.27 dependent: set(hyper_res).
% 180.18/180.27 dependent: set(unit_deletion).
% 180.18/180.27 dependent: set(factor).
% 180.18/180.27
% 180.18/180.27 ------------> process usable:
% 180.18/180.27 ** KEPT (pick-wt=20): 1 [] -class_Orderings_Olinorder(A)| -class_Int_Onumber(A)|c_lesse_quals(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A)|c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A).
% 180.18/180.27 ** KEPT (pick-wt=10): 2 [] c_Type_Otype_OFun(A,B)!=c_Type_Otype_OFun(C,D)|B=D.
% 180.18/180.27 ** KEPT (pick-wt=10): 3 [] c_Type_Otype_OFun(A,B)!=c_Type_Otype_OFun(C,D)|A=C.
% 180.18/180.27 ** KEPT (pick-wt=4): 4 [] c_Suc(A)!=A.
% 180.18/180.27 Following clause subsumed by 4 during input processing: 0 [flip.1] c_Suc(A)!=A.
% 180.18/180.27 ** KEPT (pick-wt=14): 5 [] -class_Orderings_Oorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(B,D,A)| -c_lesse_quals(D,C,A).
% 180.18/180.27 ** KEPT (pick-wt=14): 6 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(B,D,A)| -c_HOL_Oord__class_Oless(D,C,A).
% 180.18/180.27 ** KEPT (pick-wt=14): 7 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_lesse_quals(D,C,A).
% 180.18/180.27 ** KEPT (pick-wt=14): 8 [] -class_Orderings_Opreorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(D,C,A)| -c_lesse_quals(B,D,A).
% 180.18/180.27 ** KEPT (pick-wt=6): 9 [] -class_Orderings_Oorder(A)|c_lesse_quals(B,B,A).
% 180.18/180.27 ** KEPT (pick-wt=6): 10 [] -class_Orderings_Opreorder(A)|c_lesse_quals(B,B,A).
% 180.18/180.27 ** KEPT (pick-wt=14): 11 [] -class_Orderings_Opreorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(D,C,A)| -c_lesse_quals(B,D,A).
% 180.18/180.27 ** KEPT (pick-wt=14): 12 [] -class_Orderings_Opreorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(D,C,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 180.18/180.27 ** KEPT (pick-wt=24): 13 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A)| -c_lesse_quals(E,D,A)| -c_lesse_quals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E),A).
% 180.18/180.27 ** KEPT (pick-wt=9): 14 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=9): 15 [] c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=14): 16 [] c_Suc(c_HOL_Ominus__class_Ominus(A,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))=A| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=19): 17 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,E,A)|c_lesse_quals(E,D,A)| -c_lesse_quals(C,B,A).
% 180.18/180.27 ** KEPT (pick-wt=19): 18 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,E,A)|c_lesse_quals(C,B,A)| -c_lesse_quals(E,D,A).
% 180.18/180.27 ** KEPT (pick-wt=19): 19 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,E,A)|c_HOL_Oord__class_Oless(D,E,A)| -c_HOL_Oord__class_Oless(B,C,A).
% 180.18/180.27 ** KEPT (pick-wt=19): 20 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,E,A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(D,E,A).
% 180.18/180.27 ** KEPT (pick-wt=13): 21 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,c_Suc(B),tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=13): 22 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)|C=B| -c_lesse_quals(B,C,A).
% 180.18/180.27 Following clause subsumed by 22 during input processing: 0 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(B,C,A)|C=B.
% 180.18/180.27 ** KEPT (pick-wt=13): 23 [] -class_Orderings_Oorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(B,C,A).
% 180.18/180.27 Following clause subsumed by 23 during input processing: 0 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)|B=C| -c_lesse_quals(B,C,A).
% 180.18/180.27 Following clause subsumed by 23 during input processing: 0 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)|B=C| -c_lesse_quals(B,C,A).
% 180.18/180.27 Following clause subsumed by 23 during input processing: 0 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(B,C,A)|B=C.
% 180.18/180.27 ** KEPT (pick-wt=13): 24 [] -class_Orderings_Olinorder(A)|B=C| -c_lesse_quals(B,C,A)|c_HOL_Oord__class_Oless(B,C,A).
% 180.18/180.27 Following clause subsumed by 24 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(B,C,A).
% 180.18/180.27 ** KEPT (pick-wt=10): 25 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,C,A)|c_lesse_quals(C,B,A).
% 180.18/180.27 ** KEPT (pick-wt=13): 26 [] c_Suc(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat))=A| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 180.18/180.27 Following clause subsumed by 26 during input processing: 0 [flip.1] c_Suc(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat))=A| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=14): 27 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A).
% 180.18/180.27 ** KEPT (pick-wt=14): 28 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,C,A).
% 180.18/180.27 ** KEPT (pick-wt=22): 29 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 180.18/180.27 ** KEPT (pick-wt=19): 31 [copy,30,factor_simp] -class_OrderedGroup_Opordered__comm__monoid__add(A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),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).
% 180.18/180.27 ** KEPT (pick-wt=17): 32 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 180.18/180.27 ** KEPT (pick-wt=17): 33 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A).
% 180.18/180.27 ** KEPT (pick-wt=22): 34 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)| -class_OrderedGroup_Ocomm__monoid__add(A)|c_lesse_quals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A)| -c_lesse_quals(B,D,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A).
% 180.18/180.27 ** KEPT (pick-wt=22): 35 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)| -class_OrderedGroup_Ocomm__monoid__add(A)|c_lesse_quals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A)| -c_lesse_quals(B,C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),D,A).
% 180.18/180.27 ** KEPT (pick-wt=25): 36 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=c_HOL_Ozero__class_Ozero(A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)|C=c_HOL_Ozero__class_Ozero(A).
% 180.18/180.27 ** KEPT (pick-wt=25): 37 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=c_HOL_Ozero__class_Ozero(A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)|B=c_HOL_Ozero__class_Ozero(A).
% 180.18/180.27 ** KEPT (pick-wt=17): 38 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 180.18/180.27 ** KEPT (pick-wt=17): 39 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A).
% 180.18/180.27 ** KEPT (pick-wt=22): 40 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 180.18/180.27 ** KEPT (pick-wt=24): 41 [] -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_lesse_quals(C,E,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 180.18/180.27 ** KEPT (pick-wt=24): 42 [] -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_lesse_quals(B,D,A).
% 180.18/180.27 ** KEPT (pick-wt=8): 43 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A).
% 180.18/180.27 ** KEPT (pick-wt=8): 44 [] -class_Ring__and__Field_Oordered__semidom(A)| -c_lesse_quals(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A).
% 180.18/180.27 ** KEPT (pick-wt=9): 45 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A).
% 180.18/180.27 Following clause subsumed by 45 during input processing: 0 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A).
% 180.18/180.27 ** KEPT (pick-wt=10): 46 [] 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).
% 180.18/180.27 ** KEPT (pick-wt=16): 47 [] hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)))| -c_HOL_Oord__class_Oless(B,C,tc_nat)| -hBOOL(hAPP(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat))).
% 180.18/180.27 ** KEPT (pick-wt=12): 48 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(B,A,tc_nat),tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=12): 49 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(B,A,tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=17): 50 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=21): 51 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(B,D,A).
% 180.18/180.27 ** KEPT (pick-wt=15): 52 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 180.18/180.27 ** KEPT (pick-wt=13): 53 [] -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).
% 180.18/180.27 ** KEPT (pick-wt=19): 54 [] 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)).
% 180.18/180.27 ** KEPT (pick-wt=19): 55 [] 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).
% 180.18/180.27 ** KEPT (pick-wt=19): 56 [] 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)).
% 180.18/180.27 ** KEPT (pick-wt=19): 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))|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=20): 58 [] 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)).
% 180.18/180.27 ** KEPT (pick-wt=18): 59 [] 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).
% 180.18/180.27 ** KEPT (pick-wt=20): 60 [] 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)).
% 180.18/180.27 ** KEPT (pick-wt=18): 61 [] 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).
% 180.18/180.27 ** KEPT (pick-wt=16): 62 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat)| -c_HOL_Oord__class_Oless(A,c_HOL_Ominus__class_Ominus(C,B,tc_nat),tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=16): 63 [] c_HOL_Oord__class_Oless(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=15): 64 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,C,A),A)| -c_lesse_quals(c_HOL_Oone__class_Oone(A),B,A).
% 180.18/180.27 ** KEPT (pick-wt=12): 65 [] c_Lambda_Oliftn(A,c_Lambda_OdB_OVar(B),C)=c_Lambda_OdB_OVar(B)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=18): 66 [] c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),D)| -c_Type_Otyping(A,C,E)| -c_Type_Otyping(A,B,c_Type_Otype_OFun(E,D)).
% 180.18/180.27 ** KEPT (pick-wt=20): 67 [] -class_Orderings_Olinorder(A)| -class_Int_Onumber(A)| -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A)| -c_lesse_quals(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A).
% 180.18/180.27 ** KEPT (pick-wt=23): 68 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_Power_Opower__class_Opower(B,c_Suc(D),A),c_Power_Opower__class_Opower(C,c_Suc(D),A),A).
% 180.18/180.27 ** KEPT (pick-wt=20): 69 [] -class_OrderedGroup_Opordered__ab__semigroup__add(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A)| -c_lesse_quals(C,D,A).
% 180.18/180.27 ** KEPT (pick-wt=20): 70 [] -class_OrderedGroup_Opordered__ab__semigroup__add(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A)| -c_lesse_quals(B,D,A).
% 180.18/180.27 ** KEPT (pick-wt=20): 71 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A).
% 180.18/180.27 ** KEPT (pick-wt=20): 72 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A)| -c_lesse_quals(C,D,A).
% 180.18/180.27 ** KEPT (pick-wt=20): 73 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A).
% 180.18/180.27 ** KEPT (pick-wt=20): 74 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A)| -c_lesse_quals(B,D,A).
% 180.18/180.27 ** KEPT (pick-wt=13): 75 [] 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).
% 180.18/180.27 ** KEPT (pick-wt=10): 76 [] -class_Orderings_Opreorder(A)|c_lesse_quals(B,C,A)| -c_HOL_Oord__class_Oless(B,C,A).
% 180.18/180.27 ** KEPT (pick-wt=10): 77 [] -class_Orderings_Oorder(A)|c_lesse_quals(B,C,A)| -c_HOL_Oord__class_Oless(B,C,A).
% 180.18/180.27 ** KEPT (pick-wt=14): 78 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,C,A).
% 180.18/180.27 ** KEPT (pick-wt=14): 79 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A).
% 180.18/180.27 ** KEPT (pick-wt=13): 80 [] -class_Orderings_Oorder(A)|B=C| -c_lesse_quals(B,C,A)| -c_lesse_quals(C,B,A).
% 180.18/180.27 Following clause subsumed by 80 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_lesse_quals(C,B,A)| -c_lesse_quals(B,C,A).
% 180.18/180.27 Following clause subsumed by 80 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_lesse_quals(C,B,A)| -c_lesse_quals(B,C,A).
% 180.18/180.27 ** KEPT (pick-wt=14): 81 [] -class_Orderings_Opreorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_lesse_quals(C,B,A)| -c_lesse_quals(B,C,A).
% 180.18/180.27 ** KEPT (pick-wt=11): 82 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=12): 83 [] A=B| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)|c_HOL_Oord__class_Oless(A,B,tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=12): 84 [] A=B| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 180.18/180.27 Following clause subsumed by 83 during input processing: 0 [] A=B|c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=8): 85 [] c_Suc(A)!=c_Suc(B)|A=B.
% 180.18/180.27 Following clause subsumed by 85 during input processing: 0 [] c_Suc(A)!=c_Suc(B)|A=B.
% 180.18/180.27 ** KEPT (pick-wt=18): 86 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_HOL_Ominus__class_Ominus(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(C,A,tc_nat)| -c_HOL_Oord__class_Oless(C,B,tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=13): 87 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ominus__class_Ominus(B,C,A)),C)=B.
% 180.18/180.27 ** KEPT (pick-wt=16): 88 [] -hBOOL(hAPP(A,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),B,tc_nat)))|hBOOL(hAPP(A,C)).
% 180.18/180.27 Following clause subsumed by 88 during input processing: 0 [] -hBOOL(hAPP(A,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),B,tc_nat)))|hBOOL(hAPP(A,C)).
% 180.18/180.27 ** KEPT (pick-wt=24): 89 [] -class_OrderedGroup_Opordered__ab__semigroup__add(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A)| -c_lesse_quals(C,E,A)| -c_lesse_quals(B,D,A).
% 180.18/180.27 ** KEPT (pick-wt=10): 90 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_lesse_quals(C,B,A).
% 180.18/180.27 ** KEPT (pick-wt=10): 91 [] -class_Orderings_Olinorder(A)| -c_lesse_quals(B,B,A)| -c_HOL_Oord__class_Oless(B,B,A).
% 180.18/180.27 Following clause subsumed by 90 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,B,A)|c_lesse_quals(B,B,A).
% 180.18/180.27 ** KEPT (pick-wt=10): 92 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(C,B,A).
% 180.18/180.27 Following clause subsumed by 90 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,C,A)|c_HOL_Oord__class_Oless(C,B,A).
% 180.18/180.27 Following clause subsumed by 92 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_lesse_quals(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 180.18/180.27 Following clause subsumed by 90 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_lesse_quals(C,B,A).
% 180.18/180.27 ** KEPT (pick-wt=10): 93 [] -class_Orderings_Opreorder(A)| -c_lesse_quals(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 180.18/180.27 ** KEPT (pick-wt=16): 94 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat__aux(B,c_Suc(C),D,A)=c_Nat_Osemiring__1__class_Oof__nat__aux(B,C,hAPP(B,D),A).
% 180.18/180.27 ** KEPT (pick-wt=14): 95 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,D,A)|B=C.
% 180.18/180.27 ** KEPT (pick-wt=14): 96 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)!=c_HOL_Ominus__class_Ominus(C,D,A)|C=D.
% 180.18/180.27 ** KEPT (pick-wt=14): 97 [] -class_Int_Oring__char__0(A)| -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(B,A)!=c_Int_Onumber__class_Onumber__of(C,A)|B=C.
% 180.18/180.27 Following clause subsumed by 26 during input processing: 0 [flip.1] c_Suc(c_HOL_Ominus__class_Ominus(c_Int_Onumber__class_Onumber__of(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat))=c_Int_Onumber__class_Onumber__of(A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=13): 98 [] c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat)|c_Suc(A)=B| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=9): 99 [] -c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=26): 100 [] -class_Ring__and__Field_Oordered__semidom(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)!=c_Power_Opower__class_Opower(D,c_Suc(C),A)|B=D| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),D,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 180.18/180.27 ** KEPT (pick-wt=13): 101 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A)=B.
% 180.18/180.27 ** KEPT (pick-wt=10): 102 [] c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=10): 103 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat).
% 180.18/180.27 Following clause subsumed by 102 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).
% 180.18/180.27 ** KEPT (pick-wt=11): 104 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 180.18/180.27 ** KEPT (pick-wt=9): 105 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 180.18/180.27 ** KEPT (pick-wt=9): 106 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 180.18/180.27 Following clause subsumed by 105 during input processing: 0 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 180.18/180.27 ** KEPT (pick-wt=9): 107 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 180.18/180.27 ** KEPT (pick-wt=14): 108 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 180.18/180.27 ** KEPT (pick-wt=12): 109 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 180.18/180.27 ** KEPT (pick-wt=12): 110 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 180.18/180.27 ** KEPT (pick-wt=10): 111 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat__aux(B,c_HOL_Ozero__class_Ozero(tc_nat),C,A)=C.
% 180.18/180.27 ** KEPT (pick-wt=5): 112 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.18/180.27 Following clause subsumed by 112 during input processing: 0 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=17): 113 [] c_HOL_Ominus__class_Ominus(A,B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Ominus__class_Ominus(B,A,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|B=A.
% 180.18/180.27 Following clause subsumed by 112 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.18/180.27 Following clause subsumed by 112 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=22): 114 [] -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_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 180.18/180.27 ** KEPT (pick-wt=22): 115 [] -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_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 180.18/180.27 ** KEPT (pick-wt=22): 116 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)| -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A)| -c_lesse_quals(B,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A).
% 180.18/180.27 ** KEPT (pick-wt=22): 117 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)| -class_OrderedGroup_Ocomm__monoid__add(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_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A).
% 180.18/180.27 ** KEPT (pick-wt=22): 118 [] -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_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 180.18/180.27 ** KEPT (pick-wt=22): 119 [] -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_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 180.18/180.27 ** KEPT (pick-wt=21): 120 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A).
% 180.18/180.27 ** KEPT (pick-wt=16): 121 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,c_Suc(C),A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A).
% 180.18/180.27 ** KEPT (pick-wt=16): 122 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A)).
% 180.18/180.27 ** KEPT (pick-wt=19): 123 [] hAPP(c_Type_Oshift(A,B,C,D),E)=hAPP(A,c_HOL_Ominus__class_Ominus(E,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(B,E,tc_nat).
% 180.18/180.27 ** KEPT (pick-wt=21): 124 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,c_Suc(C),A),c_HOL_Oone__class_Oone(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 180.18/180.27 ** KEPT (pick-wt=10): 125 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A)=c_HOL_Oone__class_Oone(A).
% 180.18/180.28 ** KEPT (pick-wt=28): 126 [] -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.
% 180.18/180.28 ** KEPT (pick-wt=20): 127 [] 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).
% 180.18/180.28 ** KEPT (pick-wt=25): 128 [] -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)).
% 180.18/180.28 ** KEPT (pick-wt=25): 129 [] -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)).
% 180.18/180.28 ** KEPT (pick-wt=25): 130 [] -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).
% 180.18/180.28 Following clause subsumed by 128 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 180.18/180.28 ** KEPT (pick-wt=25): 131 [] -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)).
% 180.18/180.28 ** KEPT (pick-wt=25): 132 [] -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)).
% 180.18/180.28 ** KEPT (pick-wt=25): 133 [] -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)).
% 180.18/180.28 ** KEPT (pick-wt=25): 134 [] -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)).
% 180.18/180.28 Following clause subsumed by 128 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 180.18/180.28 ** KEPT (pick-wt=14): 135 [] -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).
% 180.18/180.28 ** KEPT (pick-wt=14): 136 [] -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).
% 180.18/180.28 ** KEPT (pick-wt=16): 137 [] c_List_Olist_OCons(A,c_List_Olist_ONil(B),B)!=c_List_Orev(C,B)|C=c_List_Olist_OCons(A,c_List_Olist_ONil(B),B).
% 180.18/180.28 ** KEPT (pick-wt=16): 138 [] -c_ListOrder_Ostep1(A,B,C,D)|c_ListOrder_Ostep1(A,c_List_Oappend(B,E,D),c_List_Oappend(C,E,D),D).
% 180.18/180.28 ** KEPT (pick-wt=16): 139 [] c_ListOrder_Ostep1(A,c_List_Oappend(B,C,D),c_List_Oappend(B,E,D),D)| -c_ListOrder_Ostep1(A,C,E,D).
% 180.18/180.28 ** KEPT (pick-wt=18): 140 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(A)),c_Lambda_OdB_OAbs(B)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),B)).
% 180.18/180.28 ** KEPT (pick-wt=11): 141 [] c_List_Olistsp(A,B,C)| -c_List_Olistsp(A,c_List_Oappend(B,D,C),C).
% 180.18/180.28 ** KEPT (pick-wt=11): 142 [] c_List_Olistsp(A,B,C)| -c_List_Olistsp(A,c_List_Oappend(D,B,C),C).
% 180.18/180.28 ** KEPT (pick-wt=17): 143 [] A=B|C=D| -c_ListOrder_Ostep1(E,c_List_Olist_OCons(B,D,F),c_List_Olist_OCons(A,C,F),F).
% 180.18/180.28 ** KEPT (pick-wt=17): 144 [] -hBOOL(hAPP(hAPP(A,B),C))|c_ListOrder_Ostep1(A,c_List_Olist_OCons(B,D,E),c_List_Olist_OCons(C,D,E),E).
% 180.18/180.28 ** KEPT (pick-wt=12): 145 [] c_List_Oappend(A,B,C)!=c_List_Oappend(D,B,C)|A=D.
% 180.18/180.28 ** KEPT (pick-wt=12): 146 [] c_List_Oappend(A,B,C)!=c_List_Oappend(A,D,C)|B=D.
% 180.18/180.28 ** KEPT (pick-wt=24): 147 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),E),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),E)).
% 180.18/180.28 ** KEPT (pick-wt=19): 149 [copy,148,flip.2] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(A)))|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(A))=A|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 180.18/180.28 ** KEPT (pick-wt=26): 150 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),D),C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,B),D)).
% 180.18/180.28 ** KEPT (pick-wt=26): 151 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(D,C,tc_nat).
% 180.18/180.28 ** KEPT (pick-wt=13): 152 [] 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).
% 180.18/180.28 ** KEPT (pick-wt=13): 153 [] 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).
% 180.18/180.28 ** KEPT (pick-wt=13): 154 [] 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).
% 180.18/180.28 Following clause subsumed by 152 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).
% 180.18/180.28 Following clause subsumed by 153 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).
% 180.18/180.28 ** KEPT (pick-wt=15): 155 [] -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).
% 180.18/180.28 ** KEPT (pick-wt=15): 156 [] -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).
% 180.18/180.28 ** KEPT (pick-wt=21): 157 [] 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).
% 180.18/180.28 Following clause subsumed by 155 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).
% 180.18/180.28 ** KEPT (pick-wt=28): 158 [] hBOOL(hAPP(hAPP(A,B),C))|B=C| -c_ListOrder_Ostep1(A,c_List_Oappend(D,c_List_Olist_OCons(B,c_List_Olist_ONil(E),E),E),c_List_Oappend(F,c_List_Olist_OCons(C,c_List_Olist_ONil(E),E),E),E).
% 180.18/180.28 ** KEPT (pick-wt=12): 159 [] -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.
% 180.18/180.28 ** KEPT (pick-wt=16): 160 [] c_List_Orev(A,B)!=c_List_Olist_OCons(C,c_List_Olist_ONil(B),B)|A=c_List_Olist_OCons(C,c_List_Olist_ONil(B),B).
% 180.18/180.28 ** KEPT (pick-wt=28): 161 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),hAPP(hAPP(hAPP(c_Lambda_Osubst,D),B),C)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),D)).
% 180.18/180.28 ** KEPT (pick-wt=28): 162 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),D),C)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),B),D)).
% 180.18/180.28 ** KEPT (pick-wt=9): 163 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A)=B.
% 180.18/180.28 ** KEPT (pick-wt=9): 164 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A)=B.
% 180.18/180.28 ** KEPT (pick-wt=14): 165 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(A,C),D)).
% 180.18/180.28 ** KEPT (pick-wt=6): 166 [] -c_ListOrder_Ostep1(A,c_List_Olist_ONil(B),C,B).
% 180.18/180.28 ** KEPT (pick-wt=6): 167 [] -c_ListOrder_Ostep1(A,B,c_List_Olist_ONil(C),C).
% 180.18/180.28 ** KEPT (pick-wt=17): 168 [] -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).
% 180.18/180.28 ** KEPT (pick-wt=17): 169 [] -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).
% 180.18/180.28 ** KEPT (pick-wt=17): 170 [] -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).
% 180.18/180.28 ** KEPT (pick-wt=17): 171 [] -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).
% 180.18/180.28 ** KEPT (pick-wt=15): 172 [] -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).
% 180.18/180.28 ** KEPT (pick-wt=28): 173 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(A)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(A),tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(A)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(A),tc_Lambda_OdB,tc_Lambda_OdB))).
% 180.18/180.28 ** KEPT (pick-wt=28): 174 [] -hBOOL(hAPP(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(A)),c_ListApplication_Osko__ListApplication__Xlem__1__4(A),tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(A)),c_ListApplication_Osko__ListApplication__Xlem__1__2(A),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(A,B)).
% 180.18/180.28 ** KEPT (pick-wt=48): 175 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),hAPP(hAPP(c_Lambda_Olift,B),C)),c_Suc(D))),hAPP(hAPP(hAPP(c_Lambda_Osubst,E),B),D)),C)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),E),C)),B),D)| -c_HOL_Oord__class_Oless(C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 180.18/180.28 ** KEPT (pick-wt=26): 176 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 180.18/180.28 ** KEPT (pick-wt=19): 177 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(B,A)=c_Nat_Osemiring__1__class_Oof__nat__aux(c_COMBC(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A),A,A,A),B,c_HOL_Ozero__class_Ozero(A),A).
% 180.18/180.28 ** KEPT (pick-wt=16): 178 [] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,C)=c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(C,A,tc_nat).
% 180.18/180.28 ** KEPT (pick-wt=16): 179 [] c_Type_Otyping(A,c_Lambda_OdB_OAbs(B),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).
% 180.18/180.28 ** KEPT (pick-wt=17): 180 [] 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).
% 180.18/180.28 ** KEPT (pick-wt=17): 181 [] 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).
% 180.18/180.28 ** KEPT (pick-wt=30): 182 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,A),B)),c_Suc(C))=hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,A),C)),B)| -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 180.18/180.28 ** KEPT (pick-wt=19): 183 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),C)=c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(C,A,tc_nat).
% 180.18/180.28 Following clause subsumed by 183 during input processing: 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),C)=c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(C,A,tc_nat).
% 180.18/180.28 ** KEPT (pick-wt=18): 184 [] c_Int_Onumber__class_Onumber__of(A,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_List_Otake(c_Int_Onumber__class_Onumber__of(A,tc_nat),c_List_Olist_OCons(B,C,D),D)=c_List_Olist_ONil(D).
% 180.18/180.28 ** KEPT (pick-wt=29): 185 [] -class_Ring__and__Field_Oordered__semidom(A)|c_Power_Opower__class_Opower(B,C,A)!=c_Power_Opower__class_Opower(D,C,A)|B=D| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),D,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 180.18/180.28 ** KEPT (pick-wt=9): 186 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 180.18/180.28 ** KEPT (pick-wt=30): 187 [] hBOOL(hAPP(hAPP(A,B),C))|c_ListOrder_Ostep1(A,D,E,F)| -c_ListOrder_Ostep1(A,c_List_Oappend(D,c_List_Olist_OCons(B,c_List_Olist_ONil(F),F),F),c_List_Oappend(E,c_List_Olist_OCons(C,c_List_Olist_ONil(F),F),F),F).
% 180.18/180.28 ** KEPT (pick-wt=20): 188 [] c_List_Orev(A,B)!=c_List_Olist_OCons(C,D,B)|A=c_List_Oappend(c_List_Orev(D,B),c_List_Olist_OCons(C,c_List_Olist_ONil(B),B),B).
% 180.18/180.28 ** KEPT (pick-wt=20): 189 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A).
% 180.18/180.28 ** KEPT (pick-wt=43): 190 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),D)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),D)),hAPP(hAPP(c_Lambda_Olift,B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)))| -c_HOL_Oord__class_Oless(D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 180.18/180.28 ** KEPT (pick-wt=22): 191 [] -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).
% 180.18/180.28 ** KEPT (pick-wt=24): 192 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),hAPP(hAPP(c_Lambda_OdB_OApp,A),C)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),B),C)).
% 180.18/180.28 ** KEPT (pick-wt=24): 193 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),hAPP(hAPP(c_Lambda_OdB_OApp,C),B)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),C)).
% 180.18/180.28 ** KEPT (pick-wt=15): 194 [] c_List_Otake(A,B,C)!=c_List_Olist_ONil(C)|B=c_List_Olist_ONil(C)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.18/180.28 ** KEPT (pick-wt=30): 196 [copy,195,flip.1,flip.2] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(A))),v_sko__InductTermi__XIT__Xcases__5(A)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)=A|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(A))=A|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 180.18/180.28 ** KEPT (pick-wt=16): 197 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)|B=C.
% 180.18/180.28 ** KEPT (pick-wt=16): 198 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B)|A=C.
% 180.18/180.28 Following clause subsumed by 197 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.
% 180.18/180.28 ** KEPT (pick-wt=20): 199 [] -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.
% 180.18/180.28 ** KEPT (pick-wt=18): 200 [] -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.
% 180.18/180.28 ** KEPT (pick-wt=18): 201 [] -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.
% 180.18/180.28 ** KEPT (pick-wt=18): 202 [] -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.
% 180.18/180.28 ** KEPT (pick-wt=7): 203 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 180.18/180.28 Following clause subsumed by 203 during input processing: 0 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 180.18/180.28 ** KEPT (pick-wt=20): 204 [] A=B|hBOOL(hAPP(hAPP(C,B),A))| -c_ListOrder_Ostep1(C,c_List_Olist_OCons(B,D,E),c_List_Olist_OCons(A,F,E),E).
% 180.18/180.28 ** KEPT (pick-wt=35): 205 [] -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)).
% 180.18/180.28 ** KEPT (pick-wt=32): 206 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),hAPP(hAPP(c_Lambda_OdB_OApp,C),D)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),B),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),C)).
% 180.18/180.28 ** KEPT (pick-wt=9): 207 [] -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).
% 180.18/180.28 ** KEPT (pick-wt=16): 208 [] c_Type_Otyping(A,B,C)| -c_Type_Otyping(A,D,C)| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),D),B)).
% 180.18/180.28 ** KEPT (pick-wt=10): 209 [] c_List_Orev(A,B)!=c_List_Olist_ONil(B)|A=c_List_Olist_ONil(B).
% 180.18/180.28 ** KEPT (pick-wt=6): 210 [] c_List_Olist_OCons(A,B,C)!=B.
% 180.18/180.28 Following clause subsumed by 210 during input processing: 0 [flip.1] c_List_Olist_OCons(B,A,C)!=A.
% 180.18/180.28 ** KEPT (pick-wt=36): 212 [copy,211,flip.1,flip.3] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(A))),v_sko__InductTermi__XIT__Xcases__5(A)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)=A|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(A)))|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(A)),v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 180.18/180.28 ** KEPT (pick-wt=43): 213 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),D)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,B),D)),C)| -c_HOL_Oord__class_Oless(C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 180.18/180.28 ** KEPT (pick-wt=22): 214 [] -c_Type_Otyping(A,B,C)| -c_Type_Otyping(c_Type_Oshift(A,D,C,tc_Type_Otype),E,F)|c_Type_Otyping(A,hAPP(hAPP(hAPP(c_Lambda_Osubst,E),B),D),F).
% 180.18/180.28 ** KEPT (pick-wt=27): 215 [] A=B|c_ListOrder_Ostep1(C,A,B,D)| -c_ListOrder_Ostep1(C,c_List_Oappend(A,c_List_Olist_OCons(E,c_List_Olist_ONil(D),D),D),c_List_Oappend(B,c_List_Olist_OCons(F,c_List_Olist_ONil(D),D),D),D).
% 180.18/180.28 ** KEPT (pick-wt=14): 216 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)),A).
% 180.18/180.28 ** KEPT (pick-wt=14): 217 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(A)),c_Lambda_OdB_OAbs(B)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),B)).
% 180.18/180.28 ** KEPT (pick-wt=11): 218 [] hAPP(hAPP(A,B),C)=B| -c_OrderedGroup_Omonoid__add(C,A,D).
% 180.18/180.28 ** KEPT (pick-wt=11): 219 [] hAPP(hAPP(A,B),C)=C| -c_OrderedGroup_Omonoid__add(B,A,D).
% 180.18/180.28 Following clause subsumed by 153 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).
% 180.18/180.28 Following clause subsumed by 152 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).
% 180.18/180.28 ** KEPT (pick-wt=17): 220 [] -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).
% 180.18/180.28 ** KEPT (pick-wt=17): 221 [] -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).
% 180.18/180.28 ** KEPT (pick-wt=12): 222 [] c_List_Olist__update(A,B,C,D)!=c_List_Olist_ONil(D)|A=c_List_Olist_ONil(D).
% 180.18/180.28 ** KEPT (pick-wt=25): 224 [copy,223,flip.2,flip.3] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(A)))|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(A))=A|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(A)),v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 180.18/180.28 ** KEPT (pick-wt=33): 225 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(A)),v_sko__InductTermi__XIT__Xcases__5(A)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(A)))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 180.18/180.28 ** KEPT (pick-wt=39): 227 [copy,226,flip.2,flip.3] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(A)),v_sko__InductTermi__XIT__Xcases__5(A)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)))|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(A))=A|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(A)),v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 180.18/180.28 ** KEPT (pick-wt=19): 228 [] -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).
% 180.18/180.28 ** KEPT (pick-wt=13): 229 [] -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).
% 180.18/180.28 ** KEPT (pick-wt=7): 231 [copy,230,flip.2] -class_Ring__and__Field_Ozero__ne_q__one(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Oone__class_Oone(A).
% 180.18/180.28 ** KEPT (pick-wt=15): 232 [] -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).
% 180.18/180.28 ** KEPT (pick-wt=16): 234 [copy,233,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).
% 180.18/180.28 ** KEPT (pick-wt=13): 235 [] -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).
% 180.18/180.28 Following clause subsumed by 231 during input processing: 0 [] -class_Ring__and__Field_Ozero__ne_q__one(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Oone__class_Oone(A).
% 180.18/180.28 ** KEPT (pick-wt=11): 236 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 180.18/180.28 ** KEPT (pick-wt=11): 237 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 180.18/180.28 ** KEPT (pick-wt=13): 239 [copy,238,flip.3] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 180.18/180.28 ** KEPT (pick-wt=11): 240 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 180.18/180.28 ** KEPT (pick-wt=11): 241 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 180.18/180.28 ** KEPT (pick-wt=11): 242 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 180.18/180.28 ** KEPT (pick-wt=11): 243 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 180.18/180.28 Following clause subsumed by 236 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.
% 180.18/180.28 ** KEPT (pick-wt=13): 244 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 180.18/180.28 ** KEPT (pick-wt=6): 245 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 180.18/180.28 ** KEPT (pick-wt=13): 246 [] 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).
% 180.18/180.28 ** KEPT (pick-wt=13): 247 [] 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).
% 180.18/180.28 ** KEPT (pick-wt=12): 249 [copy,248,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.18/180.28 Following clause subsumed by 249 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.18/180.28 ** KEPT (pick-wt=5): 250 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 180.18/180.28 Following clause subsumed by 250 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 180.18/180.28 ** KEPT (pick-wt=8): 251 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 180.18/180.28 ** KEPT (pick-wt=8): 252 [] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 180.18/180.28 ** KEPT (pick-wt=21): 253 [] -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))).
% 180.18/180.28 Following clause subsumed by 253 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))).
% 180.18/180.28 ** KEPT (pick-wt=20): 254 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),hAPP(hAPP(c_Lambda_OdB_OApp,A),C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,B),C)).
% 180.18/180.28 ** KEPT (pick-wt=20): 255 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),hAPP(hAPP(c_Lambda_OdB_OApp,C),B)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),C)).
% 180.18/180.28 ** KEPT (pick-wt=12): 256 [] c_List_Omap(A,B,C,D)!=c_List_Olist_ONil(D)|B=c_List_Olist_ONil(C).
% 180.18/180.28 ** KEPT (pick-wt=12): 257 [] c_List_Olist_ONil(A)!=c_List_Omap(B,C,D,A)|C=c_List_Olist_ONil(D).
% 180.18/180.28 ** KEPT (pick-wt=8): 258 [] -class_Ring__and__Field_Oordered__semidom(A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A).
% 180.18/180.28 ** KEPT (pick-wt=11): 259 [] c_List_Olist_ONil(A)!=c_List_Oappend(B,C,A)|B=c_List_Olist_ONil(A).
% 180.18/180.28 ** KEPT (pick-wt=11): 260 [] c_List_Olist_ONil(A)!=c_List_Oappend(B,C,A)|C=c_List_Olist_ONil(A).
% 180.26/180.28 ** KEPT (pick-wt=8): 261 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OAbs(B)|A=B.
% 180.26/180.28 ** KEPT (pick-wt=11): 262 [] c_List_Oappend(A,B,C)!=c_List_Olist_ONil(C)|A=c_List_Olist_ONil(C).
% 180.26/180.28 ** KEPT (pick-wt=11): 263 [] c_List_Oappend(A,B,C)!=c_List_Olist_ONil(C)|B=c_List_Olist_ONil(C).
% 180.26/180.28 ** KEPT (pick-wt=19): 264 [] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(A)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(A)))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 180.26/180.28 ** KEPT (pick-wt=4): 265 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 180.26/180.28 Following clause subsumed by 265 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 180.26/180.28 ** KEPT (pick-wt=6): 266 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 180.26/180.28 ** KEPT (pick-wt=6): 267 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 180.26/180.28 ** KEPT (pick-wt=6): 268 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 180.26/180.28 ** KEPT (pick-wt=24): 269 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,A),B)),hAPP(hAPP(c_Lambda_Olift,C),B)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),C)).
% 180.26/180.28 ** KEPT (pick-wt=22): 270 [] -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).
% 180.26/180.28 ** KEPT (pick-wt=19): 271 [] c_ListOrder_Ostep1(A,B,C,D)|C=B| -c_ListOrder_Ostep1(A,c_List_Olist_OCons(E,B,D),c_List_Olist_OCons(F,C,D),D).
% 180.26/180.28 ** KEPT (pick-wt=22): 272 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_OrderedGroup_Osemigroup__add(A,E).
% 180.26/180.28 ** KEPT (pick-wt=33): 274 [copy,273,flip.2] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(A)),v_sko__InductTermi__XIT__Xcases__5(A)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)))|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(A))=A|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 180.26/180.28 ** KEPT (pick-wt=13): 275 [] -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.
% 180.26/180.28 ** KEPT (pick-wt=13): 276 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(C,B,A)|c_HOL_Oord__class_Oless(B,C,A).
% 180.26/180.28 Following clause subsumed by 276 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.
% 180.26/180.28 Following clause subsumed by 276 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).
% 180.26/180.28 Following clause subsumed by 276 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).
% 180.26/180.28 ** KEPT (pick-wt=24): 277 [] -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).
% 180.26/180.28 ** KEPT (pick-wt=22): 278 [] 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).
% 180.26/180.28 ** KEPT (pick-wt=7): 279 [] c_List_Olist_ONil(A)!=c_List_Olist_OCons(B,C,A).
% 180.26/180.28 ** KEPT (pick-wt=14): 280 [] -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).
% 180.26/180.28 ** KEPT (pick-wt=14): 281 [] -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).
% 180.26/180.29 ** KEPT (pick-wt=8): 282 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A).
% 180.26/180.29 ** KEPT (pick-wt=36): 284 [copy,283,flip.1,flip.2,flip.3] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(A))),v_sko__InductTermi__XIT__Xcases__5(A)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)=A|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(A))=A|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(A)),v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 180.26/180.29 ** KEPT (pick-wt=12): 285 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)),A).
% 180.26/180.29 ** KEPT (pick-wt=10): 286 [] c_List_Orev(A,B)!=c_List_Orev(C,B)|A=C.
% 180.26/180.29 ** KEPT (pick-wt=14): 287 [] -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).
% 180.26/180.29 ** KEPT (pick-wt=14): 288 [] -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).
% 180.26/180.29 ** KEPT (pick-wt=25): 289 [] A=B|C=D| -c_ListOrder_Ostep1(E,c_List_Oappend(A,c_List_Olist_OCons(C,c_List_Olist_ONil(F),F),F),c_List_Oappend(B,c_List_Olist_OCons(D,c_List_Olist_ONil(F),F),F),F).
% 180.26/180.29 ** KEPT (pick-wt=19): 290 [] -class_Ring__and__Field_Oordered__semidom(A)|c_Power_Opower__class_Opower(B,C,A)!=c_Power_Opower__class_Opower(B,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A)|C=D.
% 180.26/180.29 ** KEPT (pick-wt=10): 291 [] -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 180.26/180.29 ** KEPT (pick-wt=10): 292 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 180.26/180.29 ** KEPT (pick-wt=15): 293 [] c_List_Olistsp(A,c_List_Oappend(B,C,D),D)| -c_List_Olistsp(A,C,D)| -c_List_Olistsp(A,B,D).
% 180.26/180.29 ** KEPT (pick-wt=6): 294 [] -class_OrderedGroup_Osemigroup__add(A)|c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(A),A).
% 180.26/180.29 ** KEPT (pick-wt=15): 295 [] hAPP(c_Type_Oshift(A,B,C,D),E)=hAPP(A,E)| -c_HOL_Oord__class_Oless(E,B,tc_nat).
% 180.26/180.29 ** KEPT (pick-wt=10): 296 [] c_List_Olist_ONil(A)!=c_List_Orev(B,A)|B=c_List_Olist_ONil(A).
% 180.26/180.29 ** KEPT (pick-wt=20): 297 [] -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).
% 180.26/180.29 ** KEPT (pick-wt=16): 298 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OAbs(E),t_a)))|hBOOL(hAPP(A,hAPP(D,E))).
% 180.26/180.29 Following clause subsumed by 298 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))).
% 180.26/180.29 ** KEPT (pick-wt=21): 299 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A).
% 180.26/180.29 ** KEPT (pick-wt=21): 300 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A).
% 180.26/180.29 Following clause subsumed by 299 during input processing: 0 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A)| -c_HOL_Oord__class_Oless(C,D,tc_nat).
% 180.26/180.29 Following clause subsumed by 300 during input processing: 0 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A).
% 180.26/180.29 ** KEPT (pick-wt=9): 301 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat).
% 180.26/180.29 ** KEPT (pick-wt=9): 302 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat).
% 180.26/180.29 ** KEPT (pick-wt=10): 303 [] c_List_Oappend(A,B,C)!=A|B=c_List_Olist_ONil(C).
% 180.26/180.29 Following clause subsumed by 303 during input processing: 0 [flip.1] c_List_Oappend(A,B,C)!=A|B=c_List_Olist_ONil(C).
% 180.26/180.29 ** KEPT (pick-wt=10): 304 [] c_List_Oappend(A,B,C)!=B|A=c_List_Olist_ONil(C).
% 180.26/180.29 Following clause subsumed by 304 during input processing: 0 [flip.1] c_List_Oappend(B,A,C)!=A|B=c_List_Olist_ONil(C).
% 180.26/180.29 ** KEPT (pick-wt=20): 305 [] -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).
% 180.26/180.29 ** KEPT (pick-wt=20): 306 [] -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).
% 180.26/180.29 ** KEPT (pick-wt=20): 307 [] -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).
% 180.26/180.29 ** KEPT (pick-wt=20): 308 [] -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).
% 180.26/180.29 ** KEPT (pick-wt=20): 309 [] -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).
% 180.26/180.29 ** KEPT (pick-wt=20): 310 [] -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).
% 180.26/180.29 ** KEPT (pick-wt=18): 311 [] 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).
% 180.26/180.29 ** KEPT (pick-wt=18): 312 [] 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).
% 180.26/180.29 ** KEPT (pick-wt=18): 313 [] 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).
% 180.26/180.29 ** KEPT (pick-wt=30): 315 [copy,314,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(A))),v_sko__InductTermi__XIT__Xcases__5(A)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)=A|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(A)))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 180.26/180.29 ** KEPT (pick-wt=12): 316 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_OCons(D,E,C)|A=D.
% 180.26/180.29 ** KEPT (pick-wt=12): 317 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_OCons(D,E,C)|B=E.
% 180.26/180.29 ** KEPT (pick-wt=14): 318 [] c_Type_Otyping(A,B,C)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,D),B))| -c_Type_Otyping(A,D,C).
% 180.26/180.29 ** KEPT (pick-wt=22): 319 [] c_ListOrder_Ostep1(A,B,C,D)|hBOOL(hAPP(hAPP(A,E),F))| -c_ListOrder_Ostep1(A,c_List_Olist_OCons(E,B,D),c_List_Olist_OCons(F,C,D),D).
% 180.26/180.29 ** KEPT (pick-wt=16): 320 [] c_ListOrder_Ostep1(A,c_List_Olist_OCons(B,C,D),c_List_Olist_OCons(B,E,D),D)| -c_ListOrder_Ostep1(A,C,E,D).
% 180.26/180.29 ** KEPT (pick-wt=24): 321 [] c_Fun_Ocomp(A,B,C,D,E)!=c_Fun_Ocomp(F,G,H,D,E)|hAPP(A,hAPP(B,I))=hAPP(F,hAPP(G,I)).
% 180.26/180.29 ** KEPT (pick-wt=28): 322 [] hAPP(A,hAPP(B,C))!=hAPP(D,hAPP(E,F))|hAPP(c_Fun_Ocomp(A,B,G,H,I),C)=hAPP(c_Fun_Ocomp(D,E,J,H,K),F).
% 180.26/180.29 ** KEPT (pick-wt=21): 323 [] -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)).
% 180.26/180.29 ** KEPT (pick-wt=20): 324 [] 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.
% 180.26/180.29 ** KEPT (pick-wt=20): 325 [] 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.
% 180.26/180.29 ** KEPT (pick-wt=16): 326 [] c_Type_Otyping(c_Type_Oshift(A,B,C,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,D),B),E)| -c_Type_Otyping(A,D,E).
% 180.26/180.29 ** KEPT (pick-wt=10): 327 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 180.26/180.29 ** KEPT (pick-wt=22): 328 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),E),D))| -hBOOL(hAPP(hAPP(A,C),E)).
% 180.26/180.29 ** KEPT (pick-wt=22): 329 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(A,E),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),E)).
% 180.26/180.29 ** KEPT (pick-wt=10): 330 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 180.26/180.29 ** KEPT (pick-wt=10): 331 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 180.26/180.29 Following clause subsumed by 331 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 180.26/180.29 ** KEPT (pick-wt=28): 332 [] hAPP(A,c_List_Osko__List__Xmap__ext__1__1(A,B,C,D,E))!=hAPP(B,c_List_Osko__List__Xmap__ext__1__1(A,B,C,D,E))|c_List_Omap(A,C,D,E)=c_List_Omap(B,C,D,E).
% 180.26/180.29 ** KEPT (pick-wt=28): 333 [] hAPP(A,c_List_Osko__List__Xmap__cong__1__1(A,B,C,D,E))!=hAPP(B,c_List_Osko__List__Xmap__cong__1__1(A,B,C,D,E))|c_List_Omap(A,C,D,E)=c_List_Omap(B,C,D,E).
% 180.26/180.29 ** KEPT (pick-wt=28): 334 [] hAPP(A,c_List_Osko__List__Xmap__e_q__conv__1__1(A,B,C,D,E))!=hAPP(B,c_List_Osko__List__Xmap__e_q__conv__1__1(A,B,C,D,E))|c_List_Omap(A,C,D,E)=c_List_Omap(B,C,D,E).
% 180.26/180.29 ** KEPT (pick-wt=26): 335 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,C,B,tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),C)).
% 180.26/180.29 ** KEPT (pick-wt=21): 336 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,A,C,tc_Lambda_OdB,tc_Lambda_OdB)))| -c_ListOrder_Ostep1(c_Lambda_Obeta,B,C,tc_Lambda_OdB).
% 180.26/180.29 ** KEPT (pick-wt=13): 337 [] 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).
% 180.26/180.29 ** KEPT (pick-wt=28): 339 [copy,338,flip.2] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_List_Ofoldl(c_Lambda_OdB_OApp,C,D,tc_Lambda_OdB,tc_Lambda_OdB)|c_List_Ofoldl(c_Lambda_OdB_OApp,C,c_ListApplication_Osko__ListApplication__XApp__e_q__foldl__conv__1__1(A,B,C,D),tc_Lambda_OdB,tc_Lambda_OdB)=A|D=c_List_Olist_ONil(tc_Lambda_OdB).
% 180.26/180.29 ** KEPT (pick-wt=13): 340 [] 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).
% 180.26/180.29 ** KEPT (pick-wt=24): 342 [copy,341,flip.1] hAPP(hAPP(A,B),c_List_Ofoldl(A,C,D,E,E))=c_List_Ofoldl(A,hAPP(hAPP(A,B),C),D,E,E)| -c_OrderedGroup_Osemigroup__add(A,E).
% 180.26/180.29 ** KEPT (pick-wt=27): 344 [copy,343,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).
% 180.26/180.29 ** KEPT (pick-wt=21): 345 [] hAPP(hAPP(A,B),c_List_Ofoldl(A,C,D,E,E))=c_List_Ofoldl(A,B,D,E,E)| -c_OrderedGroup_Omonoid__add(C,A,E).
% 180.26/180.29 ** KEPT (pick-wt=17): 347 [copy,346,factor_simp] hBOOL(hAPP(A,c_ListApplication_Osko__ListApplication__Xlem__1__3(A)))| -hBOOL(hAPP(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(A)),c_ListApplication_Osko__ListApplication__Xlem__1__2(A),tc_Lambda_OdB,tc_Lambda_OdB))).
% 180.26/180.29 ** KEPT (pick-wt=18): 348 [] 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).
% 180.26/180.29 ** KEPT (pick-wt=17): 350 [copy,349,factor_simp] hBOOL(hAPP(A,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(A)))| -hBOOL(hAPP(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(A)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(A),tc_Lambda_OdB,tc_Lambda_OdB))).
% 180.26/180.29 ** KEPT (pick-wt=37): 351 [] 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).
% 180.26/180.29 ** KEPT (pick-wt=20): 352 [] c_ListOrder_Ostep1(c_Lambda_Obeta,A,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(B,A,C),tc_Lambda_OdB)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(B),A,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 180.26/180.29 ** KEPT (pick-wt=39): 354 [copy,353,flip.3] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(A)),v_sko__InductTermi__XIT__Xcases__5(A)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(A)))|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(A)),v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 180.26/180.29 ** KEPT (pick-wt=24): 355 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),hAPP(hAPP(hAPP(c_Lambda_Osubst,D),B),C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),D)).
% 180.26/180.29 ** KEPT (pick-wt=25): 357 [copy,356,flip.3] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(A)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(A)))|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(A)),v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 180.26/180.29 ** KEPT (pick-wt=5): 358 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 180.26/180.29 ** KEPT (pick-wt=16): 359 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OVar(E),t_a)))|hBOOL(hAPP(A,hAPP(B,E))).
% 180.26/180.29 Following clause subsumed by 359 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))).
% 180.26/180.29 ** KEPT (pick-wt=7): 360 [] -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(A)),B)).
% 180.26/180.29 ** KEPT (pick-wt=5): 361 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 180.26/180.29 ** KEPT (pick-wt=10): 362 [] hAPP(A,B)=C| -c_Type_Otyping(A,c_Lambda_OdB_OVar(B),C).
% 180.26/180.29 ** KEPT (pick-wt=9): 363 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(A)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 180.26/180.29 ** KEPT (pick-wt=20): 364 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,A),B)),hAPP(hAPP(c_Lambda_Olift,C),B)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),C)).
% 180.26/180.29 ** KEPT (pick-wt=24): 366 [copy,365,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(A,B,C),tc_Lambda_OdB,tc_Lambda_OdB)=C| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 180.26/180.29 ** KEPT (pick-wt=20): 367 [] -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).
% 180.26/180.30 ** KEPT (pick-wt=16): 368 [] -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).
% 180.26/180.30 ** KEPT (pick-wt=16): 369 [] -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).
% 180.26/180.30 ** KEPT (pick-wt=9): 370 [] -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).
% 180.26/180.30 ** KEPT (pick-wt=23): 371 [] -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).
% 180.26/180.30 ** KEPT (pick-wt=20): 372 [] 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.
% 180.26/180.30 ** KEPT (pick-wt=13): 373 [] 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).
% 180.26/180.30 ** KEPT (pick-wt=18): 374 [] 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.
% 180.26/180.30 ** KEPT (pick-wt=18): 375 [] 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.
% 180.26/180.30 ** KEPT (pick-wt=22): 376 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,C,B,tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),C)).
% 180.26/180.30 ** KEPT (pick-wt=13): 377 [] 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.
% 180.26/180.30 ** KEPT (pick-wt=32): 378 [] c_Type_Otypings(A,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,B,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),C,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),D,tc_Lambda_OdB,tc_Lambda_OdB),E)| -c_Type_Otypings(c_Type_Oshift(A,C,F,tc_Type_Otype),D,E)| -c_Type_Otyping(A,B,F).
% 180.26/180.30 ** KEPT (pick-wt=15): 379 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),C)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=21): 380 [] c_Type_Otypings(c_Type_Oshift(A,B,C,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,B,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),D,tc_Lambda_OdB,tc_Lambda_OdB),E)| -c_Type_Otypings(A,D,E).
% 180.26/180.30 ** KEPT (pick-wt=13): 381 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(A)),B)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=23): 382 [] 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).
% 180.26/180.30 ** KEPT (pick-wt=15): 383 [] 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).
% 180.26/180.30 ** KEPT (pick-wt=13): 384 [] 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).
% 180.26/180.30 ** KEPT (pick-wt=14): 385 [] 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).
% 180.26/180.30 ** KEPT (pick-wt=14): 386 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)))| -c_List_Olistsp(c_InductTermi_OIT,B,tc_Lambda_OdB).
% 180.26/180.30 ** KEPT (pick-wt=34): 387 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B),C,tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(c_InductTermi_OIT,B))| -hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_Lambda_OdB,tc_Lambda_OdB))).
% 180.26/180.30 ** KEPT (pick-wt=18): 388 [] c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),A,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)| -c_List_Olistsp(c_InductTermi_OIT,A,tc_Lambda_OdB).
% 180.26/180.30 ** KEPT (pick-wt=8): 389 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OVar(B)|A=B.
% 180.26/180.30 ** KEPT (pick-wt=18): 390 [] 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.
% 180.26/180.30 ** KEPT (pick-wt=18): 391 [] 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.
% 180.26/180.30 ** KEPT (pick-wt=15): 392 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),c_Lambda_OdB_OVar(B)),C)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 180.26/180.30 ** KEPT (pick-wt=14): 393 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|A=C.
% 180.26/180.30 ** KEPT (pick-wt=14): 394 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|B=D.
% 180.26/180.30 ** KEPT (pick-wt=13): 395 [] 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.
% 180.26/180.30 ** KEPT (pick-wt=8): 396 [] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 180.26/180.30 ** KEPT (pick-wt=12): 397 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,A),B)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 180.26/180.30 ** KEPT (pick-wt=16): 398 [] 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.
% 180.26/180.30 ** KEPT (pick-wt=13): 399 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,A),c_Lambda_OdB_OVar(B))))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 180.26/180.30 ** KEPT (pick-wt=8): 400 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 180.26/180.30 ** KEPT (pick-wt=37): 401 [] -hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))).
% 180.26/180.30 ** KEPT (pick-wt=6): 402 [] class_Orderings_Opreorder(tc_fun(A,B))| -class_Orderings_Opreorder(B).
% 180.26/180.30 ** KEPT (pick-wt=6): 403 [] class_Orderings_Oorder(tc_fun(A,B))| -class_Orderings_Oorder(B).
% 180.26/180.30 ** KEPT (pick-wt=7): 404 [] A=B| -c_fe_qual(A,B,C).
% 180.26/180.30 90 back subsumes 1.
% 180.26/180.30 92 back subsumes 91.
% 180.26/180.30 92 back subsumes 67.
% 180.26/180.30 Following clause subsumed by 279 during input processing: 0 [copy,203,flip.1] c_List_Olist_ONil(A)!=c_List_Olist_OCons(B,C,A).
% 180.26/180.30 250 back subsumes 245.
% 180.26/180.30 Following clause subsumed by 252 during input processing: 0 [copy,251,flip.1] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 180.26/180.30 Following clause subsumed by 251 during input processing: 0 [copy,252,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 180.26/180.30 Following clause subsumed by 203 during input processing: 0 [copy,279,flip.1] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 180.26/180.30 291 back subsumes 244.
% 180.26/180.30 Following clause subsumed by 361 during input processing: 0 [copy,358,flip.1] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 180.26/180.30 Following clause subsumed by 358 during input processing: 0 [copy,361,flip.1] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 180.26/180.30 ** KEPT (pick-wt=15): 440 [copy,383,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).
% 180.26/180.30 ** KEPT (pick-wt=14): 441 [copy,385,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).
% 180.26/180.30 Following clause subsumed by 400 during input processing: 0 [copy,396,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 180.26/180.30 Following clause subsumed by 396 during input processing: 0 [copy,400,flip.1] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 180.26/180.30 Following clause subsumed by 383 during input processing: 0 [copy,440,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).
% 180.26/180.30 Following clause subsumed by 385 during input processing: 0 [copy,441,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).
% 180.26/180.30
% 180.26/180.30 ------------> process sos:
% 180.26/180.30 ** KEPT (pick-wt=3): 442 [] A=A.
% 180.26/180.30 ** KEPT (pick-wt=22): 444 [copy,443,flip.1] c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=6): 445 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat).
% 180.26/180.30 Following clause subsumed by 445 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat).
% 180.26/180.30 Following clause subsumed by 445 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).
% 180.26/180.30 ** KEPT (pick-wt=12): 446 [] c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=13): 448 [copy,447,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)).
% 180.26/180.30 ---> New Demodulator: 449 [new_demod,448] 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)).
% 180.26/180.30 ** KEPT (pick-wt=13): 450 [] 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)).
% 180.26/180.30 ---> New Demodulator: 451 [new_demod,450] 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)).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,451] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,449] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 180.26/180.30 ** KEPT (pick-wt=10): 452 [] c_HOL_Oord__class_Oless(A,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=10): 453 [] c_HOL_Oord__class_Oless(A,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A)),tc_nat).
% 180.26/180.30 Following clause subsumed by 452 during input processing: 0 [] c_HOL_Oord__class_Oless(A,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=15): 454 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ominus__class_Ominus(B,A,tc_nat))=B|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=6): 456 [copy,455,flip.1] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(tc_nat).
% 180.26/180.30 ---> New Demodulator: 457 [new_demod,456] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=29): 458 [] c_List_Otake(c_Int_Onumber__class_Onumber__of(A,tc_nat),c_List_Olist_OCons(B,C,D),D)=c_List_Olist_OCons(B,c_List_Otake(c_HOL_Ominus__class_Ominus(c_Int_Onumber__class_Onumber__of(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),C,D),D)|c_Int_Onumber__class_Onumber__of(A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=10): 459 [] c_Suc(A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)).
% 180.26/180.30 ---> New Demodulator: 460 [new_demod,459] c_Suc(A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)).
% 180.26/180.30 ** KEPT (pick-wt=15): 462 [copy,461,demod,460] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A).
% 180.26/180.30 ** KEPT (pick-wt=21): 464 [copy,463,demod,460] c_List_Otake(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),c_List_Olist_OCons(B,C,D),D)=c_List_Olist_OCons(B,c_List_Otake(A,C,D),D).
% 180.26/180.30 ---> New Demodulator: 465 [new_demod,464] c_List_Otake(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),c_List_Olist_OCons(B,C,D),D)=c_List_Olist_OCons(B,c_List_Otake(A,C,D),D).
% 180.26/180.30 ** KEPT (pick-wt=23): 467 [copy,466,demod,460] c_List_Olist__update(c_List_Olist_OCons(A,B,C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)),E,C)=c_List_Olist_OCons(A,c_List_Olist__update(B,D,E,C),C).
% 180.26/180.30 ** KEPT (pick-wt=27): 469 [copy,468,demod,460] c_Type_Oshift(c_Type_Oshift(A,B,C,D),c_HOL_Ozero__class_Ozero(tc_nat),E,D)=c_Type_Oshift(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),E,D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)),C,D).
% 180.26/180.30 ** KEPT (pick-wt=10): 471 [copy,470,demod,460] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 180.26/180.30 Following clause subsumed by 471 during input processing: 0 [demod,460] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=21): 473 [copy,472,demod,460,460] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)=c_HOL_Ominus__class_Ominus(A,B,tc_nat).
% 180.26/180.30 ---> New Demodulator: 474 [new_demod,473] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)=c_HOL_Ominus__class_Ominus(A,B,tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=19): 476 [copy,475,demod,460] c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),B,C)=hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(A,B,C)),C).
% 180.26/180.30 ** KEPT (pick-wt=13): 478 [copy,477,demod,460] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 180.26/180.30 ---> New Demodulator: 479 [new_demod,478] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 180.26/180.30 ** KEPT (pick-wt=25): 481 [copy,480,demod,460,460] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_HOL_Oone__class_Oone(tc_nat)).
% 180.26/180.30 ** KEPT (pick-wt=25): 483 [copy,482,demod,460,460,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_HOL_Oone__class_Oone(tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))).
% 180.26/180.30 ---> New Demodulator: 484 [new_demod,483] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_HOL_Oone__class_Oone(tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))).
% 180.26/180.30 ** KEPT (pick-wt=13): 486 [copy,485,demod,460] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=17): 487 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=25): 489 [copy,488,demod,460,460] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))).
% 180.26/180.30 ** KEPT (pick-wt=19): 490 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat)=c_HOL_Ominus__class_Ominus(A,C,tc_nat).
% 180.26/180.30 ---> New Demodulator: 491 [new_demod,490] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat)=c_HOL_Ominus__class_Ominus(A,C,tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=19): 492 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat)=c_HOL_Ominus__class_Ominus(B,C,tc_nat).
% 180.26/180.30 ---> New Demodulator: 493 [new_demod,492] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat)=c_HOL_Ominus__class_Ominus(B,C,tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=15): 494 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,C,tc_nat),B,tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=27): 496 [copy,495,demod,460,460] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),B,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat).
% 180.26/180.30 ---> New Demodulator: 497 [new_demod,496] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),B,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=19): 499 [copy,498,demod,460] c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),B,tc_nat).
% 180.26/180.30 Following clause subsumed by 471 during input processing: 0 [demod,460,unit_del,265] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=14): 501 [copy,500,demod,460] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=11): 502 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat)=A.
% 180.26/180.30 ---> New Demodulator: 503 [new_demod,502] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat)=A.
% 180.26/180.30 ** KEPT (pick-wt=11): 504 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat)=B.
% 180.26/180.30 ---> New Demodulator: 505 [new_demod,504] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat)=B.
% 180.26/180.30 ** KEPT (pick-wt=7): 506 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 180.26/180.30 ---> New Demodulator: 507 [new_demod,506] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 180.26/180.30 ** KEPT (pick-wt=7): 508 [] c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 180.26/180.30 ---> New Demodulator: 509 [new_demod,508] c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 180.26/180.30 ** KEPT (pick-wt=7): 510 [] c_HOL_Ominus__class_Ominus(A,A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=8): 511 [] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.26/180.30 ---> New Demodulator: 512 [new_demod,511] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=20): 514 [copy,513,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).
% 180.26/180.30 ---> New Demodulator: 515 [new_demod,514] 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).
% 180.26/180.30 ** KEPT (pick-wt=17): 516 [] 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).
% 180.26/180.30 ** KEPT (pick-wt=17): 518 [copy,517,flip.1] c_Lambda_OdB_OAbs(c_Lambda_Oliftn(A,B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=c_Lambda_Oliftn(A,c_Lambda_OdB_OAbs(B),C).
% 180.26/180.30 ---> New Demodulator: 519 [new_demod,518] c_Lambda_OdB_OAbs(c_Lambda_Oliftn(A,B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=c_Lambda_Oliftn(A,c_Lambda_OdB_OAbs(B),C).
% 180.26/180.30 ** KEPT (pick-wt=16): 521 [copy,520,flip.1] hAPP(hAPP(hAPP(c_Lambda_Osubst,A),c_Lambda_Oliftn(B,C,c_HOL_Ozero__class_Ozero(tc_nat))),B)=c_Lambda_Osubstn(A,C,B).
% 180.26/180.30 ---> New Demodulator: 522 [new_demod,521] hAPP(hAPP(hAPP(c_Lambda_Osubst,A),c_Lambda_Oliftn(B,C,c_HOL_Ozero__class_Ozero(tc_nat))),B)=c_Lambda_Osubstn(A,C,B).
% 180.26/180.30 ** KEPT (pick-wt=19): 523 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(A)),B)=c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)))|c_HOL_Oord__class_Oless(A,B,tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=23): 524 [] 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)).
% 180.26/180.30 ---> New Demodulator: 525 [new_demod,524] 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)).
% 180.26/180.30 ** KEPT (pick-wt=23): 526 [] 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)).
% 180.26/180.30 ** KEPT (pick-wt=14): 527 [] c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(A,B,C),C)=c_List_Olist_OCons(A,c_List_Olist_ONil(C),C).
% 180.26/180.30 ** KEPT (pick-wt=11): 528 [] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(C,D).
% 180.26/180.30 ** KEPT (pick-wt=5): 529 [] c_List_Olistsp(A,c_List_Olist_ONil(B),B).
% 180.26/180.30 ** KEPT (pick-wt=8): 530 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),C)).
% 180.26/180.30 Following clause subsumed by 530 during input processing: 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),C)).
% 180.26/180.30 ** KEPT (pick-wt=8): 531 [] c_List_Otake(A,c_List_Olist_ONil(B),B)=c_List_Olist_ONil(B).
% 180.26/180.30 ---> New Demodulator: 532 [new_demod,531] c_List_Otake(A,c_List_Olist_ONil(B),B)=c_List_Olist_ONil(B).
% 180.26/180.30 ** KEPT (pick-wt=7): 533 [] c_List_Oappend(A,c_List_Olist_ONil(B),B)=A.
% 180.26/180.30 ---> New Demodulator: 534 [new_demod,533] c_List_Oappend(A,c_List_Olist_ONil(B),B)=A.
% 180.26/180.30 ** KEPT (pick-wt=7): 536 [copy,535,flip.1] c_List_Oappend(c_List_Olist_ONil(A),B,A)=B.
% 180.26/180.30 ---> New Demodulator: 537 [new_demod,536] c_List_Oappend(c_List_Olist_ONil(A),B,A)=B.
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,534] A=A.
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,537] B=B.
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,537] A=A.
% 180.26/180.30 ** KEPT (pick-wt=7): 539 [copy,538,flip.1] c_List_Orev(c_List_Orev(A,B),B)=A.
% 180.26/180.30 ---> New Demodulator: 540 [new_demod,539] c_List_Orev(c_List_Orev(A,B),B)=A.
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,540] A=A.
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,540] A=A.
% 180.26/180.30 ** KEPT (pick-wt=17): 542 [copy,541,flip.1] c_Lambda_OdB_OAbs(c_Lambda_Osubstn(A,B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=c_Lambda_Osubstn(c_Lambda_OdB_OAbs(A),B,C).
% 180.26/180.30 ---> New Demodulator: 543 [new_demod,542] c_Lambda_OdB_OAbs(c_Lambda_Osubstn(A,B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=c_Lambda_Osubstn(c_Lambda_OdB_OAbs(A),B,C).
% 180.26/180.30 ** KEPT (pick-wt=13): 544 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 180.26/180.30 ** KEPT (pick-wt=14): 545 [] hAPP(c_Fun_Ocomp(A,B,C,D,E),F)=hAPP(A,hAPP(B,F)).
% 180.26/180.30 ---> New Demodulator: 546 [new_demod,545] hAPP(c_Fun_Ocomp(A,B,C,D,E),F)=hAPP(A,hAPP(B,F)).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,546] hAPP(A,hAPP(B,C))=hAPP(A,hAPP(B,C)).
% 180.26/180.30 ** KEPT (pick-wt=18): 548 [copy,547,demod,460] 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)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))).
% 180.26/180.30 ---> New Demodulator: 549 [new_demod,548] 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)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))).
% 180.26/180.30 ** KEPT (pick-wt=27): 551 [copy,550,demod,460,525] 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)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)))).
% 180.26/180.30 ---> New Demodulator: 552 [new_demod,551] 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)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)))).
% 180.26/180.30 ** KEPT (pick-wt=11): 554 [copy,553,unit_del,265] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 180.26/180.30 ---> New Demodulator: 555 [new_demod,554] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 180.26/180.30 ** KEPT (pick-wt=20): 557 [copy,556,demod,460] c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(A),tc_Lambda_OdB)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))).
% 180.26/180.30 ---> New Demodulator: 558 [new_demod,557] c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(A),tc_Lambda_OdB)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))).
% 180.26/180.30 ** KEPT (pick-wt=30): 560 [copy,559,demod,460,525,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(B,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))))=c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),tc_Lambda_OdB).
% 180.26/180.30 ---> New Demodulator: 561 [new_demod,560] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(B,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))))=c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),tc_Lambda_OdB).
% 180.26/180.30 ** KEPT (pick-wt=23): 562 [] c_List_Otake(A,c_List_Olist_OCons(B,C,D),D)=c_List_Olist_OCons(B,c_List_Otake(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),C,D),D)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=17): 563 [] c_List_Orev(c_List_Olist_OCons(A,B,C),C)=c_List_Oappend(c_List_Orev(B,C),c_List_Olist_OCons(A,c_List_Olist_ONil(C),C),C).
% 180.26/180.30 ** KEPT (pick-wt=13): 564 [] c_List_Orev(c_List_Olist_OCons(A,c_List_Olist_ONil(B),B),B)=c_List_Olist_OCons(A,c_List_Olist_ONil(B),B).
% 180.26/180.30 ---> New Demodulator: 565 [new_demod,564] c_List_Orev(c_List_Olist_OCons(A,c_List_Olist_ONil(B),B),B)=c_List_Olist_OCons(A,c_List_Olist_ONil(B),B).
% 180.26/180.30 ** KEPT (pick-wt=15): 567 [copy,566,flip.1] c_List_Olist_OCons(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 180.26/180.30 ---> New Demodulator: 568 [new_demod,567] c_List_Olist_OCons(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,568] c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C)=c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C).
% 180.26/180.30 ** KEPT (pick-wt=9): 569 [] c_List_Olist__update(c_List_Olist_ONil(A),B,C,A)=c_List_Olist_ONil(A).
% 180.26/180.30 ---> New Demodulator: 570 [new_demod,569] c_List_Olist__update(c_List_Olist_ONil(A),B,C,A)=c_List_Olist_ONil(A).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,570] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,570] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,568] c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,568] c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 180.26/180.30 ** KEPT (pick-wt=17): 571 [] c_List_Orev(c_List_Oappend(c_List_Orev(A,B),c_List_Olist_OCons(C,c_List_Olist_ONil(B),B),B),B)=c_List_Olist_OCons(C,A,B).
% 180.26/180.30 ---> New Demodulator: 572 [new_demod,571] c_List_Orev(c_List_Oappend(c_List_Orev(A,B),c_List_Olist_OCons(C,c_List_Olist_ONil(B),B),B),B)=c_List_Olist_OCons(C,A,B).
% 180.26/180.30 ** KEPT (pick-wt=14): 573 [] c_List_Olist__update(c_List_Olist_OCons(A,B,C),c_HOL_Ozero__class_Ozero(tc_nat),D,C)=c_List_Olist_OCons(D,B,C).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,537] c_List_Olist_OCons(A,B,C)=c_List_Olist_OCons(A,B,C).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,565] c_List_Olist_OCons(A,c_List_Olist_ONil(B),B)=c_List_Olist_OCons(A,c_List_Olist_ONil(B),B).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,534] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 180.26/180.30 ** KEPT (pick-wt=9): 574 [] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(A,B),B)=c_Transitive__Closure_Ortranclp(A,B).
% 180.26/180.30 ---> New Demodulator: 575 [new_demod,574] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(A,B),B)=c_Transitive__Closure_Ortranclp(A,B).
% 180.26/180.30 ** KEPT (pick-wt=7): 576 [] c_List_Orev(c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 180.26/180.30 ---> New Demodulator: 577 [new_demod,576] c_List_Orev(c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 180.26/180.30 ** KEPT (pick-wt=15): 578 [] c_List_Orev(c_List_Oappend(A,B,C),C)=c_List_Oappend(c_List_Orev(B,C),c_List_Orev(A,C),C).
% 180.26/180.30 ---> New Demodulator: 579 [new_demod,578] c_List_Orev(c_List_Oappend(A,B,C),C)=c_List_Oappend(c_List_Orev(B,C),c_List_Orev(A,C),C).
% 180.26/180.30 ** KEPT (pick-wt=9): 580 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=11): 581 [] 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).
% 180.26/180.30 ---> New Demodulator: 582 [new_demod,581] 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).
% 180.26/180.30 ** KEPT (pick-wt=9): 584 [copy,583,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 180.26/180.30 ---> New Demodulator: 585 [new_demod,584] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 180.26/180.30 ** KEPT (pick-wt=9): 586 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 180.26/180.30 ---> New Demodulator: 587 [new_demod,586] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,585] A=A.
% 180.26/180.30 ** KEPT (pick-wt=16): 588 [] c_Lambda_OdB_OdB__case(A,B,C,hAPP(hAPP(c_Lambda_OdB_OApp,D),E),F)=hAPP(hAPP(B,D),E).
% 180.26/180.30 ** KEPT (pick-wt=30): 590 [copy,589,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).
% 180.26/180.30 ---> New Demodulator: 591 [new_demod,590] 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).
% 180.26/180.30 ** KEPT (pick-wt=20): 593 [copy,592,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).
% 180.26/180.30 ---> New Demodulator: 594 [new_demod,593] 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).
% 180.26/180.30 ** KEPT (pick-wt=21): 596 [copy,595,flip.1] c_List_Oappend(c_List_Omap(A,B,C,D),c_List_Omap(A,E,C,D),D)=c_List_Omap(A,c_List_Oappend(B,E,C),C,D).
% 180.26/180.30 ---> New Demodulator: 597 [new_demod,596] c_List_Oappend(c_List_Omap(A,B,C,D),c_List_Omap(A,E,C,D),D)=c_List_Omap(A,c_List_Oappend(B,E,C),C,D).
% 180.26/180.30 ** KEPT (pick-wt=9): 598 [] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 180.26/180.30 ---> New Demodulator: 599 [new_demod,598] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 180.26/180.30 ** KEPT (pick-wt=15): 600 [] 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).
% 180.26/180.30 ** KEPT (pick-wt=11): 601 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 180.26/180.30 Following clause subsumed by 601 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).
% 180.26/180.30 Following clause subsumed by 601 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 180.26/180.30 ** KEPT (pick-wt=8): 602 [] c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Olist_ONil(B).
% 180.26/180.30 Following clause subsumed by 602 during input processing: 0 [] c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(A,B,C),C)=c_List_Olist_ONil(C).
% 180.26/180.30 ** KEPT (pick-wt=23): 604 [copy,603,flip.1] c_Fun_Ocomp(c_Fun_Ocomp(A,B,C,D,E),F,E,D,G)=c_Fun_Ocomp(A,c_Fun_Ocomp(B,F,E,C,G),C,D,G).
% 180.26/180.30 ---> New Demodulator: 605 [new_demod,604] c_Fun_Ocomp(c_Fun_Ocomp(A,B,C,D,E),F,E,D,G)=c_Fun_Ocomp(A,c_Fun_Ocomp(B,F,E,C,G),C,D,G).
% 180.26/180.30 ** KEPT (pick-wt=18): 606 [] 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)).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,537] c_List_Olist_OCons(B,C,A)=c_List_Olist_OCons(B,C,A).
% 180.26/180.30 ** KEPT (pick-wt=22): 607 [] c_List_Olist__update(c_List_Olist__update(A,B,C,D),E,F,D)=c_List_Olist__update(c_List_Olist__update(A,E,F,D),B,C,D)|B=E.
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,577] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,534] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 180.26/180.30 ** KEPT (pick-wt=19): 609 [copy,608,flip.1] c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(A)),B).
% 180.26/180.30 ---> New Demodulator: 610 [new_demod,609] c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(A)),B).
% 180.26/180.30 ** KEPT (pick-wt=15): 611 [] c_List_Olist__update(c_List_Olist__update(A,B,C,D),B,E,D)=c_List_Olist__update(A,B,E,D).
% 180.26/180.30 ---> New Demodulator: 612 [new_demod,611] c_List_Olist__update(c_List_Olist__update(A,B,C,D),B,E,D)=c_List_Olist__update(A,B,E,D).
% 180.26/180.30 ** KEPT (pick-wt=15): 613 [] c_List_Oappend(c_List_Oappend(A,B,C),D,C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 180.26/180.30 ---> New Demodulator: 614 [new_demod,613] c_List_Oappend(c_List_Oappend(A,B,C),D,C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,614] c_List_Oappend(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(A,c_List_Oappend(B,C,D),D).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,614] c_List_Oappend(A,c_List_Oappend(B,D,C),C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,614] c_List_Oappend(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(A,c_List_Oappend(B,C,D),D).
% 180.26/180.30 ** KEPT (pick-wt=15): 615 [] c_List_Orev(c_List_Omap(A,B,C,D),D)=c_List_Omap(A,c_List_Orev(B,C),C,D).
% 180.26/180.30 ---> New Demodulator: 616 [new_demod,615] c_List_Orev(c_List_Omap(A,B,C,D),D)=c_List_Omap(A,c_List_Orev(B,C),C,D).
% 180.26/180.30 ** KEPT (pick-wt=17): 617 [] c_List_Otake(A,c_List_Omap(B,C,D,E),E)=c_List_Omap(B,c_List_Otake(A,C,D),D,E).
% 180.26/180.30 ---> New Demodulator: 618 [new_demod,617] c_List_Otake(A,c_List_Omap(B,C,D,E),E)=c_List_Omap(B,c_List_Otake(A,C,D),D,E).
% 180.26/180.30 ** KEPT (pick-wt=9): 619 [] c_List_Omap(A,c_List_Olist_ONil(B),B,C)=c_List_Olist_ONil(C).
% 180.26/180.30 ** KEPT (pick-wt=20): 621 [copy,620,flip.1] c_List_Omap(c_Fun_Ocomp(A,B,C,D,E),F,E,D)=c_List_Omap(A,c_List_Omap(B,F,E,C),C,D).
% 180.26/180.30 ---> New Demodulator: 622 [new_demod,621] c_List_Omap(c_Fun_Ocomp(A,B,C,D,E),F,E,D)=c_List_Omap(A,c_List_Omap(B,F,E,C),C,D).
% 180.26/180.30 ** KEPT (pick-wt=19): 624 [copy,623,flip.1] c_List_Olist_OCons(hAPP(A,B),c_List_Omap(A,C,D,E),E)=c_List_Omap(A,c_List_Olist_OCons(B,C,D),D,E).
% 180.26/180.30 ---> New Demodulator: 625 [new_demod,624] c_List_Olist_OCons(hAPP(A,B),c_List_Omap(A,C,D,E),E)=c_List_Omap(A,c_List_Olist_OCons(B,C,D),D,E).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,625] c_List_Omap(A,c_List_Olist_OCons(B,C,D),D,E)=c_List_Omap(A,c_List_Olist_OCons(B,C,D),D,E).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,625] c_List_Omap(A,c_List_Olist_OCons(B,C,D),D,E)=c_List_Omap(A,c_List_Olist_OCons(B,C,D),D,E).
% 180.26/180.30 ** KEPT (pick-wt=21): 626 [] c_List_Omap(A,c_List_Olist__update(B,C,D,E),E,F)=c_List_Olist__update(c_List_Omap(A,B,E,F),C,hAPP(A,D),F).
% 180.26/180.30 ** KEPT (pick-wt=9): 627 [] c_List_Olist_ONil(A)=c_List_Omap(B,c_List_Olist_ONil(C),C,A).
% 180.26/180.30 ** KEPT (pick-wt=11): 629 [copy,628,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).
% 180.26/180.30 ---> New Demodulator: 630 [new_demod,629] 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).
% 180.26/180.30 ** KEPT (pick-wt=10): 632 [copy,631,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(A),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A.
% 180.26/180.30 ---> New Demodulator: 633 [new_demod,632] c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(A),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A.
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,630] c_Lambda_OdB_OAbs(A)=c_Lambda_OdB_OAbs(A).
% 180.26/180.30 ** KEPT (pick-wt=9): 634 [] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 180.26/180.30 ---> New Demodulator: 635 [new_demod,634] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 180.26/180.30 ** KEPT (pick-wt=20): 636 [] 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).
% 180.26/180.30 ** KEPT (pick-wt=21): 637 [] 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).
% 180.26/180.30 ** KEPT (pick-wt=28): 639 [copy,638,flip.1] c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,A),hAPP(hAPP(c_Lambda_Olift,B),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(A)),B),C).
% 180.26/180.30 ---> New Demodulator: 640 [new_demod,639] c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,A),hAPP(hAPP(c_Lambda_Olift,B),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(A)),B),C).
% 180.26/180.30 ** KEPT (pick-wt=11): 641 [] c_Lambda_OdB_OdB__rec(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 180.26/180.30 ** KEPT (pick-wt=11): 642 [] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 180.26/180.30 ** KEPT (pick-wt=7): 643 [] c_Type_Otyping(A,c_Lambda_OdB_OVar(B),hAPP(A,B)).
% 180.26/180.30 ** KEPT (pick-wt=4): 644 [] hBOOL(hAPP(c_InductTermi_OIT,v_ua______)).
% 180.26/180.30 ** KEPT (pick-wt=18): 645 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B)),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat)))).
% 180.26/180.30 ** KEPT (pick-wt=3): 646 [] v_n____=v_i____.
% 180.26/180.30 ---> New Demodulator: 647 [new_demod,646] v_n____=v_i____.
% 180.26/180.30 ** KEPT (pick-wt=14): 649 [copy,648,flip.1] hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 180.26/180.30 ---> New Demodulator: 650 [new_demod,649] hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 180.26/180.30 ** KEPT (pick-wt=7): 651 [] c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(A),tc_Lambda_OdB)=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.26/180.30 ---> New Demodulator: 652 [new_demod,651] c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(A),tc_Lambda_OdB)=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=6): 653 [] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(A))=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.26/180.30 ---> New Demodulator: 654 [new_demod,653] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(A))=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,635] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)=hAPP(hAPP(c_Lambda_OdB_OApp,A),B).
% 180.26/180.30 ** KEPT (pick-wt=18): 655 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),C)=c_Lambda_OdB_OVar(A)|A=C|c_HOL_Oord__class_Oless(C,A,tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=10): 657 [copy,656,unit_del,265] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),A)=B.
% 180.26/180.30 ---> New Demodulator: 658 [new_demod,657] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),A)=B.
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,635] c_Lambda_OdB_OVar(A)=c_Lambda_OdB_OVar(A).
% 180.26/180.30 ** KEPT (pick-wt=29): 659 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),C),D)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),C),D)),hAPP(hAPP(hAPP(c_Lambda_Osubst,B),C),D)).
% 180.26/180.30 Following clause subsumed by 442 during input processing: 0 [demod,658] B=B.
% 180.26/180.30 ** KEPT (pick-wt=30): 660 [] hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,A),C),c_List_Omap(c_COMBC(c_Lambda_Olift,C,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),B,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 180.26/180.30 ---> New Demodulator: 661 [new_demod,660] hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,A),C),c_List_Omap(c_COMBC(c_Lambda_Olift,C,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),B,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 180.26/180.30 ** KEPT (pick-wt=5): 662 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(A))).
% 180.26/180.30 ** KEPT (pick-wt=23): 663 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),C)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,A),C)),hAPP(hAPP(c_Lambda_Olift,B),C)).
% 180.26/180.30 ** KEPT (pick-wt=41): 664 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C),D)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),C),D),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,C,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),D,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),B,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 180.26/180.30 ** KEPT (pick-wt=14): 665 [] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 180.26/180.30 ** KEPT (pick-wt=4): 666 [] hBOOL(hAPP(c_InductTermi_OIT,v_u____)).
% 180.26/180.30 ** KEPT (pick-wt=13): 667 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),B)),C),B)=A.
% 180.26/180.30 ---> New Demodulator: 668 [new_demod,667] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),B)),C),B)=A.
% 180.26/180.30 ** KEPT (pick-wt=30): 669 [] c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB).
% 180.26/180.30 ** KEPT (pick-wt=2): 670 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=2): 671 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=2): 672 [] class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=2): 673 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=2): 674 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 180.26/180.30 ** KEPT (pick-wt=2): 675 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=2): 676 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=2): 677 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=2): 678 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=2): 679 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=2): 680 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=2): 681 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=2): 682 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=2): 683 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=2): 684 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=2): 685 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=2): 686 [] class_OrderedGroup_Omonoid__mult(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=2): 687 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=2): 688 [] class_Nat_Osemiring__char__0(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=2): 689 [] class_Orderings_Opreorder(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=2): 690 [] class_Orderings_Olinorder(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=2): 691 [] class_Orderings_Oorder(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=2): 692 [] class_Power_Opower(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=2): 693 [] class_Int_Onumber(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=2): 694 [] class_Orderings_Opreorder(tc_bool).
% 180.26/180.31 ** KEPT (pick-wt=2): 695 [] class_Orderings_Oorder(tc_bool).
% 180.26/180.31 ** KEPT (pick-wt=2): 696 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 697 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 698 [] class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 699 [] class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 700 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 701 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 702 [] class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 703 [] class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 704 [] class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 705 [] class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 706 [] class_Ring__and__Field_Oordered__semidom(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 707 [] class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 708 [] class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 709 [] class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 710 [] class_Ring__and__Field_Ozero__ne_q__one(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 711 [] class_Ring__and__Field_Oordered__idom(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 712 [] class_OrderedGroup_Osemigroup__add(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 713 [] class_Ring__and__Field_Osemiring__1(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 714 [] class_Ring__and__Field_Osemiring__0(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 715 [] class_OrderedGroup_Oab__group__add(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 716 [] class_Ring__and__Field_Omult__zero(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 717 [] class_OrderedGroup_Omonoid__mult(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 718 [] class_OrderedGroup_Omonoid__add(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 719 [] class_OrderedGroup_Ogroup__add(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 720 [] class_Ring__and__Field_Oidom(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 721 [] class_Nat_Osemiring__char__0(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 722 [] class_Orderings_Opreorder(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 723 [] class_Orderings_Olinorder(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 724 [] class_Orderings_Oorder(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 725 [] class_Int_Oring__char__0(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 726 [] class_Int_Onumber__ring(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 727 [] class_Power_Opower(tc_Int_Oint).
% 180.26/180.31 ** KEPT (pick-wt=2): 728 [] class_Int_Onumber(tc_Int_Oint).
% 180.26/180.31 Following clause subsumed by 665 during input processing: 0 [] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 180.26/180.31 ** KEPT (pick-wt=13): 729 [] c_COMBB(A,B,C,D,E,F)=hAPP(A,hAPP(B,C)).
% 180.26/180.31 ** KEPT (pick-wt=4): 730 [] c_fe_qual(A,A,B).
% 180.26/180.31 Following clause subsumed by 442 during input processing: 0 [copy,442,flip.1] A=A.
% 180.26/180.31 442 back subsumes 439.
% 180.26/180.31 442 back subsumes 432.
% 180.26/180.31 442 back subsumes 431.
% 180.26/180.31 442 back subsumes 427.
% 180.26/180.31 442 back subsumes 421.
% 180.26/180.31 442 back subsumes 420.
% 180.26/180.31 442 back subsumes 417.
% 180.26/180.31 ** KEPT (pick-wt=12): 731 [copy,446,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat).
% 180.26/180.31 >>>> Starting back demodulation with 449.
% 180.26/180.31 >>>> Starting back demodulation with 451.
% 180.26/180.31 >>>> Starting back demodulation with 457.
% 180.26/180.31 >> back demodulating 450 with 457.
% 180.26/180.31 >> back demodulating 448 with 457.
% 180.26/180.31 >> back demodulating 416 with 457.
% 180.26/180.31 >> back demodulating 415 with 457.
% 180.26/180.31 >> back demodulating 414 with 457.
% 180.26/180.31 >> back demodulating 413 with 457.
% 180.26/180.31 >> back demodulating 61 with 457.
% 180.26/180.31 >> back demodulating 60 with 457.
% 180.26/180.31 >> back demodulating 59 with 457.
% 180.26/180.31 >> back demodulating 58 with 457.
% 180.26/180.31 >> back demodulating 57 with 457.
% 180.26/180.31 >> back demodulating 56 with 457.
% 180.26/180.31 >> back demodulating 55 with 457.
% 180.26/180.31 >> back demodulating 54 with 457.
% 180.26/180.31 >> back demodulating 46 with 457.
% 180.26/180.31 >> back demodulating 16 with 457.
% 180.26/180.31 >>>> Starting back demodulation with 460.
% 180.26/180.31 >> back demodulating 456 with 460.
% 180.26/180.31 >> back demodulating 453 with 460.
% 180.26/180.31 >> back demodulating 452 with 460.
% 180.26/180.31 >> back demodulating 445 with 460.
% 180.26/180.31 >> back demodulating 444 with 460.
% 180.26/180.31 >> back demodulating 182 with 460.
% 180.26/180.31 >> back demodulating 175 with 460.
% 180.26/180.31 >> back demodulating 124 with 460.
% 180.26/180.31 >> back demodulating 122 with 460.
% 180.26/180.31 >> back demodulating 121 with 460.
% 180.26/180.31 >> back demodulating 112 with 460.
% 180.26/180.31 >> back demodulating 103 with 460.
% 180.26/180.31 >> back demodulating 102 with 460.
% 180.26/180.31 >> back demodulating 100 with 460.
% 180.26/180.31 >> back demodulating 99 with 460.
% 180.26/180.31 >> back demodulating 98 with 460.
% 180.26/180.31 >> back demodulating 94 with 460.
% 180.26/180.31 >> back demodulating 85 with 460.
% 180.26/180.31 >> back demodulating 84 with 460.
% 180.26/180.31 >> back demodulating 83 with 460.
% 180.26/180.31 >> back demodulating 75 with 460.
% 180.26/180.31 >> back demodulating 68 with 460.
% 180.26/180.31 >> back demodulating 53 with 460.
% 180.26/180.31 >> back demodulating 26 with 460.
% 180.26/180.31 >> back demodulating 21 with 460.
% 180.26/180.31 >> back demodulating 15 with 460.
% 180.26/180.31 >> back demodulating 14 with 460.
% 180.26/180.31 >> back demodulating 4 with 460.
% 180.26/180.31 Following clause subsumed by 544 during input processing: 0 [copy,462,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)).
% 180.26/180.31 >>>> Starting back demodulation with 465.
% 180.26/180.31 ** KEPT (pick-wt=23): 762 [copy,467,flip.1] c_List_Olist_OCons(A,c_List_Olist__update(B,C,D,E),E)=c_List_Olist__update(c_List_Olist_OCons(A,B,E),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),D,E).
% 180.26/180.31 ** KEPT (pick-wt=27): 763 [copy,469,flip.1] c_Type_Oshift(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),B,C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)),E,C)=c_Type_Oshift(c_Type_Oshift(A,D,E,C),c_HOL_Ozero__class_Ozero(tc_nat),B,C).
% 180.26/180.31 >>>> Starting back demodulation with 474.
% 180.26/180.31 ** KEPT (pick-wt=19): 764 [copy,476,flip.1] hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(A,B,C)),C)=c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),B,C).
% 180.26/180.31 >>>> Starting back demodulation with 479.
% 180.26/180.31 ** KEPT (pick-wt=25): 765 [copy,481,flip.1,demod,525,525] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),B)).
% 180.26/180.31 >>>> Starting back demodulation with 484.
% 180.26/180.31 >> back demodulating 481 with 484.
% 180.26/180.31 ** KEPT (pick-wt=17): 767 [copy,487,flip.1] c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat).
% 180.26/180.31 Following clause subsumed by 765 during input processing: 0 [copy,489,flip.1,demod,525] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),B)).
% 180.26/180.31 >>>> Starting back demodulation with 491.
% 180.26/180.31 >> back demodulating 473 with 491.
% 180.26/180.31 >>>> Starting back demodulation with 493.
% 180.26/180.31 Following clause subsumed by 494 during input processing: 0 [copy,494,flip.1] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,C,tc_nat),B,tc_nat).
% 180.26/180.31 >>>> Starting back demodulation with 497.
% 180.26/180.31 ** KEPT (pick-wt=19): 768 [copy,499,flip.1] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),B,tc_nat)=c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 180.26/180.31 >>>> Starting back demodulation with 503.
% 180.26/180.31 >> back demodulating 478 with 503.
% 180.26/180.31 >>>> Starting back demodulation with 505.
% 180.26/180.31 >> back demodulating 88 with 505.
% 180.26/180.31 >>>> Starting back demodulation with 507.
% 180.26/180.31 >>>> Starting back demodulation with 509.
% 180.26/180.31 ** KEPT (pick-wt=7): 769 [copy,510,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ominus__class_Ominus(A,A,tc_nat).
% 180.26/180.31 >>>> Starting back demodulation with 512.
% 180.26/180.31 >>>> Starting back demodulation with 515.
% 180.26/180.31 >>>> Starting back demodulation with 519.
% 180.26/180.31 >>>> Starting back demodulation with 522.
% 180.26/180.31 >>>> Starting back demodulation with 525.
% 180.26/180.31 >> back demodulating 489 with 525.
% 180.26/180.31 >> back demodulating 483 with 525.
% 180.26/180.31 Following clause subsumed by 526 during input processing: 0 [copy,526,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)).
% 180.26/180.31 ** KEPT (pick-wt=14): 770 [copy,527,flip.1] c_List_Olist_OCons(A,c_List_Olist_ONil(B),B)=c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(A,C,B),B).
% 180.26/180.31 ** KEPT (pick-wt=11): 771 [copy,528,flip.1] hAPP(A,B)=c_Lambda_OdB_OdB__case(C,D,A,c_Lambda_OdB_OAbs(B),E).
% 180.26/180.31 >>>> Starting back demodulation with 532.
% 180.26/180.31 >>>> Starting back demodulation with 534.
% 180.26/180.31 >>>> Starting back demodulation with 537.
% 180.26/180.31 >>>> Starting back demodulation with 540.
% 180.26/180.31 >>>> Starting back demodulation with 543.
% 180.26/180.31 Following clause subsumed by 544 during input processing: 0 [copy,544,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 180.26/180.31 544 back subsumes 462.
% 180.26/180.31 >>>> Starting back demodulation with 546.
% 180.26/180.31 >> back demodulating 322 with 546.
% 180.26/180.31 >>>> Starting back demodulation with 549.
% 180.26/180.31 >>>> Starting back demodulation with 552.
% 180.26/180.31 >>>> Starting back demodulation with 555.
% 180.26/180.31 >>>> Starting back demodulation with 558.
% 180.26/180.31 >>>> Starting back demodulation with 561.
% 180.26/180.31 562 back subsumes 458.
% 180.26/180.31 ** KEPT (pick-wt=17): 772 [copy,563,flip.1] c_List_Oappend(c_List_Orev(A,B),c_List_Olist_OCons(C,c_List_Olist_ONil(B),B),B)=c_List_Orev(c_List_Olist_OCons(C,A,B),B).
% 180.26/180.31 >>>> Starting back demodulation with 565.
% 180.26/180.31 >>>> Starting back demodulation with 568.
% 180.26/180.31 >>>> Starting back demodulation with 570.
% 180.26/180.31 >>>> Starting back demodulation with 572.
% 180.26/180.31 ** KEPT (pick-wt=14): 773 [copy,573,flip.1] c_List_Olist_OCons(A,B,C)=c_List_Olist__update(c_List_Olist_OCons(D,B,C),c_HOL_Ozero__class_Ozero(tc_nat),A,C).
% 180.26/180.31 >>>> Starting back demodulation with 575.
% 180.26/180.31 >>>> Starting back demodulation with 577.
% 180.26/180.31 >>>> Starting back demodulation with 579.
% 180.26/180.31 >> back demodulating 571 with 579.
% 180.26/180.31 >>>> Starting back demodulation with 582.
% 180.26/180.31 >>>> Starting back demodulation with 585.
% 180.26/180.31 >> back demodulating 581 with 585.
% 180.26/180.31 >>>> Starting back demodulation with 587.
% 180.26/180.31 >> back demodulating 560 with 587.
% 180.26/180.31 >> back demodulating 557 with 587.
% 180.26/180.31 >> back demodulating 551 with 587.
% 180.26/180.31 >> back demodulating 548 with 587.
% 180.26/180.31 ** KEPT (pick-wt=16): 783 [copy,588,flip.1] hAPP(hAPP(A,B),C)=c_Lambda_OdB_OdB__case(D,A,E,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),F).
% 180.26/180.31 >>>> Starting back demodulation with 591.
% 180.26/180.31 >>>> Starting back demodulation with 594.
% 180.26/180.31 >>>> Starting back demodulation with 597.
% 180.26/180.31 >>>> Starting back demodulation with 599.
% 180.26/180.31 ** KEPT (pick-wt=8): 784 [copy,602,flip.1] c_List_Olist_ONil(A)=c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),B,A).
% 180.26/180.31 >>>> Starting back demodulation with 605.
% 180.26/180.31 ** KEPT (pick-wt=18): 785 [copy,606,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).
% 180.26/180.31 >>>> Starting back demodulation with 610.
% 180.26/180.31 >>>> Starting back demodulation with 612.
% 180.26/180.31 >>>> Starting back demodulation with 614.
% 180.26/180.31 >>>> Starting back demodulation with 616.
% 180.26/180.31 >>>> Starting back demodulation with 618.
% 180.26/180.31 Following clause subsumed by 627 during input processing: 0 [copy,619,flip.1] c_List_Olist_ONil(A)=c_List_Omap(B,c_List_Olist_ONil(C),C,A).
% 180.26/180.31 >>>> Starting back demodulation with 622.
% 180.26/180.31 >>>> Starting back demodulation with 625.
% 180.26/180.31 ** KEPT (pick-wt=21): 786 [copy,626,flip.1] c_List_Olist__update(c_List_Omap(A,B,C,D),E,hAPP(A,F),D)=c_List_Omap(A,c_List_Olist__update(B,E,F,C),C,D).
% 180.26/180.31 Following clause subsumed by 619 during input processing: 0 [copy,627,flip.1] c_List_Omap(A,c_List_Olist_ONil(B),B,C)=c_List_Olist_ONil(C).
% 180.26/180.31 >>>> Starting back demodulation with 630.
% 180.26/180.31 >>>> Starting back demodulation with 633.
% 180.26/180.31 >>>> Starting back demodulation with 635.
% 180.26/180.31 >> back demodulating 629 with 635.
% 180.26/180.31 >> back demodulating 372 with 635.
% 180.26/180.31 ** KEPT (pick-wt=20): 787 [copy,636,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).
% 180.26/180.31 ** KEPT (pick-wt=21): 788 [copy,637,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).
% 180.26/180.31 >>>> Starting back demodulation with 640.
% 180.26/180.31 ** KEPT (pick-wt=11): 789 [copy,641,flip.1] hAPP(A,B)=c_Lambda_OdB_OdB__rec(A,C,D,c_Lambda_OdB_OVar(B),E).
% 180.26/180.31 ** KEPT (pick-wt=11): 790 [copy,642,flip.1] hAPP(A,B)=c_Lambda_OdB_OdB__case(A,C,D,c_Lambda_OdB_OVar(B),E).
% 180.26/180.31 >>>> Starting back demodulation with 647.
% 180.26/180.31 >>>> Starting back demodulation with 650.
% 180.26/180.31 >> back demodulating 645 with 650.
% 180.26/180.31 >> back demodulating 387 with 650.
% 180.26/180.31 >> back demodulating 354 with 650.
% 180.26/180.31 >> back demodulating 274 with 650.
% 180.26/180.31 >> back demodulating 227 with 650.
% 180.26/180.31 >> back demodulating 225 with 650.
% 180.26/180.31 >>>> Starting back demodulation with 652.
% 180.26/180.31 >>>> Starting back demodulation with 654.
% 180.26/180.31 >>>> Starting back demodulation with 658.
% 180.26/180.31 ** KEPT (pick-wt=29): 797 [copy,659,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),hAPP(hAPP(hAPP(c_Lambda_Osubst,D),B),C))=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,A),D)),B),C).
% 180.26/180.31 >>>> Starting back demodulation with 661.
% 180.26/180.31 ** KEPT (pick-wt=23): 798 [copy,663,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,A),B)),hAPP(hAPP(c_Lambda_Olift,C),B))=hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,A),C)),B).
% 180.26/180.31 ** KEPT (pick-wt=41): 799 [copy,664,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,B,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),C,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),D,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,A,D,tc_Lambda_OdB,tc_Lambda_OdB)),B),C).
% 180.26/180.31 ** KEPT (pick-wt=14): 800 [copy,665,flip.1] hAPP(hAPP(A,B),C)=hAPP(c_COMBC(A,C,D,E,F),B).
% 180.26/180.31 >>>> Starting back demodulation with 668.
% 180.26/180.31 ** KEPT (pick-wt=13): 801 [copy,729,flip.1] hAPP(A,hAPP(B,C))=c_COMBB(A,B,C,D,E,F).
% 180.26/180.31 Following clause subsumed by 446 during input processing: 0 [copy,731,flip.1] c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.26/180.31 ** KEPT (pick-wt=10): 802 [copy,749,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)).
% 180.26/180.31 Following clause subsumed by 467 during input processing: 0 [copy,762,flip.1] c_List_Olist__update(c_List_Olist_OCons(A,B,C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)),E,C)=c_List_Olist_OCons(A,c_List_Olist__update(B,D,E,C),C).
% 180.26/180.31 Following clause subsumed by 469 during input processing: 0 [copy,763,flip.1] c_Type_Oshift(c_Type_Oshift(A,B,C,D),c_HOL_Ozero__class_Ozero(tc_nat),E,D)=c_Type_Oshift(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),E,D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)),C,D).
% 180.26/180.31 Following clause subsumed by 476 during input processing: 0 [copy,764,flip.1] c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),B,C)=hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(A,B,C)),C).
% 180.26/180.31 Following clause subsumed by 766 during input processing: 0 [copy,765,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))).
% 180.26/180.31 Following clause subsumed by 765 during input processing: 0 [copy,766,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),B)).
% 180.26/180.31 Following clause subsumed by 487 during input processing: 0 [copy,767,flip.1] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat).
% 180.26/180.31 Following clause subsumed by 499 during input processing: 0 [copy,768,flip.1] c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),B,tc_nat).
% 180.26/180.31 Following clause subsumed by 510 during input processing: 0 [copy,769,flip.1] c_HOL_Ominus__class_Ominus(A,A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 180.26/180.31 Following clause subsumed by 527 during input processing: 0 [copy,770,flip.1] c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(A,B,C),C)=c_List_Olist_OCons(A,c_List_Olist_ONil(C),C).
% 180.26/180.31 Following clause subsumed by 528 during input processing: 0 [copy,771,flip.1] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(C,D).
% 180.26/180.31 Following clause subsumed by 563 during input processing: 0 [copy,772,flip.1] c_List_Orev(c_List_Olist_OCons(A,B,C),C)=c_List_Oappend(c_List_Orev(B,C),c_List_Olist_OCons(A,c_List_Olist_ONil(C),C),C).
% 180.26/180.31 Following clause subsumed by 573 during input processing: 0 [copy,773,flip.1] c_List_Olist__update(c_List_Olist_OCons(A,B,C),c_HOL_Ozero__class_Ozero(tc_nat),D,C)=c_List_Olist_OCons(D,B,C).
% 180.26/180.31 ** KEPT (pick-wt=13): 803 [copy,774,flip.1] c_List_Olist_OCons(A,B,C)=c_List_Oappend(c_List_Olist_OCons(A,c_List_Olist_ONil(C),C),B,C).
% 180.26/180.31 >>>> Starting back demodulation with 776.
% 180.26/180.31 >>>> Starting back demodulation with 778.
% 180.26/180.31 >>>> Starting back demodulation with 780.
% 180.26/180.31 >>>> Starting back demodulation with 782.
% 180.26/180.31 Following clause subsumed by 588 during input processing: 0 [copy,783,flip.1] c_Lambda_OdB_OdB__case(A,B,C,hAPP(hAPP(c_Lambda_OdB_OApp,D),E),F)=hAPP(hAPP(B,D),E).
% 180.26/180.31 Following clause subsumed by 602 during input processing: 0 [copy,784,flip.1] c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Olist_ONil(B).
% 180.26/180.31 Following clause subsumed by 606 during input processing: 0 [copy,785,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)).
% 180.26/180.31 Following clause subsumed by 626 during input processing: 0 [copy,786,flip.1] c_List_Omap(A,c_List_Olist__update(B,C,D,E),E,F)=c_List_Olist__update(c_List_Omap(A,B,E,F),C,hAPP(A,D),F).
% 180.26/180.31 Following clause subsumed by 636 during input processing: 0 [copy,787,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).
% 180.26/180.31 Following clause subsumed by 637 during input processing: 0 [copy,788,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).
% 180.26/180.31 Following clause subsumed by 641 during input processing: 0 [copy,789,flip.1] c_Lambda_OdB_OdB__rec(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 180.26/180.31 Following clause subsumed by 642 during input processing: 0 [copy,790,flip.1] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 181.29/181.39 Following clause subsumed by 659 during input processing: 0 [copy,797,flip.1] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),C),D)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),C),D)),hAPP(hAPP(hAPP(c_Lambda_Osubst,B),C),D)).
% 181.29/181.39 Following clause subsumed by 663 during input processing: 0 [copy,798,flip.1] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),C)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,A),C)),hAPP(hAPP(c_Lambda_Olift,B),C)).
% 181.29/181.39 Following clause subsumed by 664 during input processing: 0 [copy,799,flip.1] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C),D)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),C),D),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,C,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),D,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),B,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 181.29/181.39 Following clause subsumed by 665 during input processing: 0 [copy,800,flip.1] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 181.29/181.39 Following clause subsumed by 729 during input processing: 0 [copy,801,flip.1] c_COMBB(A,B,C,D,E,F)=hAPP(A,hAPP(B,C)).
% 181.29/181.39 Following clause subsumed by 749 during input processing: 0 [copy,802,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))!=c_HOL_Ozero__class_Ozero(tc_nat).
% 181.29/181.39 Following clause subsumed by 774 during input processing: 0 [copy,803,flip.1] c_List_Oappend(c_List_Olist_OCons(A,c_List_Olist_ONil(B),B),C,B)=c_List_Olist_OCons(A,C,B).
% 181.29/181.39
% 181.29/181.39 ======= end of input processing =======
% 181.29/181.39
% 181.29/181.39 =========== start of search ===========
% 181.29/181.39
% 181.29/181.39
% 181.29/181.39 Resetting weight limit to 2.
% 181.29/181.39
% 181.29/181.39
% 181.29/181.39 Resetting weight limit to 2.
% 181.29/181.39
% 181.29/181.39 sos_size=228
% 181.29/181.39
% 181.29/181.39 Search stopped in tp_alloc by max_mem option.
% 181.29/181.39
% 181.29/181.39 Search stopped in tp_alloc by max_mem option.
% 181.29/181.39
% 181.29/181.39 ============ end of search ============
% 181.29/181.39
% 181.29/181.39 -------------- statistics -------------
% 181.29/181.39 clauses given 184
% 181.29/181.39 clauses generated 103286
% 181.29/181.39 clauses kept 671
% 181.29/181.39 clauses forward subsumed 166
% 181.29/181.39 clauses back subsumed 14
% 181.29/181.39 Kbytes malloced 11718
% 181.29/181.39
% 181.29/181.39 ----------- times (seconds) -----------
% 181.29/181.39 user CPU time 1.16 (0 hr, 0 min, 1 sec)
% 181.29/181.39 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 181.29/181.39 wall-clock time 181 (0 hr, 3 min, 1 sec)
% 181.29/181.39
% 181.29/181.39 Process 29114 finished Wed Jul 27 09:26:54 2022
% 181.29/181.39 Otter interrupted
% 181.29/181.39 PROOF NOT FOUND
%------------------------------------------------------------------------------