TSTP Solution File: LCL836-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL836-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:05:35 EDT 2022
% Result : Unknown 271.31s 271.38s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL836-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 09:49:03 EDT 2022
% 0.13/0.33 % CPUTime :
% 270.53/270.70 ----- Otter 3.3f, August 2004 -----
% 270.53/270.70 The process was started by sandbox on n023.cluster.edu,
% 270.53/270.70 Wed Jul 27 09:49:03 2022
% 270.53/270.70 The command was "./otter". The process ID is 17782.
% 270.53/270.70
% 270.53/270.70 set(prolog_style_variables).
% 270.53/270.70 set(auto).
% 270.53/270.70 dependent: set(auto1).
% 270.53/270.70 dependent: set(process_input).
% 270.53/270.70 dependent: clear(print_kept).
% 270.53/270.70 dependent: clear(print_new_demod).
% 270.53/270.70 dependent: clear(print_back_demod).
% 270.53/270.70 dependent: clear(print_back_sub).
% 270.53/270.70 dependent: set(control_memory).
% 270.53/270.70 dependent: assign(max_mem, 12000).
% 270.53/270.70 dependent: assign(pick_given_ratio, 4).
% 270.53/270.70 dependent: assign(stats_level, 1).
% 270.53/270.70 dependent: assign(max_seconds, 10800).
% 270.53/270.70 clear(print_given).
% 270.53/270.70
% 270.53/270.70 list(usable).
% 270.53/270.70 0 [] A=A.
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(V_x,V_y,T_a)=V_x| -c_lesse_quals(V_y,V_x,T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(V_x,V_y,T_a)!=V_y|c_lesse_quals(V_x,V_y,T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(V_x,V_y,T_a)=V_y| -c_lesse_quals(V_x,V_y,T_a).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_lesse_quals(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_lesse_quals(V_k,V_l,tc_nat)| -c_lesse_quals(V_i,V_j,tc_nat).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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)).
% 270.53/270.70 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)).
% 270.53/270.70 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.
% 270.53/270.70 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)).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(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_lesse_quals(V_m,V_n,tc_nat).
% 270.53/270.70 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(V_m,V_n,tc_nat)| -c_lesse_quals(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_HOL_Oord__class_Oless(V_m,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k),tc_nat)| -c_lesse_quals(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a).
% 270.53/270.70 0 [] c_List_Oreplicate(V_m,V_x,T_a)!=c_List_Oreplicate(V_n,V_y,T_a)|V_m=V_n.
% 270.53/270.70 0 [] c_List_Oappend(V_ys,V_xs,T_a)!=c_List_Oappend(V_zs,V_xs,T_a)|V_ys=V_zs.
% 270.53/270.70 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Oappend(V_xs,V_zs,T_a)|V_ys=V_zs.
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)| -c_HOL_Oord__class_Oless(V_y,V_z,T_a)| -c_HOL_Oord__class_Oless(V_x,V_z,T_a).
% 270.53/270.70 0 [] c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_lesse_quals(V_m,V_n,tc_nat).
% 270.53/270.70 0 [] c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_lesse_quals(V_m,V_n,tc_nat).
% 270.53/270.70 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).
% 270.53/270.70 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)).
% 270.53/270.70 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)).
% 270.53/270.70 0 [] c_Wellfounded_Oaccp(V_r,V_b,T_a)| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a))| -c_Wellfounded_Oaccp(V_r,V_a,T_a).
% 270.53/270.70 0 [] c_Wellfounded_Oaccp(V_r,V_b,T_a)| -c_Wellfounded_Oaccp(V_r,V_a,T_a)| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a)).
% 270.53/270.70 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)).
% 270.53/270.70 0 [] c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 270.53/270.70 0 [] hBOOL(hAPP(c_InductTermi_OIT,V_r))| -c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_r,tc_Lambda_OdB).
% 270.53/270.70 0 [] hBOOL(hAPP(V_P,V_n))|hBOOL(hAPP(V_P,V_x))| -c_HOL_Oord__class_Oless(V_x,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(V_P),tc_nat)| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 270.53/270.70 0 [] c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat)| -c_lesse_quals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)| -c_lesse_quals(V_k,V_j,tc_nat).
% 270.53/270.70 0 [] c_lesse_quals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat)| -c_lesse_quals(V_k,V_j,tc_nat).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)| -c_lesse_quals(V_y,V_z,T_a)| -c_lesse_quals(V_x,V_z,T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(c_Orderings_Oord__class_Omax(V_y,V_z,T_a),V_x,T_a)| -c_lesse_quals(V_z,V_x,T_a)| -c_lesse_quals(V_y,V_x,T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a)| -c_lesse_quals(V_b,V_x,T_a)| -c_lesse_quals(V_a,V_x,T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_y,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a).
% 270.53/270.70 0 [] c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a)=V_xs.
% 270.53/270.70 0 [] V_x=c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a).
% 270.53/270.70 0 [] V_xs=c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a).
% 270.53/270.70 0 [] c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a)=V_ys.
% 270.53/270.70 0 [] V_ys=c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a).
% 270.53/270.70 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)).
% 270.53/270.70 0 [] -class_Orderings_Obot(T_a)|c_lesse_quals(c_Orderings_Obot__class_Obot(T_a),V_x,T_a).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_List_Omap(V_f,c_List_Oreplicate(V_n,V_x,T_b),T_b,T_a)=c_List_Oreplicate(V_n,hAPP(V_f,V_x),T_a).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_List_Ofoldr(V_f,c_List_Oappend(V_xs,V_ys,T_b),V_a,T_b,T_a)=c_List_Ofoldr(V_f,V_xs,c_List_Ofoldr(V_f,V_ys,V_a,T_b,T_a),T_b,T_a).
% 270.53/270.70 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).
% 270.53/270.70 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.
% 270.53/270.70 0 [] hAPP(V_e,V_i)=V_T| -c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_z,V_y,T_a)|c_lesse_quals(V_z,V_x,T_a)| -c_lesse_quals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_List_Odrop(V_n,c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_pwr,V_x),V_p)),hAPP(hAPP(V_pwr,V_x),V_q))=hAPP(hAPP(V_pwr,V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_p),V_q))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 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)).
% 270.53/270.70 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)).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] -class_OrderedGroup_Oab__semigroup__add(T_a)|c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,V_a,T_a,T_a)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_a,V_xs,T_a,T_a).
% 270.53/270.70 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OAbs(V_dB_H).
% 270.53/270.70 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)).
% 270.53/270.70 0 [] -c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a).
% 270.53/270.70 0 [] -c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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)).
% 270.53/270.70 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)).
% 270.53/270.70 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)).
% 270.53/270.70 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)).
% 270.53/270.70 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)).
% 270.53/270.70 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)).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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)).
% 270.53/270.70 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)).
% 270.53/270.70 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).
% 270.53/270.70 0 [] hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_b),V_a))| -hBOOL(hAPP(hAPP(V_r,V_a),V_b)).
% 270.53/270.70 0 [] hBOOL(hAPP(hAPP(V_r,V_a2),V_a1))| -hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a1),V_a2)).
% 270.53/270.70 0 [] hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a),V_b))| -hBOOL(hAPP(hAPP(V_r,V_b),V_a)).
% 270.53/270.70 0 [] hBOOL(hAPP(hAPP(V_r,V_b),V_a))| -hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a),V_b)).
% 270.53/270.70 0 [] c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olist_OCons(V_x,V_xs,T_a).
% 270.53/270.70 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.
% 270.53/270.70 0 [] c_lesse_quals(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_j),tc_nat)| -c_lesse_quals(V_i,V_j,tc_nat).
% 270.53/270.70 0 [] c_lesse_quals(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_m),tc_nat)| -c_lesse_quals(V_i,V_j,tc_nat).
% 270.53/270.70 0 [] c_lesse_quals(V_k,V_n,tc_nat)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k),V_n,tc_nat).
% 270.53/270.70 0 [] c_lesse_quals(V_m,V_n,tc_nat)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k),V_n,tc_nat).
% 270.53/270.70 0 [] c_lesse_quals(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat)| -c_lesse_quals(V_x,V_z,tc_nat).
% 270.53/270.70 0 [] c_lesse_quals(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat)| -c_lesse_quals(V_x,V_y,tc_nat).
% 270.53/270.70 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).
% 270.53/270.70 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)=c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(V_x,V_z,T_a),c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a).
% 270.53/270.70 0 [] hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R)=hAPP(hAPP(V_P,V_R),V_Q).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] hBOOL(hAPP(V_P,V_n))|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(V_P),tc_nat)| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 270.53/270.70 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.
% 270.53/270.70 0 [] c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a)=V_a.
% 270.53/270.70 0 [] c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a)=c_List_Olist_ONil(T_a).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_lesse_quals(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_lesse_quals(V_m,V_n,tc_nat).
% 270.53/270.70 0 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(V_m,V_l,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_l,tc_nat),tc_nat)| -c_lesse_quals(V_m,V_n,tc_nat).
% 270.53/270.70 0 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)| -c_lesse_quals(V_m,V_n,tc_nat)| -c_lesse_quals(V_k,V_n,tc_nat)| -c_lesse_quals(V_k,V_m,tc_nat).
% 270.53/270.70 0 [] c_lesse_quals(V_m,V_n,tc_nat)| -c_lesse_quals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)| -c_lesse_quals(V_k,V_n,tc_nat)| -c_lesse_quals(V_k,V_m,tc_nat).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 0 [] c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat)!=c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat)| -c_lesse_quals(V_k,V_n,tc_nat)| -c_lesse_quals(V_k,V_m,tc_nat)|V_m=V_n.
% 270.53/270.70 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_x))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y)).
% 270.53/270.70 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_x)).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_x,V_a,T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_x,V_b,T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)| -c_HOL_Oord__class_Oless(V_z,V_x,T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)| -c_HOL_Oord__class_Oless(V_z,V_y,T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_z,T_a)| -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_y,V_z,T_a)| -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a).
% 270.53/270.70 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Olistsum(c_List_Olist_ONil(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 270.53/270.70 0 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat).
% 270.53/270.70 0 [] c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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)).
% 270.53/270.70 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)).
% 270.53/270.70 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)| -c_lesse_quals(V_k,V_n,tc_nat)| -c_lesse_quals(V_k,V_m,tc_nat).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_c,tc_nat),c_HOL_Ominus__class_Ominus(V_b,V_c,tc_nat),tc_nat)| -c_lesse_quals(V_c,V_a,tc_nat)| -c_HOL_Oord__class_Oless(V_a,V_b,tc_nat).
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_lesse_quals(V_m,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_k,tc_nat),tc_nat)| -c_lesse_quals(V_k,V_n,tc_nat).
% 270.53/270.70 0 [] c_List_Olist_OCons(V_x,V_xa,T_a)!=c_List_Olist_ONil(T_a).
% 270.53/270.70 0 [] c_List_Olist_OCons(V_a_H,V_list_H,T_a)!=c_List_Olist_ONil(T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_pwr,hAPP(hAPP(V_mul,V_x),V_y)),V_q)=hAPP(hAPP(V_mul,hAPP(hAPP(V_pwr,V_x),V_q)),hAPP(hAPP(V_pwr,V_y),V_q))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_add,V_y),V_z))=hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_x),V_y)),hAPP(hAPP(V_mul,V_x),V_z))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_mul,V_x),V_y)=hAPP(hAPP(V_mul,V_y),V_x)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_mul,V_y),V_z))=hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_x),V_y)),V_z)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_mul,V_r1),V_x)=V_x| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_mul,V_r0),V_x)=V_r0| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_add,V_x),V_y)=hAPP(hAPP(V_add,V_y),V_x)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_add,V_x),hAPP(hAPP(V_add,V_y),V_z))=hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_x),V_y)),V_z)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_add,V_r0),V_x)=V_x| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_add,V_a),hAPP(hAPP(V_add,V_c),V_d))=hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_c)),V_d)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_y,V_z,T_a)| -c_lesse_quals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_x,V_z,T_a)| -c_lesse_quals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)| -c_lesse_quals(V_z,V_y,T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)| -c_lesse_quals(V_z,V_x,T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)| -c_lesse_quals(V_x,V_b,T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)| -c_lesse_quals(V_x,V_a,T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_b,V_x,T_a)| -c_lesse_quals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_a,V_x,T_a)| -c_lesse_quals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a).
% 270.53/270.70 0 [] c_lesse_quals(V_j,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),tc_nat)| -c_lesse_quals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat).
% 270.53/270.70 0 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat)| -c_lesse_quals(V_j,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),tc_nat).
% 270.53/270.70 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).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_z,V_y,T_a)|c_HOL_Oord__class_Oless(V_z,V_x,T_a)| -c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a).
% 270.53/270.70 0 [] hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x)=V_T.
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_List_Olist_ONil(T_a)!=c_List_Oappend(V_xs,V_ys,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 270.53/270.70 0 [] c_List_Olist_ONil(T_a)!=c_List_Oappend(V_xs,V_ys,T_a)|V_ys=c_List_Olist_ONil(T_a).
% 270.53/270.70 0 [] c_Lambda_OdB_OAbs(V_dB)!=c_Lambda_OdB_OAbs(V_dB_H)|V_dB=V_dB_H.
% 270.53/270.70 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_a).
% 270.53/270.70 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Olist_ONil(T_a)|V_ys=c_List_Olist_ONil(T_a).
% 270.53/270.70 0 [] c_Predicate_Oconversep(c_fe_qual(T_a),T_a,T_a)=c_fe_qual(T_a).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_k,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat))| -c_lesse_quals(V_k,V_j,tc_nat).
% 270.53/270.70 0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_k,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),V_i)| -c_lesse_quals(V_k,V_j,tc_nat).
% 270.53/270.70 0 [] c_HOL_Ominus__class_Ominus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat)| -c_lesse_quals(V_k,V_j,tc_nat).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_List_Olist_ONil(T_a)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a).
% 270.53/270.70 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).
% 270.53/270.70 0 [] -c_HOL_Oord__class_Oless(V_x,V_x,tc_nat).
% 270.53/270.70 0 [] -c_HOL_Oord__class_Oless(V_n,V_n,tc_nat).
% 270.53/270.70 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 270.53/270.70 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 270.53/270.70 0 [] -c_lesse_quals(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_i),tc_nat)|c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_i),V_i,tc_nat)=V_k.
% 270.53/270.70 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).
% 270.53/270.70 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)).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_lesse_quals(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),tc_nat).
% 270.53/270.70 0 [] c_lesse_quals(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat).
% 270.53/270.70 0 [] c_lesse_quals(V_m,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_x),tc_nat).
% 270.53/270.70 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).
% 270.53/270.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat)),V_m)=c_Orderings_Oord__class_Omax(V_n,V_m,tc_nat).
% 270.53/270.70 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).
% 270.53/270.70 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Olistsum(c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Olistsum(V_xs,T_a)).
% 270.53/270.70 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).
% 270.53/270.70 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.
% 270.53/270.70 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).
% 270.53/270.70 0 [] V_m=V_n| -c_lesse_quals(V_n,V_m,tc_nat)| -c_lesse_quals(V_m,V_n,tc_nat).
% 270.53/270.70 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.
% 270.53/270.70 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).
% 270.53/270.70 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.
% 270.53/270.70 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).
% 270.53/270.70 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.
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_k,V_x,T_a),T_a)=c_List_Oappend(c_List_Oreplicate(V_k,V_x,T_a),c_List_Oreplicate(V_n,V_x,T_a),T_a).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(V_x,V_x,T_a)=V_x.
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_lesse_quals(V_x,V_y,tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_y,tc_nat).
% 270.53/270.70 0 [] c_lesse_quals(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_List_Olist_ONil(T_a)!=c_List_Olist_OCons(V_a_H,V_list_H,T_a).
% 270.53/270.70 0 [] -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_lesse_quals(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_lesse_quals(V_i,V_j,tc_nat).
% 270.53/270.70 0 [] c_lesse_quals(V_m,V_n,tc_nat)| -c_lesse_quals(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).
% 270.53/270.70 0 [] c_lesse_quals(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_lesse_quals(V_m,V_n,tc_nat).
% 270.53/270.70 0 [] -c_lesse_quals(V_i,V_j,tc_nat)|V_j=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat)),V_i).
% 270.53/270.70 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_lesse_quals(V_n,V_m,tc_nat).
% 270.53/270.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)),V_n)=V_m| -c_lesse_quals(V_n,V_m,tc_nat).
% 270.53/270.70 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Olistsum(V_xs,T_a)=c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat))=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_k,tc_nat)| -c_lesse_quals(V_k,V_j,tc_nat).
% 270.53/270.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),V_i)=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_k,tc_nat)| -c_lesse_quals(V_k,V_j,tc_nat).
% 270.53/270.70 0 [] c_List_Odrop(V_n,c_List_Odrop(V_m,V_xs,T_a),T_a)=c_List_Odrop(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_xs,T_a).
% 270.53/270.70 0 [] c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_x,T_a)=c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_m,V_x,T_a),T_a).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_List_Oreplicate(V_n,V_x,T_a)!=c_List_Olist_ONil(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.53/270.70 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).
% 270.53/270.70 0 [] hAPP(hAPP(V_add,V_a),V_c)=hAPP(hAPP(V_add,V_c),V_a)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_b)),V_c)=hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_c)),V_b)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_add,V_a),hAPP(hAPP(V_add,V_c),V_d))=hAPP(hAPP(V_add,V_c),hAPP(hAPP(V_add,V_a),V_d))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_b)),V_c)=hAPP(hAPP(V_add,V_a),hAPP(hAPP(V_add,V_b),V_c))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_b)),hAPP(hAPP(V_add,V_c),V_d))=hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_c)),hAPP(hAPP(V_add,V_b),V_d))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_rx),V_ry))=hAPP(hAPP(V_mul,V_rx),hAPP(hAPP(V_mul,V_lx),V_ry))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_rx),V_ry))=hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_rx)),V_ry)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),V_rx)=hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_ly),V_rx))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),V_rx)=hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_rx)),V_ly)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),hAPP(hAPP(V_mul,V_rx),V_ry))=hAPP(hAPP(V_mul,V_rx),hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),V_ry))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),hAPP(hAPP(V_mul,V_rx),V_ry))=hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_ly),hAPP(hAPP(V_mul,V_rx),V_ry)))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),hAPP(hAPP(V_mul,V_rx),V_ry))=hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_rx)),hAPP(hAPP(V_mul,V_ly),V_ry))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_mul,V_a),V_r1)=V_a| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_mul,V_r1),V_a)=V_a| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_mul,V_a),V_r0)=V_r0| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_mul,V_r0),V_a)=V_r0| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_b)),V_c)=hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_a),V_c)),hAPP(hAPP(V_mul,V_b),V_c))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_mul,V_a),V_b)=hAPP(hAPP(V_mul,V_b),V_a)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_add,V_a),V_r0)=V_a| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_add,V_r0),V_a)=V_a| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_add,V_m),V_m)=hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_r1),V_r1)),V_m)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_add,V_m),hAPP(hAPP(V_mul,V_a),V_m))=hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_r1)),V_m)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_a),V_m)),V_m)=hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_r1)),V_m)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_a),V_m)),hAPP(hAPP(V_mul,V_b),V_m))=hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_b)),V_m)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 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).
% 270.53/270.70 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)).
% 270.53/270.70 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)).
% 270.53/270.70 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).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(V_x,V_y,T_a)=c_Orderings_Oord__class_Omax(V_y,V_x,T_a).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_List_Odrop(V_i,c_List_Oreplicate(V_k,V_x,T_a),T_a)=c_List_Oreplicate(c_HOL_Ominus__class_Ominus(V_k,V_i,tc_nat),V_x,T_a).
% 270.53/270.70 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)).
% 270.53/270.70 0 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a)=c_List_Olist_ONil(T_a).
% 270.53/270.70 0 [] c_HOL_Ominus__class_Ominus(V_n,c_HOL_Ominus__class_Ominus(V_n,V_i,tc_nat),tc_nat)=V_i| -c_lesse_quals(V_i,V_n,tc_nat).
% 270.53/270.70 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).
% 270.53/270.70 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)).
% 270.53/270.70 0 [] c_List_Olist_OCons(V_x,V_t,T_a)!=V_t.
% 270.53/270.70 0 [] V_xs!=c_List_Olist_OCons(V_x,V_xs,T_a).
% 270.53/270.70 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)).
% 270.53/270.70 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).
% 270.53/270.70 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Orderings_Oord__class_Omax(V_x,V_y,T_a)),V_z)=c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z),T_a).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_List_Olist_ONil(T_a)=c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a).
% 270.53/270.70 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).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)=c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a)=c_Orderings_Oord__class_Omax(V_y,c_Orderings_Oord__class_Omax(V_x,V_z,T_a),T_a).
% 270.53/270.70 0 [] c_List_Olist_ONil(T_a)=c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a)=c_Transitive__Closure_Ortranclp(V_r,T_a).
% 270.53/270.70 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)).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)=c_Orderings_Oord__class_Omax(V_x,V_y,T_a).
% 270.53/270.70 0 [] c_List_Oappend(c_List_Oreplicate(V_i,V_x,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a)=c_List_Olist_OCons(V_x,c_List_Oreplicate(V_i,V_x,T_a),T_a).
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 0 [] hAPP(hAPP(V_plus,V_a),V_zero)=V_a| -c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a).
% 270.53/270.70 0 [] hAPP(hAPP(V_plus,V_zero),V_a)=V_a| -c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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.
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 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)).
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 0 [] c_lesse_quals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 270.53/270.70 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 270.53/270.70 0 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k)=V_t.
% 270.53/270.70 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).
% 270.53/270.70 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.
% 270.53/270.70 0 [] V_n=c_HOL_Ozero__class_Ozero(tc_nat)| -c_lesse_quals(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_Nat_Onat_Onat__case(V_x,V_f,c_HOL_Ozero__class_Ozero(tc_nat),T_a)=V_x.
% 270.53/270.70 0 [] c_Nat_Onat_Onat__case(V_f1,V_f2,c_HOL_Ozero__class_Ozero(tc_nat),T_a)=V_f1.
% 270.53/270.70 0 [] c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=V_m.
% 270.53/270.70 0 [] c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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)).
% 270.53/270.70 0 [] -class_OrderedGroup_Osemigroup__add(T_a)|c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(T_a),T_a).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_List_Olist_ONil(T_a)!=c_List_Oreplicate(V_n,V_x,T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.53/270.70 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)| -c_lesse_quals(V_k,V_n,tc_nat)| -c_lesse_quals(V_k,V_m,tc_nat).
% 270.53/270.70 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_lesse_quals(V_k,V_n,tc_nat)| -c_lesse_quals(V_k,V_m,tc_nat).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a)=hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a)).
% 270.53/270.70 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))).
% 270.53/270.70 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))).
% 270.53/270.70 0 [] c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a)=V_r.
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat).
% 270.53/270.70 0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat).
% 270.53/270.70 0 [] -class_Ring__and__Field_Oring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a)=c_HOL_Ominus__class_Ominus(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_lesse_quals(V_n,V_m,tc_nat).
% 270.53/270.70 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=V_xs|V_ys=c_List_Olist_ONil(T_a).
% 270.53/270.70 0 [] V_xs!=c_List_Oappend(V_xs,V_ys,T_a)|V_ys=c_List_Olist_ONil(T_a).
% 270.53/270.70 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=V_ys|V_xs=c_List_Olist_ONil(T_a).
% 270.53/270.70 0 [] V_ys!=c_List_Oappend(V_xs,V_ys,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_lesse_quals(V_n,V_n,tc_nat).
% 270.53/270.70 0 [] c_lesse_quals(V_i,V_k,tc_nat)| -c_lesse_quals(V_j,V_k,tc_nat)| -c_lesse_quals(V_i,V_j,tc_nat).
% 270.53/270.70 0 [] c_lesse_quals(V_x,V_x,tc_nat).
% 270.53/270.70 0 [] -class_Orderings_Oorder(T_a)|c_lesse_quals(V_x,V_x,T_a).
% 270.53/270.70 0 [] -class_Orderings_Opreorder(T_a)|c_lesse_quals(V_x,V_x,T_a).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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))).
% 270.53/270.70 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))).
% 270.53/270.70 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))).
% 270.53/270.70 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OVar(V_nat_H)|V_nat=V_nat_H.
% 270.53/270.70 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=c_Lambda_OdB_OVar(V_nat).
% 270.53/270.70 0 [] c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olist_OCons(V_x,c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),V_xs,T_a),T_a).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_List_Odrop(V_n,c_List_Omap(V_f,V_xs,T_b,T_a),T_a)=c_List_Omap(V_f,c_List_Odrop(V_n,V_xs,T_b),T_b,T_a).
% 270.53/270.70 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)).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Olistsum(c_List_Oappend(V_xs,V_ys,T_a),T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_List_Olistsum(V_xs,T_a)),c_List_Olistsum(V_ys,T_a)).
% 270.53/270.70 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).
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 0 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 270.53/270.70 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).
% 270.53/270.70 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.
% 270.53/270.70 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)|V_m=V_n| -c_lesse_quals(V_m,V_n,tc_nat).
% 270.53/270.70 0 [] V_m=V_n|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_lesse_quals(V_m,V_n,tc_nat).
% 270.53/270.70 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)|V_m=V_n| -c_lesse_quals(V_m,V_n,tc_nat).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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.
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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)).
% 270.53/270.70 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)).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_lesse_quals(V_n,V_m,tc_nat)|c_lesse_quals(V_m,V_n,tc_nat).
% 270.53/270.70 0 [] c_Wellfounded_Oaccp(V_r,V_y,T_a)| -hBOOL(hAPP(hAPP(V_r,V_y),V_a))| -c_Wellfounded_Oaccp(V_r,V_a,T_a).
% 270.53/270.70 0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_y,V_x,T_a)|c_lesse_quals(V_x,V_y,T_a).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_Wellfounded_Oaccp(V_r,V_a,T_a)| -hBOOL(hAPP(hAPP(V_r,V_a),V_b))| -c_Wellfounded_Oaccp(V_r,V_b,T_a).
% 270.53/270.70 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).
% 270.53/270.70 0 [] -hBOOL(hAPP(V_P,c_Nat_Onat_Onat__case(V_f1,V_f2,c_HOL_Ozero__class_Ozero(tc_nat),t_a)))|hBOOL(hAPP(V_P,V_f1)).
% 270.53/270.70 0 [] hBOOL(hAPP(V_P,V_nat))|hBOOL(hAPP(V_P,v_sko__Nat__Xnat__Xinducts__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 270.53/270.70 0 [] c_Nitpick_Onat__gcd(V_x,c_HOL_Ozero__class_Ozero(tc_nat))=V_x.
% 270.53/270.70 0 [] c_nat_Onat__size(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.53/270.70 0 [] c_String_Ochar_Ochar__size(V_c)=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.53/270.70 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).
% 270.53/270.70 0 [] hBOOL(hAPP(V_P,V_nat))|hBOOL(hAPP(V_P,v_sko__Nat__Xnat__Xinduct__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 270.53/270.70 0 [] -c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 270.53/270.70 0 [] -c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 270.53/270.70 0 [] c_Orderings_Obot__class_Obot(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.53/270.70 0 [] hBOOL(hAPP(V_P,V_nat))|hBOOL(hAPP(V_P,v_sko__List__Xupt__Xinduct__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 270.53/270.70 0 [] c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),V_xs,T_a)=V_xs.
% 270.53/270.70 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.53/270.70 0 [] hBOOL(hAPP(V_P,V_n))| -hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 270.53/270.70 0 [] c_lesse_quals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 270.53/270.70 0 [] c_Nat_Osize__class_Osize(V_c,tc_String_Ochar)=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.53/270.70 0 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a).
% 270.53/270.70 0 [] c_Orderings_Oord__class_Omax(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=V_n.
% 270.53/270.70 0 [] c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=V_n.
% 270.53/270.70 0 [] c_List_Oreplicate(V_m,V_x,T_a)!=c_List_Oreplicate(V_n,V_y,T_a)|V_x=V_y|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.53/270.70 0 [] V_x=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)).
% 270.53/270.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)=V_n.
% 270.53/270.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat))=V_m.
% 270.53/270.70 0 [] hAPP(hAPP(V_pwr,V_x),c_HOL_Ozero__class_Ozero(tc_nat))=V_r1| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 270.53/270.70 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_xs,T_a,T_a)=c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a).
% 270.53/270.70 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Olistsum(V_xs,T_a)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_xs,T_a,T_a).
% 270.53/270.70 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_a,V_xs,T_a,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a)).
% 270.53/270.70 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=c_Lambda_OdB_OAbs(V_dB_H).
% 270.53/270.70 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2).
% 270.53/270.70 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))).
% 270.53/270.70 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))).
% 270.53/270.70 0 [] c_Lambda_OdB_OVar(V_nat)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H).
% 270.53/270.70 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)).
% 270.53/270.70 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).
% 270.53/270.70 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)).
% 270.53/270.70 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)).
% 270.53/270.70 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)).
% 270.53/270.70 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)).
% 270.53/270.70 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)).
% 270.53/270.70 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)!=c_Lambda_OdB_OVar(V_nat).
% 270.53/270.70 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).
% 270.53/270.70 0 [] -c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),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),tc_Lambda_OdB)| -c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_s,tc_Lambda_OdB)|c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),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),tc_Lambda_OdB).
% 270.53/270.70 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)).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b)=V_a.
% 270.53/270.70 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)).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k)=V_u.
% 270.53/270.70 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)).
% 270.53/270.70 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k)=V_t.
% 270.53/270.70 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)))| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 270.53/270.70 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))).
% 270.53/270.70 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_ua______)).
% 270.53/270.70 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r)))| -hBOOL(hAPP(c_InductTermi_OIT,V_r)).
% 270.53/270.70 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),V_u),V_i)))| -c_Type_Otyping(V_e,V_u,v_T____)| -hBOOL(hAPP(c_InductTermi_OIT,V_u))| -c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),v_a____,V_T_H).
% 270.53/270.70 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)))).
% 270.53/270.70 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).
% 270.53/270.70 0 [] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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).
% 270.53/270.70 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)).
% 270.53/270.70 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).
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 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).
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 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)).
% 270.53/270.70 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.
% 270.53/270.70 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.
% 270.53/270.70 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)).
% 270.53/270.70 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)).
% 270.53/270.70 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i)))| -c_Type_Otyping(V_e,V_u,v_T____)| -hBOOL(hAPP(c_InductTermi_OIT,V_u))| -c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),V_T_H).
% 270.53/270.70 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))).
% 270.53/270.70 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_a____)).
% 270.53/270.70 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)).
% 270.53/270.71 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))).
% 270.53/270.71 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)|V_dB1=V_dB1_H.
% 270.53/270.71 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)|V_dB2=V_dB2_H.
% 270.53/270.71 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)|V_r=V_s.
% 270.53/270.71 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_u____)).
% 270.53/270.71 0 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 270.53/270.71 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_u____)).
% 270.53/270.71 0 [] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____).
% 270.53/270.71 0 [] -hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))).
% 270.53/270.71 0 [] class_Orderings_Opreorder(tc_fun(T_2,T_1))| -class_Orderings_Opreorder(T_1).
% 270.53/270.71 0 [] class_Orderings_Oorder(tc_fun(T_2,T_1))| -class_Orderings_Oorder(T_1).
% 270.53/270.71 0 [] class_Orderings_Obot(tc_fun(T_2,T_1))| -class_Orderings_Obot(T_1).
% 270.53/270.71 0 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 270.53/270.71 0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 270.53/270.71 0 [] class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat).
% 270.53/270.71 0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 270.53/270.71 0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 270.53/270.71 0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 270.53/270.71 0 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 270.53/270.71 0 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 270.53/270.71 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 270.53/270.71 0 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 270.53/270.71 0 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 270.53/270.71 0 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 270.53/270.71 0 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 270.53/270.71 0 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 270.53/270.71 0 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 270.53/270.71 0 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 270.53/270.71 0 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 270.53/270.71 0 [] class_Nat_Osemiring__char__0(tc_nat).
% 270.53/270.71 0 [] class_Orderings_Opreorder(tc_nat).
% 270.53/270.71 0 [] class_Orderings_Olinorder(tc_nat).
% 270.53/270.71 0 [] class_Orderings_Oorder(tc_nat).
% 270.53/270.71 0 [] class_Orderings_Obot(tc_nat).
% 270.53/270.71 0 [] class_Power_Opower(tc_nat).
% 270.53/270.71 0 [] class_Orderings_Opreorder(tc_bool).
% 270.53/270.71 0 [] class_Orderings_Oorder(tc_bool).
% 270.53/270.71 0 [] class_Orderings_Obot(tc_bool).
% 270.53/270.71 0 [] hBOOL(hAPP(hAPP(c_fe_qual(T_a),V_x),V_x)).
% 270.53/270.71 0 [] V_X=V_Y| -hBOOL(hAPP(hAPP(c_fe_qual(T_a),V_X),V_Y)).
% 270.53/270.71 end_of_list.
% 270.53/270.71
% 270.53/270.71 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 270.53/270.71
% 270.53/270.71 This ia a non-Horn set with equality. The strategy will be
% 270.53/270.71 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 270.53/270.71 deletion, with positive clauses in sos and nonpositive
% 270.53/270.71 clauses in usable.
% 270.53/270.71
% 270.53/270.71 dependent: set(knuth_bendix).
% 270.53/270.71 dependent: set(anl_eq).
% 270.53/270.71 dependent: set(para_from).
% 270.53/270.71 dependent: set(para_into).
% 270.53/270.71 dependent: clear(para_from_right).
% 270.53/270.71 dependent: clear(para_into_right).
% 270.53/270.71 dependent: set(para_from_vars).
% 270.53/270.71 dependent: set(eq_units_both_ways).
% 270.53/270.71 dependent: set(dynamic_demod_all).
% 270.53/270.71 dependent: set(dynamic_demod).
% 270.53/270.71 dependent: set(order_eq).
% 270.53/270.71 dependent: set(back_demod).
% 270.53/270.71 dependent: set(lrpo).
% 270.53/270.71 dependent: set(hyper_res).
% 270.53/270.71 dependent: set(unit_deletion).
% 270.53/270.71 dependent: set(factor).
% 270.53/270.71
% 270.53/270.71 ------------> process usable:
% 270.53/270.71 ** KEPT (pick-wt=12): 1 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(B,C,A)=B| -c_lesse_quals(C,B,A).
% 270.53/270.71 ** KEPT (pick-wt=12): 2 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(B,C,A)!=C|c_lesse_quals(B,C,A).
% 270.53/270.71 ** KEPT (pick-wt=12): 3 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(B,C,A)=C| -c_lesse_quals(B,C,A).
% 270.53/270.71 ** KEPT (pick-wt=14): 4 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=14): 5 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=22): 6 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=19): 8 [copy,7,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).
% 270.53/270.71 ** KEPT (pick-wt=24): 9 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=22): 10 [] c_lesse_quals(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_lesse_quals(B,D,tc_nat)| -c_lesse_quals(A,C,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=16): 11 [] -c_ListOrder_Ostep1(A,B,C,D)|c_ListOrder_Ostep1(A,c_List_Oappend(B,E,D),c_List_Oappend(C,E,D),D).
% 270.53/270.71 ** KEPT (pick-wt=16): 12 [] c_ListOrder_Ostep1(A,c_List_Oappend(B,C,D),c_List_Oappend(B,E,D),D)| -c_ListOrder_Ostep1(A,C,E,D).
% 270.53/270.71 ** KEPT (pick-wt=16): 13 [] -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)).
% 270.53/270.71 Following clause subsumed by 13 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)).
% 270.53/270.71 ** KEPT (pick-wt=13): 14 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ominus__class_Ominus(B,C,A)),C)=B.
% 270.53/270.71 ** KEPT (pick-wt=18): 15 [] 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)).
% 270.53/270.71 ** KEPT (pick-wt=11): 16 [] c_List_Olistsp(A,B,C)| -c_List_Olistsp(A,c_List_Oappend(B,D,C),C).
% 270.53/270.71 ** KEPT (pick-wt=11): 17 [] c_List_Olistsp(A,B,C)| -c_List_Olistsp(A,c_List_Oappend(D,B,C),C).
% 270.53/270.71 ** KEPT (pick-wt=17): 18 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=17): 19 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=14): 20 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A)| -c_lesse_quals(B,C,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=14): 21 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(B,C,tc_nat)| -c_lesse_quals(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A).
% 270.53/270.71 ** KEPT (pick-wt=17): 22 [] A=B|C=D| -c_ListOrder_Ostep1(E,c_List_Olist_OCons(B,D,F),c_List_Olist_OCons(A,C,F),F).
% 270.53/270.71 ** KEPT (pick-wt=17): 23 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=18): 24 [] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_lesse_quals(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=22): 25 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=12): 26 [] c_List_Oreplicate(A,B,C)!=c_List_Oreplicate(D,E,C)|A=D.
% 270.53/270.71 ** KEPT (pick-wt=12): 27 [] c_List_Oappend(A,B,C)!=c_List_Oappend(D,B,C)|A=D.
% 270.53/270.71 ** KEPT (pick-wt=12): 28 [] c_List_Oappend(A,B,C)!=c_List_Oappend(A,D,C)|B=D.
% 270.53/270.71 ** KEPT (pick-wt=17): 29 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(B,C,A),D,A)| -c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 270.53/270.71 ** KEPT (pick-wt=11): 30 [] c_HOL_Ominus__class_Ominus(A,B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_lesse_quals(A,B,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=11): 31 [] c_HOL_Ominus__class_Ominus(A,B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_lesse_quals(A,B,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=15): 32 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=16): 33 [] c_Wellfounded_Oaccp(A,B,C)| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,C),B),D))| -c_Wellfounded_Oaccp(A,D,C).
% 270.53/270.71 Following clause subsumed by 33 during input processing: 0 [] c_Wellfounded_Oaccp(A,B,C)| -c_Wellfounded_Oaccp(A,D,C)| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,C),B),D)).
% 270.53/270.71 ** KEPT (pick-wt=24): 34 [] 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)).
% 270.53/270.71 ** KEPT (pick-wt=11): 35 [] c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),A,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 270.53/270.71 ** KEPT (pick-wt=11): 36 [] hBOOL(hAPP(c_InductTermi_OIT,A))| -c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),A,tc_Lambda_OdB).
% 270.53/270.71 ** KEPT (pick-wt=14): 38 [copy,37,factor_simp] hBOOL(hAPP(A,B))| -c_HOL_Oord__class_Oless(B,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(A),tc_nat)| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 270.53/270.71 ** KEPT (pick-wt=20): 39 [] c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat)| -c_lesse_quals(A,c_HOL_Ominus__class_Ominus(C,B,tc_nat),tc_nat)| -c_lesse_quals(B,C,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=20): 40 [] c_lesse_quals(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_nat)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat)| -c_lesse_quals(C,B,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=17): 41 [] -class_Orderings_Olinorder(A)|c_lesse_quals(c_Orderings_Oord__class_Omax(B,C,A),D,A)| -c_lesse_quals(C,D,A)| -c_lesse_quals(B,D,A).
% 270.53/270.71 Following clause subsumed by 41 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_lesse_quals(c_Orderings_Oord__class_Omax(B,C,A),D,A)| -c_lesse_quals(C,D,A)| -c_lesse_quals(B,D,A).
% 270.53/270.71 Following clause subsumed by 41 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_lesse_quals(c_Orderings_Oord__class_Omax(B,C,A),D,A)| -c_lesse_quals(C,D,A)| -c_lesse_quals(B,D,A).
% 270.53/270.71 ** KEPT (pick-wt=9): 42 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,c_Orderings_Oord__class_Omax(B,C,A),A).
% 270.53/270.71 ** KEPT (pick-wt=9): 43 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,c_Orderings_Oord__class_Omax(C,B,A),A).
% 270.53/270.71 ** KEPT (pick-wt=26): 44 [] 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)).
% 270.53/270.71 ** KEPT (pick-wt=7): 45 [] -class_Orderings_Obot(A)|c_lesse_quals(c_Orderings_Obot__class_Obot(A),B,A).
% 270.53/270.71 ** KEPT (pick-wt=22): 46 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=22): 47 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=13): 48 [] 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).
% 270.53/270.71 ** KEPT (pick-wt=13): 49 [] 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).
% 270.53/270.71 ** KEPT (pick-wt=13): 50 [] 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).
% 270.53/270.71 Following clause subsumed by 48 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).
% 270.53/270.71 Following clause subsumed by 49 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).
% 270.53/270.71 ** KEPT (pick-wt=15): 51 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=15): 52 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=21): 53 [] 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).
% 270.53/270.71 Following clause subsumed by 51 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).
% 270.53/270.71 ** KEPT (pick-wt=18): 54 [] 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).
% 270.53/270.71 ** KEPT (pick-wt=28): 55 [] 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).
% 270.53/270.71 ** KEPT (pick-wt=12): 56 [] -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.
% 270.53/270.71 ** KEPT (pick-wt=10): 57 [] hAPP(A,B)=C| -c_Type_Otyping(A,c_Lambda_OdB_OVar(B),C).
% 270.53/270.71 ** KEPT (pick-wt=17): 58 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,C,A)|c_lesse_quals(B,D,A)| -c_lesse_quals(B,c_Orderings_Oord__class_Omax(D,C,A),A).
% 270.53/270.71 ** KEPT (pick-wt=12): 59 [] c_List_Olist_ONil(A)!=c_List_Omap(B,C,D,A)|C=c_List_Olist_ONil(D).
% 270.53/270.71 ** KEPT (pick-wt=31): 60 [] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,C),E))=hAPP(hAPP(B,C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),E))| -c_Groebner__Basis_Ogb__semiring(F,A,B,G,H,I).
% 270.53/270.71 ** KEPT (pick-wt=28): 61 [] 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)).
% 270.53/270.71 ** KEPT (pick-wt=28): 62 [] 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)).
% 270.53/270.71 ** KEPT (pick-wt=25): 63 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=25): 64 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=17): 65 [] -class_OrderedGroup_Oab__semigroup__add(A)|c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,C,A,A)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,B,A,A).
% 270.53/270.71 ** KEPT (pick-wt=5): 66 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 270.53/270.71 ** KEPT (pick-wt=14): 67 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(A,C),D)).
% 270.53/270.71 ** KEPT (pick-wt=6): 68 [] -c_ListOrder_Ostep1(A,c_List_Olist_ONil(B),C,B).
% 270.53/270.71 ** KEPT (pick-wt=6): 69 [] -c_ListOrder_Ostep1(A,B,c_List_Olist_ONil(C),C).
% 270.53/270.71 ** KEPT (pick-wt=17): 70 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=17): 71 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=25): 73 [copy,72,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)).
% 270.53/270.71 ** KEPT (pick-wt=25): 74 [] -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)).
% 270.53/270.71 ** KEPT (pick-wt=25): 75 [] -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)).
% 270.53/270.71 ** KEPT (pick-wt=25): 76 [] -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)).
% 270.53/270.71 ** KEPT (pick-wt=25): 77 [] -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)).
% 270.53/270.71 Following clause subsumed by 73 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)).
% 270.53/270.71 ** KEPT (pick-wt=25): 78 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=25): 79 [] -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)).
% 270.53/270.71 Following clause subsumed by 73 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 270.53/270.71 ** KEPT (pick-wt=20): 80 [] 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).
% 270.53/270.71 ** KEPT (pick-wt=15): 81 [] hBOOL(hAPP(hAPP(c_Predicate_Oconversep(A,B,C),D),E))| -hBOOL(hAPP(hAPP(A,E),D)).
% 270.53/270.71 ** KEPT (pick-wt=15): 82 [] hBOOL(hAPP(hAPP(A,B),C))| -hBOOL(hAPP(hAPP(c_Predicate_Oconversep(A,D,E),C),B)).
% 270.53/270.71 Following clause subsumed by 81 during input processing: 0 [] hBOOL(hAPP(hAPP(c_Predicate_Oconversep(A,B,C),D),E))| -hBOOL(hAPP(hAPP(A,E),D)).
% 270.53/270.71 Following clause subsumed by 82 during input processing: 0 [] hBOOL(hAPP(hAPP(A,B),C))| -hBOOL(hAPP(hAPP(c_Predicate_Oconversep(A,D,E),C),B)).
% 270.53/270.71 ** KEPT (pick-wt=28): 83 [] -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.
% 270.53/270.71 ** KEPT (pick-wt=13): 84 [] c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_lesse_quals(A,C,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=13): 85 [] c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_lesse_quals(A,B,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=13): 86 [] c_lesse_quals(A,B,tc_nat)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),B,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=13): 87 [] c_lesse_quals(A,B,tc_nat)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 270.53/270.71 Following clause subsumed by 84 during input processing: 0 [] c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_lesse_quals(A,C,tc_nat).
% 270.53/270.71 Following clause subsumed by 85 during input processing: 0 [] c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_lesse_quals(A,B,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=20): 89 [copy,88,flip.2] -class_OrderedGroup_Opordered__ab__group__add(A)|c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ominus__class_Ominus(D,C,A),A)=c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(B,D,A),C,A).
% 270.53/270.71 ** KEPT (pick-wt=10): 90 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_lesse_quals(C,B,A).
% 270.53/270.71 ** KEPT (pick-wt=10): 91 [] -class_Orderings_Olinorder(A)| -c_lesse_quals(B,B,A)| -c_HOL_Oord__class_Oless(B,B,A).
% 270.53/270.71 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).
% 270.53/270.71 ** KEPT (pick-wt=10): 92 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(C,B,A).
% 270.53/270.71 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).
% 270.53/270.71 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).
% 270.53/270.71 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).
% 270.53/270.71 ** KEPT (pick-wt=10): 93 [] -class_Orderings_Opreorder(A)| -c_lesse_quals(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 270.53/270.71 ** KEPT (pick-wt=15): 94 [] hBOOL(hAPP(A,B))|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(A),tc_nat)| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 270.53/270.71 ** KEPT (pick-wt=22): 95 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=14): 96 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_HOL_Ominus__class_Ominus(A,C,tc_nat),tc_nat)| -c_lesse_quals(C,B,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=14): 97 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_HOL_Ominus__class_Ominus(C,B,tc_nat),tc_nat)| -c_lesse_quals(A,C,tc_nat).
% 270.53/270.71 Following clause subsumed by 97 during input processing: 0 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_HOL_Ominus__class_Ominus(C,B,tc_nat),tc_nat)| -c_lesse_quals(A,C,tc_nat)| -c_lesse_quals(B,C,tc_nat)| -c_lesse_quals(B,A,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=22): 98 [] c_lesse_quals(A,B,tc_nat)| -c_lesse_quals(c_HOL_Ominus__class_Ominus(A,C,tc_nat),c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_nat)| -c_lesse_quals(C,B,tc_nat)| -c_lesse_quals(C,A,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=21): 99 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=14): 100 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,D,A)|B=C.
% 270.53/270.71 ** KEPT (pick-wt=14): 101 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)!=c_HOL_Ominus__class_Ominus(C,D,A)|C=D.
% 270.53/270.71 ** KEPT (pick-wt=20): 102 [] c_HOL_Ominus__class_Ominus(A,B,tc_nat)!=c_HOL_Ominus__class_Ominus(C,B,tc_nat)| -c_lesse_quals(B,C,tc_nat)| -c_lesse_quals(B,A,tc_nat)|A=C.
% 270.53/270.71 ** KEPT (pick-wt=19): 103 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(A,B,B),B),D),C)).
% 270.53/270.71 ** KEPT (pick-wt=19): 104 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(A,B,B),B),C),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),D),C)).
% 270.53/270.71 ** KEPT (pick-wt=30): 105 [] 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).
% 270.53/270.71 ** KEPT (pick-wt=13): 106 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_HOL_Oord__class_Oless(B,C,A).
% 270.53/270.71 ** KEPT (pick-wt=13): 107 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_HOL_Oord__class_Oless(B,D,A).
% 270.53/270.71 Following clause subsumed by 106 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_HOL_Oord__class_Oless(B,C,A).
% 270.53/270.71 Following clause subsumed by 107 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_HOL_Oord__class_Oless(B,D,A).
% 270.53/270.71 ** KEPT (pick-wt=13): 108 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(B,D,A),C,A).
% 270.53/270.71 ** KEPT (pick-wt=13): 109 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(D,B,A),C,A).
% 270.53/270.71 ** KEPT (pick-wt=9): 110 [] -class_OrderedGroup_Omonoid__add(A)|c_List_Olistsum(c_List_Olist_ONil(A),A)=c_HOL_Ozero__class_Ozero(A).
% 270.53/270.71 ** KEPT (pick-wt=22): 111 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=26): 112 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=24): 113 [] 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)).
% 270.53/270.71 ** KEPT (pick-wt=24): 114 [] 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)).
% 270.53/270.71 ** KEPT (pick-wt=23): 115 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_HOL_Ominus__class_Ominus(C,B,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(A,C,tc_nat)| -c_lesse_quals(B,C,tc_nat)| -c_lesse_quals(B,A,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=22): 116 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=22): 117 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=18): 118 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_HOL_Ominus__class_Ominus(C,B,tc_nat),tc_nat)| -c_lesse_quals(B,A,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=16): 119 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)|B=C.
% 270.53/270.71 ** KEPT (pick-wt=16): 120 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B)|A=C.
% 270.53/270.71 Following clause subsumed by 119 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.
% 270.53/270.71 ** KEPT (pick-wt=20): 121 [] -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.
% 270.53/270.71 ** KEPT (pick-wt=18): 122 [] -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.
% 270.53/270.71 ** KEPT (pick-wt=18): 123 [] -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.
% 270.53/270.71 ** KEPT (pick-wt=18): 124 [] -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.
% 270.53/270.71 ** KEPT (pick-wt=16): 125 [] c_lesse_quals(A,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),C,tc_nat),tc_nat)| -c_lesse_quals(C,B,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=7): 126 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 270.53/270.71 Following clause subsumed by 126 during input processing: 0 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 270.53/270.71 ** KEPT (pick-wt=30): 127 [] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E)=hAPP(hAPP(B,hAPP(hAPP(A,C),E)),hAPP(hAPP(A,D),E))| -c_Groebner__Basis_Ogb__semiring(F,B,A,G,H,I).
% 270.53/270.71 ** KEPT (pick-wt=30): 129 [copy,128,flip.1] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,C),E))=hAPP(hAPP(B,C),hAPP(hAPP(A,D),E))| -c_Groebner__Basis_Ogb__semiring(A,B,F,G,H,I).
% 270.53/270.71 ** KEPT (pick-wt=18): 130 [] hAPP(hAPP(A,B),C)=hAPP(hAPP(A,C),B)| -c_Groebner__Basis_Ogb__semiring(D,A,E,F,G,H).
% 270.53/270.71 ** KEPT (pick-wt=26): 132 [copy,131,flip.1] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(E,A,F,G,H,I).
% 270.53/270.71 ** KEPT (pick-wt=14): 133 [] hAPP(hAPP(A,B),C)=C| -c_Groebner__Basis_Ogb__semiring(D,A,E,F,B,G).
% 270.53/270.71 ** KEPT (pick-wt=14): 134 [] hAPP(hAPP(A,B),C)=B| -c_Groebner__Basis_Ogb__semiring(D,A,E,B,F,G).
% 270.53/270.71 ** KEPT (pick-wt=18): 135 [] hAPP(hAPP(A,B),C)=hAPP(hAPP(A,C),B)| -c_Groebner__Basis_Ogb__semiring(A,D,E,F,G,H).
% 270.53/270.71 ** KEPT (pick-wt=26): 137 [copy,136,flip.1] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(A,E,F,G,H,I).
% 270.53/270.71 ** KEPT (pick-wt=14): 138 [] hAPP(hAPP(A,B),C)=C| -c_Groebner__Basis_Ogb__semiring(A,D,E,B,F,G).
% 270.53/270.71 Following clause subsumed by 137 during input processing: 0 [flip.1] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(A,E,F,G,H,I).
% 270.53/270.71 ** KEPT (pick-wt=17): 139 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=17): 140 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=21): 141 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=13): 142 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_Orderings_Oord__class_Omax(D,B,A),C,A).
% 270.53/270.71 ** KEPT (pick-wt=13): 143 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_Orderings_Oord__class_Omax(B,D,A),C,A).
% 270.53/270.71 ** KEPT (pick-wt=13): 144 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_lesse_quals(B,D,A).
% 270.53/270.71 ** KEPT (pick-wt=13): 145 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_lesse_quals(B,C,A).
% 270.53/270.71 Following clause subsumed by 144 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_lesse_quals(B,D,A).
% 270.53/270.71 Following clause subsumed by 145 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_lesse_quals(B,C,A).
% 270.53/270.71 Following clause subsumed by 142 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_Orderings_Oord__class_Omax(D,B,A),C,A).
% 270.53/270.71 Following clause subsumed by 143 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_Orderings_Oord__class_Omax(B,D,A),C,A).
% 270.53/270.71 ** KEPT (pick-wt=16): 146 [] c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_lesse_quals(c_HOL_Ominus__class_Ominus(A,C,tc_nat),B,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=16): 147 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)| -c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=15): 148 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=17): 149 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(B,D,A)| -c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(D,C,A),A).
% 270.53/270.71 ** KEPT (pick-wt=11): 150 [] c_List_Olist_ONil(A)!=c_List_Oappend(B,C,A)|B=c_List_Olist_ONil(A).
% 270.53/270.71 ** KEPT (pick-wt=11): 151 [] c_List_Olist_ONil(A)!=c_List_Oappend(B,C,A)|C=c_List_Olist_ONil(A).
% 270.53/270.71 ** KEPT (pick-wt=8): 152 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OAbs(B)|A=B.
% 270.53/270.71 ** KEPT (pick-wt=11): 153 [] c_List_Oappend(A,B,C)!=c_List_Olist_ONil(C)|A=c_List_Olist_ONil(C).
% 270.53/270.71 ** KEPT (pick-wt=11): 154 [] c_List_Oappend(A,B,C)!=c_List_Olist_ONil(C)|B=c_List_Olist_ONil(C).
% 270.53/270.71 ** KEPT (pick-wt=22): 155 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=22): 156 [] -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).
% 270.53/270.71 ** KEPT (pick-wt=23): 158 [copy,157,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ominus__class_Ominus(B,C,tc_nat))=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat)| -c_lesse_quals(C,B,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=23): 160 [copy,159,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(A,B,tc_nat)),C)=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat)| -c_lesse_quals(B,A,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=21): 161 [] c_HOL_Ominus__class_Ominus(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat)| -c_lesse_quals(C,B,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=11): 162 [] 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).
% 270.53/270.71 ** KEPT (pick-wt=14): 163 [] -class_Orderings_Opreorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_lesse_quals(C,B,A)| -c_lesse_quals(B,C,A).
% 270.53/270.71 ** KEPT (pick-wt=4): 164 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 270.53/270.71 Following clause subsumed by 164 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 270.53/270.71 ** KEPT (pick-wt=6): 165 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 270.53/270.71 ** KEPT (pick-wt=6): 166 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 270.53/270.71 ** KEPT (pick-wt=6): 167 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 270.53/270.71 ** KEPT (pick-wt=20): 168 [] -c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),tc_nat)|c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),A,tc_nat)=B.
% 270.53/270.71 ** KEPT (pick-wt=24): 169 [] 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)).
% 270.53/270.71 ** KEPT (pick-wt=22): 170 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=19): 171 [] 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).
% 270.53/270.72 ** KEPT (pick-wt=22): 172 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_OrderedGroup_Osemigroup__add(A,E).
% 270.53/270.72 ** KEPT (pick-wt=17): 174 [copy,173,flip.2] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Olistsum(C,A))=c_List_Olistsum(c_List_Olist_OCons(B,C,A),A).
% 270.53/270.72 ** KEPT (pick-wt=13): 175 [] -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.
% 270.53/270.72 ** KEPT (pick-wt=13): 176 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(C,B,A)|c_HOL_Oord__class_Oless(B,C,A).
% 270.53/270.72 ** KEPT (pick-wt=11): 177 [] A=B| -c_lesse_quals(B,A,tc_nat)| -c_lesse_quals(A,B,tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=13): 178 [] -class_Orderings_Oorder(A)|B=C| -c_lesse_quals(C,B,A)| -c_lesse_quals(B,C,A).
% 270.53/270.72 Following clause subsumed by 176 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.
% 270.53/270.72 Following clause subsumed by 178 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_lesse_quals(C,B,A)| -c_lesse_quals(B,C,A).
% 270.53/270.72 Following clause subsumed by 178 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_lesse_quals(B,C,A)| -c_lesse_quals(C,B,A).
% 270.53/270.72 Following clause subsumed by 176 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).
% 270.53/270.72 Following clause subsumed by 176 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).
% 270.53/270.72 ** KEPT (pick-wt=14): 179 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=14): 180 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=8): 181 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(B,B,A)=B.
% 270.53/270.72 ** KEPT (pick-wt=24): 182 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=22): 183 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat)| -c_HOL_Oord__class_Oless(B,D,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=8): 184 [] c_lesse_quals(A,B,tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 270.53/270.72 Following clause subsumed by 184 during input processing: 0 [] c_lesse_quals(A,B,tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=10): 185 [] -class_Orderings_Oorder(A)|c_lesse_quals(B,C,A)| -c_HOL_Oord__class_Oless(B,C,A).
% 270.53/270.72 ** KEPT (pick-wt=10): 186 [] -class_Orderings_Opreorder(A)|c_lesse_quals(B,C,A)| -c_HOL_Oord__class_Oless(B,C,A).
% 270.53/270.72 ** KEPT (pick-wt=7): 187 [] c_List_Olist_ONil(A)!=c_List_Olist_OCons(B,C,A).
% 270.53/270.72 ** KEPT (pick-wt=7): 188 [] -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(A)),B)).
% 270.53/270.72 ** KEPT (pick-wt=14): 189 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=14): 190 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=14): 191 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=14): 192 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=20): 193 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=20): 194 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=20): 195 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=20): 196 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=20): 197 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=20): 198 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=18): 199 [] c_lesse_quals(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_lesse_quals(A,C,tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=18): 200 [] c_lesse_quals(A,B,tc_nat)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=18): 201 [] c_lesse_quals(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_lesse_quals(B,C,tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=15): 203 [copy,202,flip.2] -c_lesse_quals(A,B,tc_nat)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(B,A,tc_nat)),A)=B.
% 270.53/270.72 ** KEPT (pick-wt=15): 204 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ominus__class_Ominus(B,A,tc_nat))=B| -c_lesse_quals(A,B,tc_nat).
% 270.53/270.72 Following clause subsumed by 203 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(A,B,tc_nat)),B)=A| -c_lesse_quals(B,A,tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=14): 205 [] -class_OrderedGroup_Omonoid__add(A)|c_List_Olistsum(B,A)=c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,c_HOL_Ozero__class_Ozero(A),A,A).
% 270.53/270.72 Following clause subsumed by 158 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ominus__class_Ominus(B,C,tc_nat))=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat)| -c_lesse_quals(C,B,tc_nat).
% 270.53/270.72 Following clause subsumed by 160 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(A,B,tc_nat)),C)=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat)| -c_lesse_quals(B,A,tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=14): 206 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=14): 207 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=25): 208 [] 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).
% 270.53/270.72 ** KEPT (pick-wt=11): 209 [] c_List_Oreplicate(A,B,C)!=c_List_Olist_ONil(C)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=15): 210 [] c_List_Olistsp(A,c_List_Oappend(B,C,D),D)| -c_List_Olistsp(A,C,D)| -c_List_Olistsp(A,B,D).
% 270.53/270.72 Following clause subsumed by 135 during input processing: 0 [] hAPP(hAPP(A,B),C)=hAPP(hAPP(A,C),B)| -c_Groebner__Basis_Ogb__semiring(A,D,E,F,G,H).
% 270.53/270.72 ** KEPT (pick-wt=26): 211 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,hAPP(hAPP(A,B),D)),C)| -c_Groebner__Basis_Ogb__semiring(A,E,F,G,H,I).
% 270.53/270.72 ** KEPT (pick-wt=26): 212 [] hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))=hAPP(hAPP(A,C),hAPP(hAPP(A,B),D))| -c_Groebner__Basis_Ogb__semiring(A,E,F,G,H,I).
% 270.53/270.72 Following clause subsumed by 137 during input processing: 0 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(A,E,F,G,H,I).
% 270.53/270.72 ** KEPT (pick-wt=34): 213 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E))=hAPP(hAPP(A,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,C),E))| -c_Groebner__Basis_Ogb__semiring(A,F,G,H,I,J).
% 270.53/270.72 ** KEPT (pick-wt=26): 214 [] hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))=hAPP(hAPP(A,C),hAPP(hAPP(A,B),D))| -c_Groebner__Basis_Ogb__semiring(E,A,F,G,H,I).
% 270.53/270.72 Following clause subsumed by 132 during input processing: 0 [flip.1] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(E,A,F,G,H,I).
% 270.53/270.72 Following clause subsumed by 132 during input processing: 0 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(E,A,F,G,H,I).
% 270.53/270.72 ** KEPT (pick-wt=26): 215 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,hAPP(hAPP(A,B),D)),C)| -c_Groebner__Basis_Ogb__semiring(E,A,F,G,H,I).
% 270.53/270.72 Following clause subsumed by 214 during input processing: 0 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E))=hAPP(hAPP(A,D),hAPP(hAPP(A,hAPP(hAPP(A,B),C)),E))| -c_Groebner__Basis_Ogb__semiring(F,A,G,H,I,J).
% 270.53/270.72 Following clause subsumed by 132 during input processing: 0 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E))=hAPP(hAPP(A,B),hAPP(hAPP(A,C),hAPP(hAPP(A,D),E)))| -c_Groebner__Basis_Ogb__semiring(F,A,G,H,I,J).
% 270.53/270.72 ** KEPT (pick-wt=34): 216 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E))=hAPP(hAPP(A,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,C),E))| -c_Groebner__Basis_Ogb__semiring(F,A,G,H,I,J).
% 270.53/270.72 ** KEPT (pick-wt=14): 217 [] hAPP(hAPP(A,B),C)=B| -c_Groebner__Basis_Ogb__semiring(D,A,E,F,C,G).
% 270.53/270.72 Following clause subsumed by 133 during input processing: 0 [] hAPP(hAPP(A,B),C)=C| -c_Groebner__Basis_Ogb__semiring(D,A,E,F,B,G).
% 270.53/270.72 ** KEPT (pick-wt=14): 218 [] hAPP(hAPP(A,B),C)=C| -c_Groebner__Basis_Ogb__semiring(D,A,E,C,F,G).
% 270.53/270.72 Following clause subsumed by 134 during input processing: 0 [] hAPP(hAPP(A,B),C)=B| -c_Groebner__Basis_Ogb__semiring(D,A,E,B,F,G).
% 270.53/270.72 ** KEPT (pick-wt=30): 219 [] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E)=hAPP(hAPP(B,hAPP(hAPP(A,C),E)),hAPP(hAPP(A,D),E))| -c_Groebner__Basis_Ogb__semiring(B,A,F,G,H,I).
% 270.53/270.72 Following clause subsumed by 130 during input processing: 0 [] hAPP(hAPP(A,B),C)=hAPP(hAPP(A,C),B)| -c_Groebner__Basis_Ogb__semiring(D,A,E,F,G,H).
% 270.53/270.72 ** KEPT (pick-wt=14): 220 [] hAPP(hAPP(A,B),C)=B| -c_Groebner__Basis_Ogb__semiring(A,D,E,C,F,G).
% 270.53/270.72 Following clause subsumed by 138 during input processing: 0 [] hAPP(hAPP(A,B),C)=C| -c_Groebner__Basis_Ogb__semiring(A,D,E,B,F,G).
% 270.53/270.72 ** KEPT (pick-wt=22): 221 [] hAPP(hAPP(A,B),B)=hAPP(hAPP(C,hAPP(hAPP(A,D),D)),B)| -c_Groebner__Basis_Ogb__semiring(A,C,E,F,D,G).
% 270.53/270.72 ** KEPT (pick-wt=26): 222 [] hAPP(hAPP(A,B),hAPP(hAPP(C,D),B))=hAPP(hAPP(C,hAPP(hAPP(A,D),E)),B)| -c_Groebner__Basis_Ogb__semiring(A,C,F,G,E,H).
% 270.53/270.72 ** KEPT (pick-wt=26): 223 [] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),D)=hAPP(hAPP(B,hAPP(hAPP(A,C),E)),D)| -c_Groebner__Basis_Ogb__semiring(A,B,F,G,E,H).
% 270.53/270.72 ** KEPT (pick-wt=30): 224 [] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,E),D))=hAPP(hAPP(B,hAPP(hAPP(A,C),E)),D)| -c_Groebner__Basis_Ogb__semiring(A,B,F,G,H,I).
% 270.53/270.72 ** KEPT (pick-wt=20): 225 [] 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).
% 270.53/270.72 ** KEPT (pick-wt=35): 226 [] -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)).
% 270.53/270.72 ** KEPT (pick-wt=32): 227 [] 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)).
% 270.53/270.72 ** KEPT (pick-wt=9): 228 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=11): 229 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(B,C,A)=c_Orderings_Oord__class_Omax(C,B,A).
% 270.53/270.72 ** KEPT (pick-wt=29): 230 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=12): 231 [] c_Lambda_Oliftn(A,c_Lambda_OdB_OVar(B),C)=c_Lambda_OdB_OVar(B)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=16): 232 [] 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)).
% 270.53/270.72 ** KEPT (pick-wt=13): 233 [] c_HOL_Ominus__class_Ominus(A,c_HOL_Ominus__class_Ominus(A,B,tc_nat),tc_nat)=B| -c_lesse_quals(B,A,tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=13): 234 [] 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).
% 270.53/270.72 ** KEPT (pick-wt=20): 235 [] 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)).
% 270.53/270.72 ** KEPT (pick-wt=6): 236 [] c_List_Olist_OCons(A,B,C)!=B.
% 270.53/270.72 Following clause subsumed by 236 during input processing: 0 [flip.1] c_List_Olist_OCons(B,A,C)!=A.
% 270.53/270.72 ** KEPT (pick-wt=26): 237 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Orderings_Oord__class_Omax(B,C,A)),D)=c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A).
% 270.53/270.72 ** KEPT (pick-wt=22): 238 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=27): 239 [] 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).
% 270.53/270.72 ** KEPT (pick-wt=17): 240 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(B,C,A),D,A)=c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(C,D,A),A).
% 270.53/270.72 ** KEPT (pick-wt=17): 241 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(C,D,A),A)=c_Orderings_Oord__class_Omax(C,c_Orderings_Oord__class_Omax(B,D,A),A).
% 270.53/270.72 ** KEPT (pick-wt=9): 242 [] -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).
% 270.53/270.72 Following clause subsumed by 242 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).
% 270.53/270.72 ** KEPT (pick-wt=14): 243 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(A)),c_Lambda_OdB_OAbs(B)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),B)).
% 270.53/270.72 ** KEPT (pick-wt=14): 244 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(B,C,A),A)=c_Orderings_Oord__class_Omax(B,C,A).
% 270.53/270.72 ** KEPT (pick-wt=13): 245 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A)=B.
% 270.53/270.72 ** KEPT (pick-wt=11): 246 [] hAPP(hAPP(A,B),C)=B| -c_OrderedGroup_Omonoid__add(C,A,D).
% 270.53/270.72 ** KEPT (pick-wt=11): 247 [] hAPP(hAPP(A,B),C)=C| -c_OrderedGroup_Omonoid__add(B,A,D).
% 270.53/270.72 ** KEPT (pick-wt=24): 248 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=24): 249 [] -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).
% 270.53/270.72 Following clause subsumed by 49 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).
% 270.53/270.72 Following clause subsumed by 48 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).
% 270.53/270.72 ** KEPT (pick-wt=17): 250 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=17): 251 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=19): 252 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=13): 253 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=15): 254 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=11): 255 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=9): 256 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 270.53/270.72 ** KEPT (pick-wt=9): 257 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 270.53/270.72 Following clause subsumed by 256 during input processing: 0 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 270.53/270.72 ** KEPT (pick-wt=9): 258 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 270.53/270.72 ** KEPT (pick-wt=16): 260 [copy,259,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).
% 270.53/270.72 ** KEPT (pick-wt=13): 261 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=14): 262 [] -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.
% 270.53/270.72 ** KEPT (pick-wt=12): 263 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 270.53/270.72 ** KEPT (pick-wt=12): 264 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 270.53/270.72 ** KEPT (pick-wt=11): 265 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 270.53/270.72 ** KEPT (pick-wt=11): 266 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 270.53/270.72 ** KEPT (pick-wt=13): 268 [copy,267,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.
% 270.53/270.72 ** KEPT (pick-wt=11): 269 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 270.53/270.72 ** KEPT (pick-wt=11): 270 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 270.53/270.72 ** KEPT (pick-wt=11): 271 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 270.53/270.72 ** KEPT (pick-wt=11): 272 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 270.53/270.72 Following clause subsumed by 265 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.
% 270.53/270.72 Following clause subsumed by 164 during input processing: 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=17): 273 [] 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.
% 270.53/270.72 ** KEPT (pick-wt=9): 274 [] A=c_HOL_Ozero__class_Ozero(tc_nat)| -c_lesse_quals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=13): 275 [] 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).
% 270.53/270.72 ** KEPT (pick-wt=13): 276 [] 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).
% 270.53/270.72 ** KEPT (pick-wt=12): 278 [copy,277,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.53/270.72 Following clause subsumed by 278 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=6): 279 [] -class_OrderedGroup_Osemigroup__add(A)|c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(A),A).
% 270.53/270.72 ** KEPT (pick-wt=15): 280 [] hAPP(c_Type_Oshift(A,B,C,D),E)=hAPP(A,E)| -c_HOL_Oord__class_Oless(E,B,tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=11): 281 [] c_List_Olist_ONil(A)!=c_List_Oreplicate(B,C,A)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=22): 282 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,C,tc_nat),c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_nat)| -c_lesse_quals(C,B,tc_nat)| -c_lesse_quals(C,A,tc_nat).
% 270.53/270.72 Following clause subsumed by 118 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_HOL_Ominus__class_Ominus(C,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat)| -c_lesse_quals(B,C,tc_nat)| -c_lesse_quals(B,A,tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=20): 283 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=15): 284 [] 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).
% 270.53/270.72 ** KEPT (pick-wt=16): 285 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OAbs(E),t_a)))|hBOOL(hAPP(A,hAPP(D,E))).
% 270.53/270.72 Following clause subsumed by 285 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))).
% 270.53/270.72 ** KEPT (pick-wt=17): 286 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=17): 287 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=9): 288 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=9): 289 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=21): 290 [] -class_Ring__and__Field_Oring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(B,C,tc_nat),A)=c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A)| -c_lesse_quals(C,B,tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=10): 291 [] c_List_Oappend(A,B,C)!=A|B=c_List_Olist_ONil(C).
% 270.53/270.72 Following clause subsumed by 291 during input processing: 0 [flip.1] c_List_Oappend(A,B,C)!=A|B=c_List_Olist_ONil(C).
% 270.53/270.72 ** KEPT (pick-wt=10): 292 [] c_List_Oappend(A,B,C)!=B|A=c_List_Olist_ONil(C).
% 270.53/270.72 Following clause subsumed by 292 during input processing: 0 [flip.1] c_List_Oappend(B,A,C)!=A|B=c_List_Olist_ONil(C).
% 270.53/270.72 ** KEPT (pick-wt=16): 293 [] 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).
% 270.53/270.72 ** KEPT (pick-wt=16): 294 [] 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).
% 270.53/270.72 ** KEPT (pick-wt=20): 295 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=20): 296 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=20): 297 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=20): 298 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=20): 299 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=20): 300 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=18): 301 [] 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).
% 270.53/270.72 ** KEPT (pick-wt=18): 302 [] 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).
% 270.53/270.72 ** KEPT (pick-wt=18): 303 [] 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).
% 270.53/270.72 ** KEPT (pick-wt=14): 304 [] -class_Orderings_Oorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(B,D,A)| -c_lesse_quals(D,C,A).
% 270.53/270.72 ** KEPT (pick-wt=14): 305 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=14): 306 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=22): 307 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=14): 308 [] -class_Orderings_Opreorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(D,C,A)| -c_lesse_quals(B,D,A).
% 270.53/270.72 ** KEPT (pick-wt=12): 309 [] c_lesse_quals(A,B,tc_nat)| -c_lesse_quals(C,B,tc_nat)| -c_lesse_quals(A,C,tc_nat).
% 270.53/270.72 ** KEPT (pick-wt=6): 310 [] -class_Orderings_Oorder(A)|c_lesse_quals(B,B,A).
% 270.53/270.72 ** KEPT (pick-wt=6): 311 [] -class_Orderings_Opreorder(A)|c_lesse_quals(B,B,A).
% 270.53/270.72 ** KEPT (pick-wt=14): 312 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=14): 313 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=24): 314 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=12): 315 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_OCons(D,E,C)|A=D.
% 270.53/270.72 ** KEPT (pick-wt=12): 316 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_OCons(D,E,C)|B=E.
% 270.53/270.72 ** KEPT (pick-wt=14): 317 [] c_Type_Otyping(A,B,C)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,D),B))| -c_Type_Otyping(A,D,C).
% 270.53/270.72 ** KEPT (pick-wt=22): 318 [] 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).
% 270.53/270.72 ** KEPT (pick-wt=16): 319 [] 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).
% 270.53/270.72 ** KEPT (pick-wt=16): 320 [] 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))).
% 270.53/270.72 ** KEPT (pick-wt=16): 321 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OVar(E),t_a)))|hBOOL(hAPP(A,hAPP(B,E))).
% 270.53/270.72 Following clause subsumed by 321 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))).
% 270.53/270.72 ** KEPT (pick-wt=8): 322 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OVar(B)|A=B.
% 270.53/270.72 ** KEPT (pick-wt=5): 323 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 270.53/270.72 ** KEPT (pick-wt=12): 324 [] 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).
% 270.53/270.72 ** KEPT (pick-wt=12): 325 [] 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).
% 270.53/270.72 ** KEPT (pick-wt=21): 326 [] -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)).
% 270.53/270.72 ** KEPT (pick-wt=17): 327 [] 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).
% 270.53/270.72 ** KEPT (pick-wt=19): 328 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=19): 329 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=19): 330 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=19): 331 [] -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).
% 270.53/270.72 ** KEPT (pick-wt=12): 332 [] c_List_Omap(A,B,C,D)!=c_List_Olist_ONil(D)|B=c_List_Olist_ONil(C).
% 270.53/270.72 ** KEPT (pick-wt=19): 334 [copy,333,flip.2] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_List_Olistsum(B,A)),c_List_Olistsum(C,A))=c_List_Olistsum(c_List_Oappend(B,C,A),A).
% 270.53/270.72 ** KEPT (pick-wt=20): 335 [] 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.
% 270.53/270.72 ** KEPT (pick-wt=20): 336 [] 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.
% 270.53/270.72 ** KEPT (pick-wt=13): 337 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)|C=B| -c_lesse_quals(B,C,A).
% 270.53/270.72 Following clause subsumed by 337 during input processing: 0 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(B,C,A)|C=B.
% 270.53/270.72 ** KEPT (pick-wt=11): 338 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|A=B| -c_lesse_quals(A,B,tc_nat).
% 270.53/270.73 Following clause subsumed by 338 during input processing: 0 [] A=B|c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_lesse_quals(A,B,tc_nat).
% 270.53/270.73 Following clause subsumed by 338 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|A=B| -c_lesse_quals(A,B,tc_nat).
% 270.53/270.73 ** KEPT (pick-wt=13): 339 [] -class_Orderings_Oorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(B,C,A).
% 270.53/270.73 Following clause subsumed by 339 during input processing: 0 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)|B=C| -c_lesse_quals(B,C,A).
% 270.53/270.73 Following clause subsumed by 339 during input processing: 0 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)|B=C| -c_lesse_quals(B,C,A).
% 270.53/270.73 Following clause subsumed by 339 during input processing: 0 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(B,C,A)|B=C.
% 270.53/270.73 ** KEPT (pick-wt=13): 340 [] -class_Orderings_Olinorder(A)|B=C| -c_lesse_quals(B,C,A)|c_HOL_Oord__class_Oless(B,C,A).
% 270.53/270.73 Following clause subsumed by 340 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(B,C,A).
% 270.53/270.73 ** KEPT (pick-wt=18): 341 [] 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).
% 270.53/270.73 ** KEPT (pick-wt=16): 342 [] 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).
% 270.53/270.73 ** KEPT (pick-wt=10): 343 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 270.53/270.73 ** KEPT (pick-wt=22): 344 [] 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)).
% 270.53/270.73 ** KEPT (pick-wt=22): 345 [] 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)).
% 270.53/270.73 ** KEPT (pick-wt=10): 346 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 270.53/270.73 ** KEPT (pick-wt=14): 347 [] c_Wellfounded_Oaccp(A,B,C)| -hBOOL(hAPP(hAPP(A,B),D))| -c_Wellfounded_Oaccp(A,D,C).
% 270.53/270.73 ** KEPT (pick-wt=10): 348 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,C,A)|c_lesse_quals(C,B,A).
% 270.53/270.73 ** KEPT (pick-wt=10): 349 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 270.53/270.73 Following clause subsumed by 347 during input processing: 0 [] c_Wellfounded_Oaccp(A,B,C)| -hBOOL(hAPP(hAPP(A,B),D))| -c_Wellfounded_Oaccp(A,D,C).
% 270.53/270.73 Following clause subsumed by 349 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 270.53/270.73 ** KEPT (pick-wt=13): 350 [] -hBOOL(hAPP(A,c_Nat_Onat_Onat__case(B,C,c_HOL_Ozero__class_Ozero(tc_nat),t_a)))|hBOOL(hAPP(A,B)).
% 270.53/270.73 ** KEPT (pick-wt=10): 352 [copy,351,factor_simp] hBOOL(hAPP(A,v_sko__Nat__Xnat__Xinducts__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 270.53/270.73 ** KEPT (pick-wt=10): 354 [copy,353,factor_simp] hBOOL(hAPP(A,v_sko__Nat__Xnat__Xinduct__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 270.53/270.73 ** KEPT (pick-wt=5): 355 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 270.53/270.73 Following clause subsumed by 355 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 270.53/270.73 ** KEPT (pick-wt=10): 357 [copy,356,factor_simp] hBOOL(hAPP(A,v_sko__List__Xupt__Xinduct__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 270.53/270.73 ** KEPT (pick-wt=14): 358 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 270.53/270.73 ** KEPT (pick-wt=16): 359 [] c_List_Oreplicate(A,B,C)!=c_List_Oreplicate(D,E,C)|B=E|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.53/270.73 ** KEPT (pick-wt=15): 360 [] hAPP(hAPP(A,B),c_HOL_Ozero__class_Ozero(tc_nat))=C| -c_Groebner__Basis_Ogb__semiring(D,E,A,F,C,G).
% 270.53/270.73 ** KEPT (pick-wt=19): 362 [copy,361,flip.2] -class_OrderedGroup_Omonoid__add(A)|c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,c_HOL_Ozero__class_Ozero(A),A,A)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),B,A,A).
% 270.53/270.73 ** KEPT (pick-wt=14): 363 [] -class_OrderedGroup_Omonoid__add(A)|c_List_Olistsum(B,A)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),B,A,A).
% 270.53/270.73 ** KEPT (pick-wt=23): 365 [copy,364,flip.2] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),C,c_HOL_Ozero__class_Ozero(A),A,A))=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A).
% 270.53/270.73 ** KEPT (pick-wt=8): 366 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 270.53/270.73 ** KEPT (pick-wt=8): 367 [] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 270.53/270.73 ** KEPT (pick-wt=21): 368 [] -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))).
% 270.53/270.73 Following clause subsumed by 368 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))).
% 270.53/270.73 ** KEPT (pick-wt=8): 369 [] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 270.53/270.73 ** KEPT (pick-wt=20): 370 [] 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)).
% 270.53/270.73 ** KEPT (pick-wt=20): 371 [] 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)).
% 270.53/270.73 ** KEPT (pick-wt=8): 372 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 270.53/270.73 ** KEPT (pick-wt=43): 373 [] -c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),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),tc_Lambda_OdB)| -c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),B,tc_Lambda_OdB)|c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),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),tc_Lambda_OdB).
% 270.53/270.73 ** KEPT (pick-wt=26): 374 [] 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)).
% 270.53/270.73 ** KEPT (pick-wt=23): 375 [] 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).
% 270.53/270.73 ** KEPT (pick-wt=21): 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,A,C,tc_Lambda_OdB,tc_Lambda_OdB)))| -c_ListOrder_Ostep1(c_Lambda_Obeta,B,C,tc_Lambda_OdB).
% 270.53/270.73 ** 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=c_List_Olist_ONil(tc_Lambda_OdB).
% 270.53/270.73 ** KEPT (pick-wt=15): 378 [] 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).
% 270.53/270.73 ** KEPT (pick-wt=28): 380 [copy,379,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).
% 270.53/270.73 ** KEPT (pick-wt=13): 381 [] 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).
% 270.53/270.73 ** KEPT (pick-wt=13): 382 [] 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).
% 270.53/270.73 ** KEPT (pick-wt=14): 383 [] 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).
% 270.67/270.73 ** KEPT (pick-wt=24): 385 [copy,384,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).
% 270.67/270.73 ** KEPT (pick-wt=27): 387 [copy,386,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).
% 270.67/270.73 ** KEPT (pick-wt=21): 388 [] 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).
% 270.67/270.73 ** KEPT (pick-wt=24): 389 [] 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)).
% 270.67/270.73 ** KEPT (pick-wt=12): 390 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,A),B)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 270.67/270.73 ** KEPT (pick-wt=9): 391 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(A)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 270.67/270.73 ** KEPT (pick-wt=26): 392 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),A),B)))| -c_Type_Otyping(C,A,v_T____)| -hBOOL(hAPP(c_InductTermi_OIT,A))| -c_Type_Otyping(c_Type_Oshift(C,B,v_T____,tc_Type_Otype),v_a____,D).
% 270.67/270.73 ** KEPT (pick-wt=14): 393 [] 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).
% 270.67/270.73 ** KEPT (pick-wt=20): 394 [] -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).
% 270.67/270.73 ** KEPT (pick-wt=16): 395 [] -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).
% 270.67/270.73 ** KEPT (pick-wt=16): 396 [] -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).
% 270.67/270.73 ** KEPT (pick-wt=9): 397 [] -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).
% 270.67/270.73 ** KEPT (pick-wt=23): 398 [] -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).
% 270.67/270.73 ** KEPT (pick-wt=18): 399 [] 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.
% 270.67/270.73 ** KEPT (pick-wt=18): 400 [] 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.
% 270.67/270.73 ** KEPT (pick-wt=20): 401 [] 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.
% 270.67/270.73 ** KEPT (pick-wt=13): 402 [] 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).
% 270.67/270.73 ** KEPT (pick-wt=18): 403 [] 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.
% 270.67/270.73 ** KEPT (pick-wt=18): 404 [] 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.
% 270.67/270.73 ** KEPT (pick-wt=22): 405 [] 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)).
% 270.67/270.73 ** KEPT (pick-wt=13): 406 [] 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.
% 270.67/270.73 ** KEPT (pick-wt=13): 407 [] 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.
% 270.67/270.73 ** KEPT (pick-wt=13): 408 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,A),c_Lambda_OdB_OVar(B))))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 270.67/270.73 ** KEPT (pick-wt=15): 409 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),c_Lambda_OdB_OVar(B)),C)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 270.67/270.73 ** KEPT (pick-wt=50): 410 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),A),B)))| -c_Type_Otyping(C,A,v_T____)| -hBOOL(hAPP(c_InductTermi_OIT,A))| -c_Type_Otyping(c_Type_Oshift(C,B,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),D).
% 270.67/270.73 ** KEPT (pick-wt=34): 411 [] 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))).
% 270.67/270.73 ** KEPT (pick-wt=14): 412 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|A=C.
% 270.67/270.73 ** KEPT (pick-wt=14): 413 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|B=D.
% 270.67/270.73 ** KEPT (pick-wt=16): 414 [] 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.
% 270.67/270.73 ** KEPT (pick-wt=22): 415 [] -hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))).
% 270.67/270.73 ** KEPT (pick-wt=6): 416 [] class_Orderings_Opreorder(tc_fun(A,B))| -class_Orderings_Opreorder(B).
% 270.67/270.73 ** KEPT (pick-wt=6): 417 [] class_Orderings_Oorder(tc_fun(A,B))| -class_Orderings_Oorder(B).
% 270.67/270.73 ** KEPT (pick-wt=6): 418 [] class_Orderings_Obot(tc_fun(A,B))| -class_Orderings_Obot(B).
% 270.67/270.73 ** KEPT (pick-wt=10): 419 [] A=B| -hBOOL(hAPP(hAPP(c_fe_qual(C),A),B)).
% 270.67/270.73 Following clause subsumed by 323 during input processing: 0 [copy,66,flip.1] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 270.67/270.73 92 back subsumes 91.
% 270.67/270.73 Following clause subsumed by 187 during input processing: 0 [copy,126,flip.1] c_List_Olist_ONil(A)!=c_List_Olist_OCons(B,C,A).
% 270.67/270.73 Following clause subsumed by 126 during input processing: 0 [copy,187,flip.1] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 270.67/270.73 Following clause subsumed by 66 during input processing: 0 [copy,323,flip.1] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 270.67/270.73 Following clause subsumed by 367 during input processing: 0 [copy,366,flip.1] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 270.67/270.73 Following clause subsumed by 366 during input processing: 0 [copy,367,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 270.67/270.73 Following clause subsumed by 372 during input processing: 0 [copy,369,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 270.67/270.73 Following clause subsumed by 369 during input processing: 0 [copy,372,flip.1] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 270.67/270.73 ** KEPT (pick-wt=15): 457 [copy,378,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).
% 270.67/270.73 ** KEPT (pick-wt=14): 458 [copy,383,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).
% 270.67/270.73 Following clause subsumed by 378 during input processing: 0 [copy,457,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).
% 270.67/270.73 Following clause subsumed by 383 during input processing: 0 [copy,458,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).
% 270.67/270.73
% 270.67/270.73 ------------> process sos:
% 270.67/270.73 ** KEPT (pick-wt=3): 459 [] A=A.
% 270.67/270.73 ** KEPT (pick-wt=18): 460 [] 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).
% 270.67/270.73 ** KEPT (pick-wt=11): 461 [] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(C,D).
% 270.67/270.73 ** KEPT (pick-wt=5): 462 [] c_List_Olistsp(A,c_List_Olist_ONil(B),B).
% 270.67/270.73 ** KEPT (pick-wt=8): 463 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),C)).
% 270.67/270.73 Following clause subsumed by 463 during input processing: 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),C)).
% 270.67/270.73 ** KEPT (pick-wt=7): 464 [] c_List_Oappend(A,c_List_Olist_ONil(B),B)=A.
% 270.67/270.73 ---> New Demodulator: 465 [new_demod,464] c_List_Oappend(A,c_List_Olist_ONil(B),B)=A.
% 270.67/270.73 ** KEPT (pick-wt=7): 467 [copy,466,flip.1] c_List_Oappend(c_List_Olist_ONil(A),B,A)=B.
% 270.67/270.73 ---> New Demodulator: 468 [new_demod,467] c_List_Oappend(c_List_Olist_ONil(A),B,A)=B.
% 270.67/270.73 Following clause subsumed by 459 during input processing: 0 [demod,465] A=A.
% 270.67/270.73 Following clause subsumed by 459 during input processing: 0 [demod,468] B=B.
% 270.67/270.73 Following clause subsumed by 459 during input processing: 0 [demod,468] A=A.
% 270.67/270.73 ** KEPT (pick-wt=15): 469 [] c_List_Omap(A,c_List_Oreplicate(B,C,D),D,E)=c_List_Oreplicate(B,hAPP(A,C),E).
% 270.67/270.73 ** KEPT (pick-wt=13): 470 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 270.67/270.73 ** KEPT (pick-wt=21): 471 [] c_List_Ofoldr(A,c_List_Oappend(B,C,D),E,D,F)=c_List_Ofoldr(A,B,c_List_Ofoldr(A,C,E,D,F),D,F).
% 270.67/270.73 ---> New Demodulator: 472 [new_demod,471] c_List_Ofoldr(A,c_List_Oappend(B,C,D),E,D,F)=c_List_Ofoldr(A,B,c_List_Ofoldr(A,C,E,D,F),D,F).
% 270.67/270.73 ** KEPT (pick-wt=8): 473 [] c_List_Odrop(A,c_List_Olist_ONil(B),B)=c_List_Olist_ONil(B).
% 270.67/270.73 ---> New Demodulator: 474 [new_demod,473] c_List_Odrop(A,c_List_Olist_ONil(B),B)=c_List_Olist_ONil(B).
% 270.67/270.73 ** KEPT (pick-wt=23): 475 [] 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)).
% 270.67/270.73 ** KEPT (pick-wt=23): 476 [] 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)).
% 270.67/270.73 ---> New Demodulator: 477 [new_demod,476] 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)).
% 270.67/270.73 ** KEPT (pick-wt=13): 478 [] c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(A,B,C),C)=c_List_Olist_OCons(A,B,C).
% 270.67/270.73 ---> New Demodulator: 479 [new_demod,478] c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(A,B,C),C)=c_List_Olist_OCons(A,B,C).
% 270.67/270.73 ** KEPT (pick-wt=11): 480 [] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 270.67/270.73 ** KEPT (pick-wt=14): 481 [] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 270.67/270.73 ** KEPT (pick-wt=10): 483 [copy,482,unit_del,164] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),A)=B.
% 270.67/270.73 ---> New Demodulator: 484 [new_demod,483] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),A)=B.
% 270.67/270.73 ** KEPT (pick-wt=9): 485 [] c_List_Ofoldr(A,c_List_Olist_ONil(B),C,B,D)=C.
% 270.67/270.73 ---> New Demodulator: 486 [new_demod,485] c_List_Ofoldr(A,c_List_Olist_ONil(B),C,B,D)=C.
% 270.67/270.73 ** KEPT (pick-wt=9): 487 [] c_List_Omap(A,c_List_Olist_ONil(B),B,C)=c_List_Olist_ONil(C).
% 270.67/270.73 ** KEPT (pick-wt=12): 488 [] 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).
% 270.67/270.73 ** KEPT (pick-wt=17): 489 [] 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).
% 270.67/270.73 ** 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).
% 270.67/270.73 ---> 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).
% 270.67/270.73 ** 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).
% 270.67/270.73 ---> 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).
% 270.67/270.73 ** KEPT (pick-wt=7): 494 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(A,B,tc_nat),A,tc_nat).
% 270.67/270.73 ** KEPT (pick-wt=7): 495 [] c_Type_Otyping(A,c_Lambda_OdB_OVar(B),hAPP(A,B)).
% 270.67/270.74 ** KEPT (pick-wt=15): 497 [copy,496,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).
% 270.67/270.74 ---> New Demodulator: 498 [new_demod,497] c_List_Olist_OCons(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 270.67/270.74 Following clause subsumed by 459 during input processing: 0 [demod,498] c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C)=c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C).
% 270.67/270.74 ** KEPT (pick-wt=15): 499 [] 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).
% 270.67/270.74 ** KEPT (pick-wt=19): 501 [copy,500,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).
% 270.67/270.74 ---> New Demodulator: 502 [new_demod,501] 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).
% 270.67/270.74 Following clause subsumed by 459 during input processing: 0 [demod,502] 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).
% 270.67/270.74 Following clause subsumed by 459 during input processing: 0 [demod,502] 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).
% 270.67/270.74 Following clause subsumed by 459 during input processing: 0 [demod,498] c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 270.67/270.74 Following clause subsumed by 459 during input processing: 0 [demod,498] c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 270.67/270.74 ** KEPT (pick-wt=9): 503 [] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 270.67/270.74 ---> New Demodulator: 504 [new_demod,503] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 270.67/270.74 ** KEPT (pick-wt=15): 505 [] 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).
% 270.67/270.74 ** KEPT (pick-wt=8): 506 [] c_Predicate_Oconversep(c_fe_qual(A),A,A)=c_fe_qual(A).
% 270.67/270.74 ---> New Demodulator: 507 [new_demod,506] c_Predicate_Oconversep(c_fe_qual(A),A,A)=c_fe_qual(A).
% 270.67/270.74 ** KEPT (pick-wt=11): 508 [] c_Lambda_OdB_OdB__rec(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 270.67/270.74 ** KEPT (pick-wt=8): 509 [] c_List_Olist_ONil(A)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),B,A).
% 270.67/270.74 ** KEPT (pick-wt=17): 510 [] 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).
% 270.67/270.74 ** KEPT (pick-wt=9): 511 [] c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=9): 512 [] c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),tc_nat).
% 270.67/270.74 Following clause subsumed by 511 during input processing: 0 [] c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=14): 513 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(A,B,tc_nat)),B)=c_Orderings_Oord__class_Omax(A,B,tc_nat).
% 270.67/270.74 ---> New Demodulator: 514 [new_demod,513] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(A,B,tc_nat)),B)=c_Orderings_Oord__class_Omax(A,B,tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=21): 516 [copy,515,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).
% 270.67/270.74 ---> New Demodulator: 517 [new_demod,516] 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).
% 270.67/270.74 ** KEPT (pick-wt=11): 518 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 270.67/270.74 Following clause subsumed by 518 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).
% 270.67/270.74 Following clause subsumed by 518 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 270.67/270.74 ** KEPT (pick-wt=21): 519 [] c_List_Oappend(c_List_Oreplicate(A,B,C),c_List_Oreplicate(D,B,C),C)=c_List_Oappend(c_List_Oreplicate(D,B,C),c_List_Oreplicate(A,B,C),C).
% 270.67/270.74 ** KEPT (pick-wt=17): 521 [copy,520,flip.1] c_List_Odrop(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,D)=c_List_Odrop(A,c_List_Odrop(B,C,D),D).
% 270.67/270.74 ---> New Demodulator: 522 [new_demod,521] c_List_Odrop(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,D)=c_List_Odrop(A,c_List_Odrop(B,C,D),D).
% 270.67/270.74 ** KEPT (pick-wt=20): 523 [] c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,D)=c_List_Oappend(c_List_Oreplicate(A,C,D),c_List_Oreplicate(B,C,D),D).
% 270.67/270.74 ---> New Demodulator: 524 [new_demod,523] c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,D)=c_List_Oappend(c_List_Oreplicate(A,C,D),c_List_Oreplicate(B,C,D),D).
% 270.67/270.74 ** KEPT (pick-wt=30): 525 [] 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).
% 270.67/270.74 ---> New Demodulator: 526 [new_demod,525] 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).
% 270.67/270.74 ** KEPT (pick-wt=15): 528 [copy,527,flip.1] c_List_Oreplicate(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,D)=c_List_Odrop(B,c_List_Oreplicate(A,C,D),D).
% 270.67/270.74 ---> New Demodulator: 529 [new_demod,528] c_List_Oreplicate(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,D)=c_List_Odrop(B,c_List_Oreplicate(A,C,D),D).
% 270.67/270.74 ** KEPT (pick-wt=8): 530 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Olist_ONil(B).
% 270.67/270.74 ** KEPT (pick-wt=11): 532 [copy,531,unit_del,164] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 270.67/270.74 ---> New Demodulator: 533 [new_demod,532] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 270.67/270.74 Following clause subsumed by 459 during input processing: 0 [demod,468] c_List_Olist_OCons(A,B,C)=c_List_Olist_OCons(A,B,C).
% 270.67/270.74 ** KEPT (pick-wt=9): 534 [] c_List_Olist_ONil(A)=c_List_Omap(B,c_List_Olist_ONil(C),C,A).
% 270.67/270.74 Following clause subsumed by 459 during input processing: 0 [demod,465] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 270.67/270.74 ** KEPT (pick-wt=9): 535 [] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(A,B),B)=c_Transitive__Closure_Ortranclp(A,B).
% 270.67/270.74 ---> New Demodulator: 536 [new_demod,535] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(A,B),B)=c_Transitive__Closure_Ortranclp(A,B).
% 270.67/270.74 ** KEPT (pick-wt=19): 537 [] c_List_Oappend(c_List_Oreplicate(A,B,C),c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C)=c_List_Olist_OCons(B,c_List_Oreplicate(A,B,C),C).
% 270.67/270.74 ** KEPT (pick-wt=11): 538 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat)=A.
% 270.67/270.74 ---> New Demodulator: 539 [new_demod,538] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat)=A.
% 270.67/270.74 ** KEPT (pick-wt=11): 540 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat)=B.
% 270.67/270.74 ---> New Demodulator: 541 [new_demod,540] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat)=B.
% 270.67/270.74 ** KEPT (pick-wt=6): 542 [] c_lesse_quals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=7): 543 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 270.67/270.74 ---> New Demodulator: 544 [new_demod,543] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 270.67/270.74 ** KEPT (pick-wt=9): 545 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=8): 546 [] c_Nat_Onat_Onat__case(A,B,c_HOL_Ozero__class_Ozero(tc_nat),C)=A.
% 270.67/270.74 ---> New Demodulator: 547 [new_demod,546] c_Nat_Onat_Onat__case(A,B,c_HOL_Ozero__class_Ozero(tc_nat),C)=A.
% 270.67/270.74 Following clause subsumed by 459 during input processing: 0 [demod,547] A=A.
% 270.67/270.74 ** KEPT (pick-wt=7): 548 [] c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 270.67/270.74 ---> New Demodulator: 549 [new_demod,548] c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 270.67/270.74 ** KEPT (pick-wt=7): 550 [] c_HOL_Ominus__class_Ominus(A,A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=18): 551 [] 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)).
% 270.67/270.74 ** KEPT (pick-wt=20): 553 [copy,552,flip.1] hAPP(hAPP(A,B),c_List_Ofoldr(A,C,D,E,F))=c_List_Ofoldr(A,c_List_Olist_OCons(B,C,E),D,E,F).
% 270.67/270.74 ---> New Demodulator: 554 [new_demod,553] hAPP(hAPP(A,B),c_List_Ofoldr(A,C,D,E,F))=c_List_Ofoldr(A,c_List_Olist_OCons(B,C,E),D,E,F).
% 270.67/270.74 ** KEPT (pick-wt=9): 555 [] c_Predicate_Oconversep(c_Predicate_Oconversep(A,B,C),C,B)=A.
% 270.67/270.74 ---> New Demodulator: 556 [new_demod,555] c_Predicate_Oconversep(c_Predicate_Oconversep(A,B,C),C,B)=A.
% 270.67/270.74 Following clause subsumed by 459 during input processing: 0 [demod,468] c_List_Olist_OCons(B,C,A)=c_List_Olist_OCons(B,C,A).
% 270.67/270.74 ** KEPT (pick-wt=4): 557 [] c_lesse_quals(A,A,tc_nat).
% 270.67/270.74 Following clause subsumed by 557 during input processing: 0 [] c_lesse_quals(A,A,tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=21): 559 [copy,558,demod,498] c_List_Oappend(c_List_Oreplicate(A,B,C),c_List_Olist_OCons(B,D,C),C)=c_List_Oappend(c_List_Olist_OCons(B,c_List_Oreplicate(A,B,C),C),D,C).
% 270.67/270.74 ** KEPT (pick-wt=17): 560 [] c_List_Odrop(A,c_List_Omap(B,C,D,E),E)=c_List_Omap(B,c_List_Odrop(A,C,D),D,E).
% 270.67/270.74 ---> New Demodulator: 561 [new_demod,560] c_List_Odrop(A,c_List_Omap(B,C,D,E),E)=c_List_Omap(B,c_List_Odrop(A,C,D),D,E).
% 270.67/270.74 ** KEPT (pick-wt=15): 562 [] 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).
% 270.67/270.74 ** KEPT (pick-wt=4): 563 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 270.67/270.74 Following clause subsumed by 459 during input processing: 0 [demod,465] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 270.67/270.74 ** KEPT (pick-wt=15): 564 [] c_List_Oappend(c_List_Oappend(A,B,C),D,C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 270.67/270.74 ---> New Demodulator: 565 [new_demod,564] c_List_Oappend(c_List_Oappend(A,B,C),D,C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 270.67/270.74 Following clause subsumed by 459 during input processing: 0 [demod,565] c_List_Oappend(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(A,c_List_Oappend(B,C,D),D).
% 270.67/270.74 Following clause subsumed by 459 during input processing: 0 [demod,565] c_List_Oappend(A,c_List_Oappend(B,D,C),C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 270.67/270.74 Following clause subsumed by 459 during input processing: 0 [demod,565] c_List_Oappend(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(A,c_List_Oappend(B,C,D),D).
% 270.67/270.74 ** KEPT (pick-wt=8): 566 [] c_lesse_quals(A,B,tc_nat)|c_lesse_quals(B,A,tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=6): 567 [] c_Nitpick_Onat__gcd(A,c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 270.67/270.74 ---> New Demodulator: 568 [new_demod,567] c_Nitpick_Onat__gcd(A,c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 270.67/270.74 ** KEPT (pick-wt=6): 569 [] c_nat_Onat__size(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.67/270.74 ---> New Demodulator: 570 [new_demod,569] c_nat_Onat__size(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=5): 571 [] c_String_Ochar_Ochar__size(A)=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.67/270.74 ---> New Demodulator: 572 [new_demod,571] c_String_Ochar_Ochar__size(A)=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=11): 573 [] 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).
% 270.67/270.74 ---> New Demodulator: 574 [new_demod,573] 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).
% 270.67/270.74 ** KEPT (pick-wt=5): 575 [] c_Orderings_Obot__class_Obot(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.67/270.74 ---> New Demodulator: 576 [new_demod,575] c_Orderings_Obot__class_Obot(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=7): 577 [] c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 270.67/270.74 ---> New Demodulator: 578 [new_demod,577] c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 270.67/270.74 ** KEPT (pick-wt=8): 579 [] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.67/270.74 ---> New Demodulator: 580 [new_demod,579] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=5): 581 [] c_lesse_quals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=6): 582 [] c_Nat_Osize__class_Osize(A,tc_String_Ochar)=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=11): 583 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),C,B).
% 270.67/270.74 ** KEPT (pick-wt=7): 584 [] c_Orderings_Oord__class_Omax(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 270.67/270.74 ---> New Demodulator: 585 [new_demod,584] c_Orderings_Oord__class_Omax(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 270.67/270.74 ** KEPT (pick-wt=7): 586 [] c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=A.
% 270.67/270.74 ---> New Demodulator: 587 [new_demod,586] c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=A.
% 270.67/270.74 ** KEPT (pick-wt=9): 589 [copy,588,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 270.67/270.74 ---> New Demodulator: 590 [new_demod,589] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 270.67/270.74 ** KEPT (pick-wt=9): 591 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 270.67/270.74 ---> New Demodulator: 592 [new_demod,591] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 270.67/270.74 Following clause subsumed by 459 during input processing: 0 [demod,590] A=A.
% 270.67/270.74 ** KEPT (pick-wt=23): 593 [] 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)).
% 270.67/270.74 ** KEPT (pick-wt=16): 594 [] c_Lambda_OdB_OdB__case(A,B,C,hAPP(hAPP(c_Lambda_OdB_OApp,D),E),F)=hAPP(hAPP(B,D),E).
% 270.67/270.74 ** KEPT (pick-wt=30): 596 [copy,595,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).
% 270.67/270.74 ---> New Demodulator: 597 [new_demod,596] 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).
% 270.67/270.74 ** KEPT (pick-wt=20): 599 [copy,598,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).
% 270.67/270.74 ---> New Demodulator: 600 [new_demod,599] 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).
% 270.67/270.74 ** KEPT (pick-wt=20): 602 [copy,601,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).
% 270.67/270.74 ---> New Demodulator: 603 [new_demod,602] 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).
% 270.67/270.74 ** KEPT (pick-wt=16): 605 [copy,604,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).
% 270.67/270.74 ---> New Demodulator: 606 [new_demod,605] 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).
% 270.67/270.74 ** KEPT (pick-wt=11): 608 [copy,607,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OVar(A).
% 270.67/270.74 ---> New Demodulator: 609 [new_demod,608] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OVar(A).
% 270.67/270.74 ** KEPT (pick-wt=11): 611 [copy,610,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).
% 270.67/270.74 ---> New Demodulator: 612 [new_demod,611] 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).
% 270.67/270.74 ** KEPT (pick-wt=10): 614 [copy,613,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.
% 270.67/270.74 ---> New Demodulator: 615 [new_demod,614] 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.
% 270.67/270.74 Following clause subsumed by 459 during input processing: 0 [demod,612] c_Lambda_OdB_OAbs(A)=c_Lambda_OdB_OAbs(A).
% 270.67/270.74 ** KEPT (pick-wt=9): 616 [] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 270.67/270.74 ---> New Demodulator: 617 [new_demod,616] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 270.67/270.74 ** KEPT (pick-wt=20): 618 [] 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).
% 270.67/270.74 ** KEPT (pick-wt=21): 619 [] 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).
% 270.67/270.74 ** KEPT (pick-wt=41): 620 [] 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).
% 270.67/270.74 Following clause subsumed by 459 during input processing: 0 [demod,484] B=B.
% 270.67/270.74 ** KEPT (pick-wt=13): 621 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),B)),C),B)=A.
% 270.67/270.74 ---> New Demodulator: 622 [new_demod,621] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),B)),C),B)=A.
% 270.67/270.74 ** KEPT (pick-wt=5): 623 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(A))).
% 270.67/270.74 ** KEPT (pick-wt=4): 624 [] hBOOL(hAPP(c_InductTermi_OIT,v_ua______)).
% 270.67/270.74 ** KEPT (pick-wt=18): 625 [] 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)))).
% 270.67/270.74 ** KEPT (pick-wt=18): 626 [] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____).
% 270.67/270.74 ** KEPT (pick-wt=14): 628 [copy,627,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)).
% 270.67/270.74 ---> New Demodulator: 629 [new_demod,628] 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)).
% 270.67/270.74 Following clause subsumed by 459 during input processing: 0 [demod,617] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)=hAPP(hAPP(c_Lambda_OdB_OApp,A),B).
% 270.67/270.74 ** KEPT (pick-wt=4): 630 [] hBOOL(hAPP(c_InductTermi_OIT,v_a____)).
% 270.67/270.74 ** KEPT (pick-wt=29): 631 [] 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)).
% 270.67/270.74 ** KEPT (pick-wt=13): 633 [copy,632,demod,629] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))).
% 270.67/270.74 ** KEPT (pick-wt=4): 634 [] hBOOL(hAPP(c_InductTermi_OIT,v_u____)).
% 270.67/270.74 Following clause subsumed by 563 during input processing: 0 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 270.67/270.74 Following clause subsumed by 634 during input processing: 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_u____)).
% 270.67/270.74 ** KEPT (pick-wt=17): 636 [copy,635,demod,629] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____).
% 270.67/270.74 ** KEPT (pick-wt=2): 637 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 638 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 639 [] class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 640 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 641 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 642 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 643 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 644 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 645 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 646 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 647 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 648 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 649 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 650 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 651 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 652 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 653 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 654 [] class_Nat_Osemiring__char__0(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 655 [] class_Orderings_Opreorder(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 656 [] class_Orderings_Olinorder(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 657 [] class_Orderings_Oorder(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 658 [] class_Orderings_Obot(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 659 [] class_Power_Opower(tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=2): 660 [] class_Orderings_Opreorder(tc_bool).
% 270.67/270.74 ** KEPT (pick-wt=2): 661 [] class_Orderings_Oorder(tc_bool).
% 270.67/270.74 ** KEPT (pick-wt=2): 662 [] class_Orderings_Obot(tc_bool).
% 270.67/270.74 ** KEPT (pick-wt=7): 663 [] hBOOL(hAPP(hAPP(c_fe_qual(A),B),B)).
% 270.67/270.74 Following clause subsumed by 459 during input processing: 0 [copy,459,flip.1] A=A.
% 270.67/270.74 459 back subsumes 456.
% 270.67/270.74 459 back subsumes 449.
% 270.67/270.74 459 back subsumes 448.
% 270.67/270.74 459 back subsumes 442.
% 270.67/270.74 459 back subsumes 441.
% 270.67/270.74 459 back subsumes 440.
% 270.67/270.74 459 back subsumes 439.
% 270.67/270.74 459 back subsumes 433.
% 270.67/270.74 ** KEPT (pick-wt=11): 664 [copy,461,flip.1] hAPP(A,B)=c_Lambda_OdB_OdB__case(C,D,A,c_Lambda_OdB_OAbs(B),E).
% 270.67/270.74 >>>> Starting back demodulation with 465.
% 270.67/270.74 >>>> Starting back demodulation with 468.
% 270.67/270.74 ** KEPT (pick-wt=15): 665 [copy,469,flip.1] c_List_Oreplicate(A,hAPP(B,C),D)=c_List_Omap(B,c_List_Oreplicate(A,C,E),E,D).
% 270.67/270.74 Following clause subsumed by 470 during input processing: 0 [copy,470,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 270.67/270.74 >>>> Starting back demodulation with 472.
% 270.67/270.74 >>>> Starting back demodulation with 474.
% 270.67/270.74 Following clause subsumed by 475 during input processing: 0 [copy,475,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)).
% 270.67/270.74 >>>> Starting back demodulation with 477.
% 270.67/270.74 >>>> Starting back demodulation with 479.
% 270.67/270.74 ** KEPT (pick-wt=11): 666 [copy,480,flip.1] hAPP(A,B)=c_Lambda_OdB_OdB__case(A,C,D,c_Lambda_OdB_OVar(B),E).
% 270.67/270.74 ** KEPT (pick-wt=14): 667 [copy,481,flip.1] hAPP(hAPP(A,B),C)=hAPP(c_COMBC(A,C,D,E,F),B).
% 270.67/270.74 >>>> Starting back demodulation with 484.
% 270.67/270.74 >>>> Starting back demodulation with 486.
% 270.67/270.74 Following clause subsumed by 534 during input processing: 0 [copy,487,flip.1] c_List_Olist_ONil(A)=c_List_Omap(B,c_List_Olist_ONil(C),C,A).
% 270.67/270.74 ** KEPT (pick-wt=12): 668 [copy,488,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).
% 270.67/270.74 ** KEPT (pick-wt=17): 669 [copy,489,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).
% 270.67/270.74 >>>> Starting back demodulation with 491.
% 270.67/270.74 >>>> Starting back demodulation with 493.
% 270.67/270.74 >>>> Starting back demodulation with 498.
% 270.67/270.74 Following clause subsumed by 499 during input processing: 0 [copy,499,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).
% 270.67/270.74 >>>> Starting back demodulation with 502.
% 270.67/270.74 >>>> Starting back demodulation with 504.
% 270.67/270.74 >>>> Starting back demodulation with 507.
% 270.67/270.74 ** KEPT (pick-wt=11): 670 [copy,508,flip.1] hAPP(A,B)=c_Lambda_OdB_OdB__rec(A,C,D,c_Lambda_OdB_OVar(B),E).
% 270.67/270.74 Following clause subsumed by 530 during input processing: 0 [copy,509,flip.1] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Olist_ONil(B).
% 270.67/270.74 >>>> Starting back demodulation with 514.
% 270.67/270.74 >> back demodulating 203 with 514.
% 270.67/270.74 >>>> Starting back demodulation with 517.
% 270.67/270.74 Following clause subsumed by 519 during input processing: 0 [copy,519,flip.1] c_List_Oappend(c_List_Oreplicate(A,B,C),c_List_Oreplicate(D,B,C),C)=c_List_Oappend(c_List_Oreplicate(D,B,C),c_List_Oreplicate(A,B,C),C).
% 270.67/270.74 >>>> Starting back demodulation with 522.
% 270.67/270.74 >>>> Starting back demodulation with 524.
% 270.67/270.74 >>>> Starting back demodulation with 526.
% 270.67/270.74 >>>> Starting back demodulation with 529.
% 270.67/270.74 Following clause subsumed by 509 during input processing: 0 [copy,530,flip.1] c_List_Olist_ONil(A)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),B,A).
% 270.67/270.74 >>>> Starting back demodulation with 533.
% 270.67/270.74 Following clause subsumed by 487 during input processing: 0 [copy,534,flip.1] c_List_Omap(A,c_List_Olist_ONil(B),B,C)=c_List_Olist_ONil(C).
% 270.67/270.74 >>>> Starting back demodulation with 536.
% 270.67/270.74 ** KEPT (pick-wt=19): 672 [copy,537,flip.1] c_List_Olist_OCons(A,c_List_Oreplicate(B,A,C),C)=c_List_Oappend(c_List_Oreplicate(B,A,C),c_List_Olist_OCons(A,c_List_Olist_ONil(C),C),C).
% 270.67/270.74 >>>> Starting back demodulation with 539.
% 270.67/270.74 >> back demodulating 168 with 539.
% 270.67/270.74 >>>> Starting back demodulation with 541.
% 270.67/270.74 >> back demodulating 13 with 541.
% 270.67/270.74 >>>> Starting back demodulation with 544.
% 270.67/270.74 >>>> Starting back demodulation with 547.
% 270.67/270.74 >> back demodulating 350 with 547.
% 270.67/270.74 >>>> Starting back demodulation with 549.
% 270.67/270.74 ** KEPT (pick-wt=7): 673 [copy,550,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ominus__class_Ominus(A,A,tc_nat).
% 270.67/270.74 ** KEPT (pick-wt=18): 674 [copy,551,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).
% 270.67/270.74 >>>> Starting back demodulation with 554.
% 270.67/270.74 >> back demodulating 365 with 554.
% 270.67/270.74 >>>> Starting back demodulation with 556.
% 270.67/270.74 557 back subsumes 542.
% 270.67/270.74 557 back subsumes 431.
% 270.67/270.74 ** KEPT (pick-wt=21): 676 [copy,559,flip.1] c_List_Oappend(c_List_Olist_OCons(A,c_List_Oreplicate(B,A,C),C),D,C)=c_List_Oappend(c_List_Oreplicate(B,A,C),c_List_Olist_OCons(A,D,C),C).
% 270.67/270.74 >>>> Starting back demodulation with 561.
% 270.67/270.74 >>>> Starting back demodulation with 565.
% 270.67/270.74 >>>> Starting back demodulation with 568.
% 270.67/270.74 >>>> Starting back demodulation with 570.
% 270.67/270.74 >>>> Starting back demodulation with 572.
% 270.67/270.74 >>>> Starting back demodulation with 574.
% 270.67/270.74 >>>> Starting back demodulation with 576.
% 270.67/270.74 >>>> Starting back demodulation with 578.
% 270.67/270.74 >> back demodulating 478 with 578.
% 270.67/270.74 >>>> Starting back demodulation with 580.
% 270.67/270.74 ** KEPT (pick-wt=6): 677 [copy,582,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)=c_Nat_Osize__class_Osize(A,tc_String_Ochar).
% 270.67/270.74 Following clause subsumed by 583 during input processing: 0 [copy,583,flip.1] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),C,B).
% 270.67/270.74 >>>> Starting back demodulation with 585.
% 270.67/270.74 >>>> Starting back demodulation with 587.
% 270.67/270.74 >>>> Starting back demodulation with 590.
% 270.67/270.74 >> back demodulating 573 with 590.
% 270.67/270.74 >>>> Starting back demodulation with 592.
% 270.67/270.74 ** KEPT (pick-wt=23): 678 [copy,593,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).
% 270.67/270.74 ** KEPT (pick-wt=16): 679 [copy,594,flip.1] hAPP(hAPP(A,B),C)=c_Lambda_OdB_OdB__case(D,A,E,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),F).
% 270.67/270.74 >>>> Starting back demodulation with 597.
% 270.67/270.74 >>>> Starting back demodulation with 600.
% 270.67/270.74 >>>> Starting back demodulation with 603.
% 270.67/270.74 >>>> Starting back demodulation with 606.
% 270.67/270.74 >>>> Starting back demodulation with 609.
% 270.67/270.74 >>>> Starting back demodulation with 612.
% 270.67/270.74 >>>> Starting back demodulation with 615.
% 270.67/270.74 >>>> Starting back demodulation with 617.
% 270.67/270.74 >> back demodulating 611 with 617.
% 270.67/270.74 >> back demodulating 608 with 617.
% 270.67/270.74 >> back demodulating 401 with 617.
% 270.67/270.74 ** KEPT (pick-wt=20): 680 [copy,618,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).
% 270.67/270.74 ** KEPT (pick-wt=21): 681 [copy,619,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).
% 270.67/270.74 ** KEPT (pick-wt=41): 682 [copy,620,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).
% 270.67/270.74 >>>> Starting back demodulation with 622.
% 270.67/270.74 >>>> Starting back demodulation with 629.
% 270.67/270.74 >> back demodulating 625 with 629.
% 270.67/270.74 >> back demodulating 415 with 629.
% 270.67/270.74 >> back demodulating 411 with 629.
% 270.67/270.74 >> back demodulating 410 with 629.
% 270.67/270.74 >> back demodulating 373 with 629.
% 270.67/270.74 ** KEPT (pick-wt=29): 688 [copy,631,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).
% 270.67/270.74 Following clause subsumed by 461 during input processing: 0 [copy,664,flip.1] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(C,D).
% 270.67/270.74 Following clause subsumed by 469 during input processing: 0 [copy,665,flip.1] c_List_Omap(A,c_List_Oreplicate(B,C,D),D,E)=c_List_Oreplicate(B,hAPP(A,C),E).
% 270.67/270.74 Following clause subsumed by 480 during input processing: 0 [copy,666,flip.1] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 270.67/270.74 Following clause subsumed by 481 during input processing: 0 [copy,667,flip.1] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 270.67/270.74 Following clause subsumed by 488 during input processing: 0 [copy,668,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).
% 270.67/270.74 Following clause subsumed by 489 during input processing: 0 [copy,669,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).
% 270.67/270.74 Following clause subsumed by 508 during input processing: 0 [copy,670,flip.1] c_Lambda_OdB_OdB__rec(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 270.67/270.74 Following clause subsumed by 537 during input processing: 0 [copy,672,flip.1] c_List_Oappend(c_List_Oreplicate(A,B,C),c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C)=c_List_Olist_OCons(B,c_List_Oreplicate(A,B,C),C).
% 270.67/270.74 Following clause subsumed by 550 during input processing: 0 [copy,673,flip.1] c_HOL_Ominus__class_Ominus(A,A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.67/270.74 Following clause subsumed by 551 during input processing: 0 [copy,674,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)).
% 270.67/270.74 Following clause subsumed by 559 during input processing: 0 [copy,676,flip.1] c_List_Oappend(c_List_Oreplicate(A,B,C),c_List_Olist_OCons(B,D,C),C)=c_List_Oappend(c_List_Olist_OCons(B,c_List_Oreplicate(A,B,C),C),D,C).
% 270.67/270.74 Following clause subsumed by 582 during input processing: 0 [copy,677,flip.1] c_Nat_Osize__class_Osize(A,tc_String_Ochar)=c_HOL_Ozero__class_Ozero(tc_nat).
% 270.67/270.74 Following clause subsumed by 593 during input processing: 0 [copy,678,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)).
% 271.31/271.38 Following clause subsumed by 594 during input processing: 0 [copy,679,flip.1] c_Lambda_OdB_OdB__case(A,B,C,hAPP(hAPP(c_Lambda_OdB_OApp,D),E),F)=hAPP(hAPP(B,D),E).
% 271.31/271.38 Following clause subsumed by 618 during input processing: 0 [copy,680,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).
% 271.31/271.38 Following clause subsumed by 619 during input processing: 0 [copy,681,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).
% 271.31/271.38 Following clause subsumed by 620 during input processing: 0 [copy,682,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).
% 271.31/271.38 Following clause subsumed by 631 during input processing: 0 [copy,688,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)).
% 271.31/271.38
% 271.31/271.38 ======= end of input processing =======
% 271.31/271.38
% 271.31/271.38 =========== start of search ===========
% 271.31/271.38
% 271.31/271.38
% 271.31/271.38 Resetting weight limit to 2.
% 271.31/271.38
% 271.31/271.38
% 271.31/271.38 Resetting weight limit to 2.
% 271.31/271.38
% 271.31/271.38 sos_size=150
% 271.31/271.38
% 271.31/271.38 Search stopped because sos empty.
% 271.31/271.38
% 271.31/271.38
% 271.31/271.38 Search stopped because sos empty.
% 271.31/271.38
% 271.31/271.38 ============ end of search ============
% 271.31/271.38
% 271.31/271.38 -------------- statistics -------------
% 271.31/271.38 clauses given 151
% 271.31/271.38 clauses generated 77747
% 271.31/271.38 clauses kept 592
% 271.31/271.38 clauses forward subsumed 149
% 271.31/271.38 clauses back subsumed 11
% 271.31/271.38 Kbytes malloced 10742
% 271.31/271.38
% 271.31/271.38 ----------- times (seconds) -----------
% 271.31/271.38 user CPU time 0.72 (0 hr, 0 min, 0 sec)
% 271.31/271.38 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 271.31/271.38 wall-clock time 271 (0 hr, 4 min, 31 sec)
% 271.31/271.38
% 271.31/271.38 Process 17782 finished Wed Jul 27 09:53:34 2022
% 271.31/271.38 Otter interrupted
% 271.31/271.38 PROOF NOT FOUND
%------------------------------------------------------------------------------