TSTP Solution File: LCL834-1 by Otter---3.3

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : LCL834-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Jul 27 13:05:34 EDT 2022

% Result   : Unknown 72.04s 72.12s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL834-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n021.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Jul 27 09:19:38 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 71.01/71.09  ----- Otter 3.3f, August 2004 -----
% 71.01/71.09  The process was started by sandbox2 on n021.cluster.edu,
% 71.01/71.09  Wed Jul 27 09:19:38 2022
% 71.01/71.09  The command was "./otter".  The process ID is 3949.
% 71.01/71.09  
% 71.01/71.09  set(prolog_style_variables).
% 71.01/71.09  set(auto).
% 71.01/71.09     dependent: set(auto1).
% 71.01/71.09     dependent: set(process_input).
% 71.01/71.09     dependent: clear(print_kept).
% 71.01/71.09     dependent: clear(print_new_demod).
% 71.01/71.09     dependent: clear(print_back_demod).
% 71.01/71.09     dependent: clear(print_back_sub).
% 71.01/71.09     dependent: set(control_memory).
% 71.01/71.09     dependent: assign(max_mem, 12000).
% 71.01/71.09     dependent: assign(pick_given_ratio, 4).
% 71.01/71.09     dependent: assign(stats_level, 1).
% 71.01/71.09     dependent: assign(max_seconds, 10800).
% 71.01/71.09  clear(print_given).
% 71.01/71.09  
% 71.01/71.09  list(usable).
% 71.01/71.09  0 [] A=A.
% 71.01/71.09  0 [] V_r!=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),V_xa,tc_Lambda_OdB,tc_Lambda_OdB)|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_Oappend(V_xa,c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 71.01/71.09  0 [] hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u)=c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Oappend(V_ts,c_List_Olist_OCons(V_u,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 71.01/71.09  0 [] c_List_Oappend(V_x,c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB)=c_List_Olist_ONil(tc_Lambda_OdB)|hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_x,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)=c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Oappend(V_x,c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 71.01/71.09  0 [] hBOOL(hAPP(c_Wellfounded_Oaccp(c_ListOrder_Ostep1(V_r,T_a),tc_List_Olist(T_a)),V_xs))| -c_List_Olistsp(c_Wellfounded_Oaccp(V_r,T_a),V_xs,T_a).
% 71.01/71.09  0 [] c_List_Orev(c_List_Oreplicate(V_n,V_x,T_a),T_a)=c_List_Oreplicate(V_n,V_x,T_a).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] c_List_Orev(c_List_Orev(V_xs,T_a),T_a)=V_xs.
% 71.01/71.09  0 [] c_List_Orev(c_List_Orev(V_ys,T_a),T_a)=V_ys.
% 71.01/71.09  0 [] V_xs=c_List_Orev(c_List_Orev(V_xs,T_a),T_a).
% 71.01/71.09  0 [] c_List_Orotate1(V_xs,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_List_Otake(V_n,c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_List_Oreplicate(V_m,V_x,T_a)!=c_List_Oreplicate(V_n,V_y,T_a)|V_m=V_n.
% 71.01/71.09  0 [] c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a).
% 71.01/71.09  0 [] c_List_Orev(c_List_Omap(V_f,V_xs,T_b,T_a),T_a)=c_List_Omap(V_f,c_List_Orev(V_xs,T_b),T_b,T_a).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] c_List_Orotate1(c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] hBOOL(hAPP(c_InductTermi_OIT,v_ua______)).
% 71.01/71.09  0 [] c_List_Otake(V_n,c_List_Omap(V_f,V_xs,T_b,T_a),T_a)=c_List_Omap(V_f,c_List_Otake(V_n,V_xs,T_b),T_b,T_a).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] c_List_Olast(c_List_Oreplicate(V_n,V_x,T_a),T_a)=V_x|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 71.01/71.09  0 [] hBOOL(hAPP(c_InductTermi_OIT,v_u____)).
% 71.01/71.09  0 [] c_List_Orev(V_xs,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_List_Orev(c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_List_Orev(c_List_Oappend(V_xs,V_ys,T_a),T_a)=c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Orev(V_xs,T_a),T_a).
% 71.01/71.09  0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat__aux(V_inc,c_HOL_Ozero__class_Ozero(tc_nat),V_i,T_a)=V_i.
% 71.01/71.09  0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 71.01/71.09  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).
% 71.01/71.09  0 [] -c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 71.01/71.09  0 [] -c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a)),T_a).
% 71.01/71.09  0 [] c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olist_ONil(T_a).
% 71.01/71.09  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_ts=c_List_Oappend(c_ListApplication_Osko__ListApplication__XApp__e_q__foldl__conv__1__1(V_r,V_s,V_t,V_ts),c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB)|V_ts=c_List_Olist_ONil(tc_Lambda_OdB).
% 71.01/71.09  0 [] c_List_Olistsp(c_Wellfounded_Oaccp(V_r,T_a),V_xs,T_a)| -hBOOL(hAPP(c_Wellfounded_Oaccp(c_ListOrder_Ostep1(V_r,T_a),tc_List_Olist(T_a)),V_xs)).
% 71.01/71.09  0 [] -c_HOL_Oord__class_Oless(V_x,V_x,tc_nat).
% 71.01/71.09  0 [] -c_HOL_Oord__class_Oless(V_n,V_n,tc_nat).
% 71.01/71.09  0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 71.01/71.09  0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 71.01/71.09  0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 71.01/71.09  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.
% 71.01/71.09  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).
% 71.01/71.09  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.
% 71.01/71.09  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).
% 71.01/71.09  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.
% 71.01/71.09  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.
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] c_List_Orev(V_xs,T_a)!=c_List_Orev(V_ys,T_a)|V_xs=V_ys.
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] c_List_Olist_ONil(T_a)!=c_List_Orev(V_xs,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xex__least__nat__less__1__1(V_P,V_n),V_n,tc_nat)| -hBOOL(hAPP(V_P,V_n))|hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 71.01/71.09  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a).
% 71.01/71.09  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a).
% 71.01/71.09  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_a,V_N,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(V_n,V_N,tc_nat).
% 71.01/71.09  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 71.01/71.09  0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat).
% 71.01/71.09  0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat).
% 71.01/71.09  0 [] c_Type_Otype_OFun(V_type1,V_type2)!=c_Type_Otype_OFun(V_type1_H,V_type2_H)|V_type2=V_type2_H.
% 71.01/71.09  0 [] c_Type_Otype_OFun(V_type1,V_type2)!=c_Type_Otype_OFun(V_type1_H,V_type2_H)|V_type1=V_type1_H.
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] c_List_Obutlast(c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_List_Olist_ONil(T_a)=c_List_Orev(c_List_Olist_ONil(T_a),T_a).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_N,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(V_n,V_N,tc_nat).
% 71.01/71.09  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 71.01/71.09  0 [] c_List_Oappend(c_List_Obutlast(V_xs,T_a),c_List_Olist_OCons(c_List_Olast(V_xs,T_a),c_List_Olist_ONil(T_a),T_a),T_a)=V_xs|V_xs=c_List_Olist_ONil(T_a).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 71.01/71.09  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a).
% 71.01/71.09  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a)),T_a).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a)=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_List_Otake(V_n,V_xs,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 71.01/71.09  0 [] c_List_Olist_ONil(T_a)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a).
% 71.01/71.09  0 [] c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),V_xs,T_a)=c_List_Olist_ONil(T_a).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a)=c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a).
% 71.01/71.09  0 [] c_List_Olast(c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olast(V_xs,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a)=c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a).
% 71.01/71.09  0 [] c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a)!=c_List_Orev(V_xs,T_a)|V_xs=c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a).
% 71.01/71.09  0 [] c_List_Orev(V_xs,T_a)!=c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a)|V_xs=c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a).
% 71.01/71.09  0 [] c_List_Obutlast(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a)=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_List_Olast(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a)=V_x.
% 71.01/71.09  0 [] c_List_Obutlast(c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olist_OCons(V_x,c_List_Obutlast(V_xs,T_a),T_a)|V_xs=c_List_Olist_ONil(T_a).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] c_List_Oappend(V_ys,V_zs,T_a)!=c_List_Olist_OCons(V_x,V_xs,T_a)|c_List_Oappend(c_List_Osko__List__Xappend__e_q__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a)=V_xs|V_zs=c_List_Olist_OCons(V_x,V_xs,T_a).
% 71.01/71.09  0 [] c_List_Olist_OCons(V_x,V_xs,T_a)!=c_List_Oappend(V_ys,V_zs,T_a)|c_List_Olist_OCons(V_x,c_List_Osko__List__XCons__e_q__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a)=V_ys|c_List_Olist_OCons(V_x,V_xs,T_a)=V_zs.
% 71.01/71.09  0 [] c_List_Oappend(V_ys,V_zs,T_a)!=c_List_Olist_OCons(V_x,V_xs,T_a)|V_ys=c_List_Olist_OCons(V_x,c_List_Osko__List__Xappend__e_q__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a)|V_zs=c_List_Olist_OCons(V_x,V_xs,T_a).
% 71.01/71.09  0 [] c_List_Olist_OCons(V_x,V_xs,T_a)!=c_List_Oappend(V_ys,V_zs,T_a)|V_xs=c_List_Oappend(c_List_Osko__List__XCons__e_q__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a)|c_List_Olist_OCons(V_x,V_xs,T_a)=V_zs.
% 71.01/71.09  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).
% 71.01/71.09  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_Power_Opower__class_Opower(V_a,V_m,T_a)!=c_Power_Opower__class_Opower(V_a,V_n,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)|V_m=V_n.
% 71.01/71.09  0 [] c_List_Obutlast(c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a),T_a)=c_List_Obutlast(V_xs,T_a).
% 71.01/71.09  0 [] c_List_Olast(c_List_Oappend(V_xs,V_ys,T_a),T_a)=c_List_Olast(V_ys,T_a)|V_ys=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_List_Olast(c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a),T_a)=c_List_Olast(V_xs,T_a).
% 71.01/71.09  0 [] c_List_Obutlast(c_List_Oappend(V_xs,V_ys,T_a),T_a)=c_List_Oappend(V_xs,c_List_Obutlast(V_ys,T_a),T_a)|V_ys=c_List_Olist_ONil(T_a).
% 71.01/71.09  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).
% 71.01/71.09  0 [] c_Type_Otyping(V_env,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_U)| -c_Type_Otyping(V_env,V_t,V_T)| -c_Type_Otyping(V_env,V_s,c_Type_Otype_OFun(V_T,V_U)).
% 71.01/71.09  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.
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] c_List_Olist_OCons(V_x,V_xs,T_a)!=c_List_Oappend(V_ys,V_zs,T_a)|V_xs=c_List_Oappend(c_List_Osko__List__XCons__e_q__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a)|V_ys=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_List_Oappend(V_ys,V_zs,T_a)!=c_List_Olist_OCons(V_x,V_xs,T_a)|V_ys=c_List_Olist_OCons(V_x,c_List_Osko__List__Xappend__e_q__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a)|V_ys=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_List_Olast(c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a)=V_x.
% 71.01/71.09  0 [] c_List_Obutlast(c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a)=V_xs.
% 71.01/71.09  0 [] c_List_Oappend(V_ys,V_zs,T_a)!=c_List_Olist_OCons(V_x,V_xs,T_a)|c_List_Oappend(c_List_Osko__List__Xappend__e_q__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a)=V_xs|V_ys=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_List_Olist_OCons(V_x,V_xs,T_a)!=c_List_Oappend(V_ys,V_zs,T_a)|c_List_Olist_OCons(V_x,c_List_Osko__List__XCons__e_q__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a)=V_ys|V_ys=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_List_Orev(c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Oappend(c_List_Orev(V_xs,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a).
% 71.01/71.09  0 [] c_List_Orev(V_xs,T_a)!=c_List_Olist_OCons(V_y,V_ys,T_a)|V_xs=c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a).
% 71.01/71.09  0 [] c_List_Orev(c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),T_a)=c_List_Olist_OCons(V_y,V_ys,T_a).
% 71.01/71.09  0 [] c_List_Orotate1(c_List_Olist_OCons(V_x,V_xs,T_b),T_b)=c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_b),T_b),T_b).
% 71.01/71.09  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).
% 71.01/71.09  0 [] c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a).
% 71.01/71.09  0 [] hBOOL(hAPP(V_P,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xex__least__nat__less__1__1(V_P,V_n)),c_HOL_Oone__class_Oone(tc_nat))))| -hBOOL(hAPP(V_P,V_n))|hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 71.01/71.09  0 [] hBOOL(hAPP(c_Wellfounded_Oaccp(c_ListOrder_Ostep1(V_r,T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(V_x,V_xs,T_a)))| -hBOOL(hAPP(c_Wellfounded_Oaccp(c_ListOrder_Ostep1(V_r,T_a),tc_List_Olist(T_a)),V_xs))| -hBOOL(hAPP(c_Wellfounded_Oaccp(V_r,T_a),V_x)).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_j)),V_i)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)))| -c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 71.01/71.09  0 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_j)),V_i)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)),V_j)| -c_HOL_Oord__class_Oless(V_j,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 71.01/71.09  0 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(V_i)),V_k)=c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)))|c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 71.01/71.09  0 [] c_Type_Otyping(V_env,c_Lambda_OdB_OAbs(V_t),c_Type_Otype_OFun(V_T,V_U))| -c_Type_Otyping(c_Type_Oshift(V_env,c_HOL_Ozero__class_Ozero(tc_nat),V_T,tc_Type_Otype),V_t,V_U).
% 71.01/71.09  0 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 71.01/71.09  0 [] c_Type_Otyping(v_ea______,v_ua______,v_T____).
% 71.01/71.09  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)).
% 71.01/71.09  0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)=c_Nat_Osemiring__1__class_Oof__nat__aux(c_COMBC(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a),T_a,T_a,T_a),V_n,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 71.01/71.09  0 [] c_Type_Otypings(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts)| -c_Type_Otypings(V_e,V_ts,V_Ts).
% 71.01/71.09  0 [] v_T____!=c_Type_Otype_OFun(V_T1,V_T2)|hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i)))| -c_Type_Otyping(V_e,V_u,V_T2)| -hBOOL(hAPP(c_InductTermi_OIT,V_u))| -c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_T2,tc_Type_Otype),V_t,V_Ta)| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 71.01/71.09  0 [] v_T____!=c_Type_Otype_OFun(V_T1,V_T2)|hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i)))| -c_Type_Otyping(V_e,V_u,V_T1)| -hBOOL(hAPP(c_InductTermi_OIT,V_u))| -c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_T1,tc_Type_Otype),V_t,V_Ta)| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 71.01/71.09  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).
% 71.01/71.09  0 [] V_rs=c_List_Olist_OCons(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(V_r,V_rs,V_s),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(V_r,V_rs,V_s),tc_Lambda_OdB)|V_s=c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB)|V_s=c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)).
% 71.01/71.09  0 [] V_rs=c_List_Olist_OCons(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(V_r,V_rs,V_s),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(V_r,V_rs,V_s),tc_Lambda_OdB)|V_s=c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB)|hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)).
% 71.01/71.09  0 [] c_Type_Otypings(V_e,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts)| -c_Type_Otypings(c_Type_Oshift(V_e,V_i,V_T,tc_Type_Otype),V_ts,V_Ts)| -c_Type_Otyping(V_e,V_u,V_T).
% 71.01/71.09  0 [] V_rs=c_List_Olist_OCons(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(V_r,V_rs,V_s),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(V_r,V_rs,V_s),tc_Lambda_OdB)|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),V_rs),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s)))|hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)).
% 71.01/71.09  0 [] V_rs=c_List_Olist_OCons(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(V_r,V_rs,V_s),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(V_r,V_rs,V_s),tc_Lambda_OdB)|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),V_rs),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s)))|V_s=c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)).
% 71.01/71.09  0 [] hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R)=hAPP(hAPP(V_P,V_R),V_Q).
% 71.01/71.09  0 [] c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a)=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),T_a)=c_HOL_Oone__class_Oone(T_a).
% 71.01/71.09  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)).
% 71.01/71.09  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)).
% 71.01/71.09  0 [] hBOOL(hAPP(hAPP(V_r,V_y),V_x))|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_ys),V_xs))| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),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))).
% 71.01/71.09  0 [] c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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.
% 71.01/71.09  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.
% 71.01/71.09  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.
% 71.01/71.09  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.
% 71.01/71.09  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.
% 71.01/71.09  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.
% 71.01/71.09  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.
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] c_List_Olist_OCons(V_x,V_xa,T_a)!=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_List_Olist_OCons(V_a_H,V_list_H,T_a)!=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] V_x=V_y|hBOOL(hAPP(hAPP(V_r,V_y),V_x))| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_OCons(V_y,V_ys,T_a)),c_List_Olist_OCons(V_x,V_xs,T_a))).
% 71.01/71.09  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)).
% 71.01/71.09  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)).
% 71.01/71.09  0 [] c_List_Olist_OCons(V_x,V_t,T_a)!=V_t.
% 71.01/71.09  0 [] V_xs!=c_List_Olist_OCons(V_x,V_xs,T_a).
% 71.01/71.09  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).
% 71.01/71.09  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)).
% 71.01/71.09  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).
% 71.01/71.09  0 [] c_List_Olist_ONil(T_a)=c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a).
% 71.01/71.09  0 [] V_ys=V_xs|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_ys),V_xs))| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),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))).
% 71.01/71.09  0 [] c_List_Olist_ONil(T_a)=c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a).
% 71.01/71.09  0 [] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a)=c_Transitive__Closure_Ortranclp(V_r,T_a).
% 71.01/71.09  0 [] hAPP(hAPP(V_plus,V_a),V_zero)=V_a| -c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a).
% 71.01/71.09  0 [] hAPP(hAPP(V_plus,V_zero),V_a)=V_a| -c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a).
% 71.01/71.09  0 [] V_s=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(V_r,V_rs,V_s)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(V_r,V_rs,V_s)),c_HOL_Ozero__class_Ozero(tc_nat)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB)|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),V_rs),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s)))|V_s=c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)).
% 71.01/71.09  0 [] V_s=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(V_r,V_rs,V_s)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(V_r,V_rs,V_s)),c_HOL_Ozero__class_Ozero(tc_nat)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB)|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),V_rs),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s)))|hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)|c_HOL_Oone__class_Oone(T_a)!=c_HOL_Ozero__class_Ozero(T_a).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)|c_HOL_Ozero__class_Ozero(T_a)!=c_HOL_Oone__class_Oone(T_a).
% 71.01/71.09  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.
% 71.01/71.09  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.
% 71.01/71.09  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)).
% 71.01/71.09  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.
% 71.01/71.09  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.
% 71.01/71.09  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.
% 71.01/71.09  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.
% 71.01/71.09  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.
% 71.01/71.09  0 [] -class_Ring__and__Field_Osemiring__0(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Oone__class_Oone(T_a).
% 71.01/71.09  0 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k)=V_t.
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] V_x=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)).
% 71.01/71.09  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)=V_n.
% 71.01/71.09  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat))=V_m.
% 71.01/71.09  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))).
% 71.01/71.09  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))).
% 71.01/71.09  0 [] c_Lambda_OdB_OVar(V_nat)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H).
% 71.01/71.09  0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a)=c_HOL_Oone__class_Oone(T_a).
% 71.01/71.09  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).
% 71.01/71.09  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.
% 71.01/71.09  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)).
% 71.01/71.09  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)).
% 71.01/71.09  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)).
% 71.01/71.09  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)).
% 71.01/71.09  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)).
% 71.01/71.09  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)).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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)).
% 71.01/71.09  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)).
% 71.01/71.09  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)).
% 71.01/71.09  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)).
% 71.01/71.09  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)).
% 71.01/71.09  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)).
% 71.01/71.09  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).
% 71.01/71.09  0 [] -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_ys),V_xs))|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Oappend(V_ys,V_x,T_a)),c_List_Oappend(V_xs,V_x,T_a))).
% 71.01/71.09  0 [] hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Oappend(V_x,V_vs,T_a)),c_List_Oappend(V_x,V_us,T_a)))| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_vs),V_us)).
% 71.01/71.09  0 [] V_x=V_y|V_xs=V_ys| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_OCons(V_y,V_ys,T_a)),c_List_Olist_OCons(V_x,V_xs,T_a))).
% 71.01/71.09  0 [] -hBOOL(hAPP(hAPP(V_r,V_y),V_xa))|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_OCons(V_y,V_x,T_a)),c_List_Olist_OCons(V_xa,V_x,T_a))).
% 71.01/71.09  0 [] c_List_Oappend(V_ys,V_xs,T_a)!=c_List_Oappend(V_zs,V_xs,T_a)|V_ys=V_zs.
% 71.01/71.09  0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Oappend(V_xs,V_zs,T_a)|V_ys=V_zs.
% 71.01/71.09  0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)).
% 71.01/71.09  0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)).
% 71.01/71.09  0 [] hBOOL(hAPP(c_Wellfounded_Oaccp(V_r,T_a),V_b))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a))| -hBOOL(hAPP(c_Wellfounded_Oaccp(V_r,T_a),V_a)).
% 71.01/71.09  0 [] hBOOL(hAPP(c_Wellfounded_Oaccp(V_r,T_a),V_b))| -hBOOL(hAPP(c_Wellfounded_Oaccp(V_r,T_a),V_a))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a)).
% 71.01/71.09  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)).
% 71.01/71.09  0 [] hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t))| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 71.01/71.09  0 [] hBOOL(hAPP(c_InductTermi_OIT,V_r))| -hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_r)).
% 71.01/71.09  0 [] c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a)=V_xs.
% 71.01/71.09  0 [] V_x=c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a).
% 71.01/71.09  0 [] V_xs=c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a).
% 71.01/71.09  0 [] c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a)=V_ys.
% 71.01/71.09  0 [] V_ys=c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a).
% 71.01/71.09  0 [] c_Lambda_Osubstn(c_Lambda_OdB_OAbs(V_t),V_s,V_k)=c_Lambda_OdB_OAbs(c_Lambda_Osubstn(V_t,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] hBOOL(hAPP(hAPP(V_r,V_y),V_x))|V_y=V_x| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),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))).
% 71.01/71.09  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.
% 71.01/71.09  0 [] hAPP(V_e,V_i)=V_T| -c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T).
% 71.01/71.09  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).
% 71.01/71.09  0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))).
% 71.01/71.09  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(V_x,c_HOL_Oone__class_Oone(tc_nat),T_a)=V_x.
% 71.01/71.09  0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a)=V_a.
% 71.01/71.09  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)).
% 71.01/71.09  0 [] -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_ONil(T_a)),V_xs)).
% 71.01/71.09  0 [] -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_xs),c_List_Olist_ONil(T_a))).
% 71.01/71.09  0 [] hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x)=V_T.
% 71.01/71.09  0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)))| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 71.01/71.09  0 [] c_List_Olist_ONil(T_a)!=c_List_Oappend(V_xs,V_ys,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_List_Olist_ONil(T_a)!=c_List_Oappend(V_xs,V_ys,T_a)|V_ys=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Olist_ONil(T_a)|V_ys=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_Predicate_Oconversep(c_fe_qual(T_a),T_a,T_a)=c_fe_qual(T_a).
% 71.01/71.09  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).
% 71.01/71.09  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)).
% 71.01/71.09  0 [] hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_ys),V_xs))|V_xs=V_ys| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_OCons(V_y,V_ys,T_a)),c_List_Olist_OCons(V_x,V_xs,T_a))).
% 71.01/71.09  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).
% 71.01/71.09  0 [] c_Lambda_Oliftn(V_n,c_Lambda_OdB_OAbs(V_s),V_k)=c_Lambda_OdB_OAbs(c_Lambda_Oliftn(V_n,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))).
% 71.01/71.09  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).
% 71.01/71.09  0 [] c_List_Olist_ONil(T_a)!=c_List_Olist_OCons(V_a_H,V_list_H,T_a).
% 71.01/71.09  0 [] V_ys=V_xs|V_y=V_x| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),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))).
% 71.01/71.09  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).
% 71.01/71.09  0 [] -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Oone__class_Oone(T_a).
% 71.01/71.09  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Oone__class_Oone(T_a).
% 71.01/71.09  0 [] -class_OrderedGroup_Osemigroup__add(T_a)|c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(T_a),T_a).
% 71.01/71.09  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)).
% 71.01/71.09  0 [] c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a)=V_r.
% 71.01/71.09  0 [] c_List_Oappend(V_xs,V_ys,T_a)!=V_xs|V_ys=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] V_xs!=c_List_Oappend(V_xs,V_ys,T_a)|V_ys=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] c_List_Oappend(V_xs,V_ys,T_a)!=V_ys|V_xs=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] V_ys!=c_List_Oappend(V_xs,V_ys,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 71.01/71.09  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).
% 71.01/71.09  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.
% 71.01/71.09  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.
% 71.01/71.09  0 [] hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_ys),V_xs))|hBOOL(hAPP(hAPP(V_r,V_y),V_x))| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_OCons(V_y,V_ys,T_a)),c_List_Olist_OCons(V_x,V_xs,T_a))).
% 71.01/71.09  0 [] hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_OCons(V_x,V_ys,T_a)),c_List_Olist_OCons(V_x,V_xs,T_a)))| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_ys),V_xs)).
% 71.01/71.09  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))).
% 71.01/71.09  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))).
% 71.01/71.09  0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OVar(V_nat_H)|V_nat=V_nat_H.
% 71.01/71.09  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)).
% 71.01/71.09  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).
% 71.01/71.09  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.
% 71.01/71.09  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.
% 71.01/71.09  0 [] c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 71.01/71.09  0 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(V_s)),V_k)=c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,V_s),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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)).
% 71.01/71.09  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)).
% 71.01/71.09  0 [] hBOOL(hAPP(c_Wellfounded_Oaccp(V_r,T_a),V_y))| -hBOOL(hAPP(hAPP(V_r,V_y),V_a))| -hBOOL(hAPP(c_Wellfounded_Oaccp(V_r,T_a),V_a)).
% 71.01/71.09  0 [] hBOOL(hAPP(c_Wellfounded_Oaccp(V_r,T_a),V_a))| -hBOOL(hAPP(hAPP(V_r,V_a),V_b))| -hBOOL(hAPP(c_Wellfounded_Oaccp(V_r,T_a),V_b)).
% 71.01/71.09  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)).
% 71.01/71.09  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).
% 71.01/71.09  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)).
% 71.01/71.09  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)).
% 71.01/71.09  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)).
% 71.01/71.09  0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)!=c_Lambda_OdB_OVar(V_nat).
% 71.01/71.09  0 [] V_u=hAPP(hAPP(c_Lambda_OdB_OApp,V_s),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(V_s,V_t,V_u))|hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),c_Lambda_Osko__Lambda__Xbeta__cases__3__2(V_s,V_t,V_u)))|V_s=c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__3__1(V_s,V_t,V_u))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_u)).
% 71.01/71.09  0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(V_s,V_t,V_u)))|V_u=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osko__Lambda__Xbeta__cases__3__2(V_s,V_t,V_u)),V_t)|V_s=c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__3__1(V_s,V_t,V_u))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_u)).
% 71.01/71.09  0 [] V_u=hAPP(hAPP(c_Lambda_OdB_OApp,V_s),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(V_s,V_t,V_u))|V_u=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osko__Lambda__Xbeta__cases__3__2(V_s,V_t,V_u)),V_t)|V_s=c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__3__1(V_s,V_t,V_u))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_u)).
% 71.01/71.09  0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(V_s,V_t,V_u)))|hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),c_Lambda_Osko__Lambda__Xbeta__cases__3__2(V_s,V_t,V_u)))|V_s=c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__3__1(V_s,V_t,V_u))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_u)).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  0 [] -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)).
% 71.01/71.09  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)).
% 71.01/71.09  0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(V_t)),V_s),V_k)=c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_s),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))).
% 71.01/71.09  0 [] V_s=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(V_r,V_rs,V_s)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(V_r,V_rs,V_s)),c_HOL_Ozero__class_Ozero(tc_nat)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB)|V_s=c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB)|hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)).
% 71.01/71.09  0 [] V_s=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(V_r,V_rs,V_s)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(V_r,V_rs,V_s)),c_HOL_Ozero__class_Ozero(tc_nat)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB)|V_s=c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB)|V_s=c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)).
% 71.01/71.09  0 [] c_Lambda_OdB_OAbs(V_dB_H)!=c_Lambda_OdB_OVar(V_nat).
% 71.01/71.09  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))).
% 71.01/71.09  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))).
% 71.01/71.09  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)).
% 71.01/71.09  0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OAbs(V_dB_H).
% 71.01/71.09  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).
% 71.01/71.09  0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r)))| -hBOOL(hAPP(c_InductTermi_OIT,V_r)).
% 71.01/71.09  0 [] V_r=c_Lambda_OdB_OAbs(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(V_r,V_rs,V_s))|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),V_rs),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s)))|hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)).
% 71.01/71.09  0 [] V_r=c_Lambda_OdB_OAbs(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(V_r,V_rs,V_s))|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),V_rs),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s)))|V_s=c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)).
% 71.01/71.09  0 [] hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),V_rs),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(V_n,V_rs,V_v)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_v)).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.09  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).
% 71.01/71.10  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).
% 71.01/71.10  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).
% 71.01/71.10  0 [] c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b)=V_a.
% 71.01/71.10  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)).
% 71.01/71.10  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).
% 71.01/71.10  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).
% 71.01/71.10  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).
% 71.01/71.10  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).
% 71.01/71.10  0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k)=V_u.
% 71.01/71.10  0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k)=V_t.
% 71.01/71.10  0 [] c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,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_Ha______).
% 71.01/71.10  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____).
% 71.01/71.10  0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(V_s,V_t,V_u)))|V_u=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osko__Lambda__Xbeta__cases__3__2(V_s,V_t,V_u)),V_t)|V_u=hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Osko__Lambda__Xbeta__cases__3__1(V_s,V_t,V_u)),V_t),c_HOL_Ozero__class_Ozero(tc_nat))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_u)).
% 71.01/71.10  0 [] V_u=hAPP(hAPP(c_Lambda_OdB_OApp,V_s),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(V_s,V_t,V_u))|hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),c_Lambda_Osko__Lambda__Xbeta__cases__3__2(V_s,V_t,V_u)))|V_u=hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Osko__Lambda__Xbeta__cases__3__1(V_s,V_t,V_u)),V_t),c_HOL_Ozero__class_Ozero(tc_nat))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_u)).
% 71.01/71.10  0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(V_s,V_t,V_u)))|hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),c_Lambda_Osko__Lambda__Xbeta__cases__3__2(V_s,V_t,V_u)))|V_u=hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Osko__Lambda__Xbeta__cases__3__1(V_s,V_t,V_u)),V_t),c_HOL_Ozero__class_Ozero(tc_nat))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_u)).
% 71.01/71.10  0 [] V_u=hAPP(hAPP(c_Lambda_OdB_OApp,V_s),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(V_s,V_t,V_u))|V_u=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osko__Lambda__Xbeta__cases__3__2(V_s,V_t,V_u)),V_t)|V_u=hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Osko__Lambda__Xbeta__cases__3__1(V_s,V_t,V_u)),V_t),c_HOL_Ozero__class_Ozero(tc_nat))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_u)).
% 71.01/71.10  0 [] V_r=c_Lambda_OdB_OAbs(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(V_r,V_rs,V_s))|V_s=c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB)|V_s=c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)).
% 71.01/71.10  0 [] V_r=c_Lambda_OdB_OAbs(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(V_r,V_rs,V_s))|V_s=c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB)|hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)).
% 71.01/71.10  0 [] hBOOL(hAPP(c_InductTermi_OIT,v_a____)).
% 71.01/71.10  0 [] V_v=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(V_n,V_rs,V_v),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_v)).
% 71.01/71.10  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).
% 71.01/71.10  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).
% 71.01/71.10  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).
% 71.01/71.10  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).
% 71.01/71.10  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).
% 71.01/71.10  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)).
% 71.01/71.10  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)).
% 71.01/71.10  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)).
% 71.01/71.10  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)).
% 71.01/71.10  0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_r)),V_s)).
% 71.01/71.10  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)).
% 71.01/71.10  0 [] V_s=c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_r)),V_s)).
% 71.01/71.10  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).
% 71.01/71.10  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.
% 71.01/71.10  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.
% 71.01/71.10  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.
% 71.01/71.10  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.
% 71.01/71.10  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)).
% 71.01/71.10  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)).
% 71.01/71.10  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)).
% 71.01/71.10  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).
% 71.01/71.10  0 [] -hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,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)))| -hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_s))|hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,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))).
% 71.01/71.10  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)).
% 71.01/71.10  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)))| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),V_rs),V_ss)).
% 71.01/71.10  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).
% 71.01/71.10  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).
% 71.01/71.10  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).
% 71.01/71.10  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).
% 71.01/71.10  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).
% 71.01/71.10  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).
% 71.01/71.10  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))).
% 71.01/71.10  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))).
% 71.01/71.10  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)).
% 71.01/71.10  0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=c_Lambda_OdB_OAbs(V_dB_H).
% 71.01/71.10  0 [] c_Lambda_OdB_OAbs(V_dB_H)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2).
% 71.01/71.10  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).
% 71.01/71.10  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.
% 71.01/71.10  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.
% 71.01/71.10  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.
% 71.01/71.10  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.
% 71.01/71.10  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)))).
% 71.01/71.10  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)).
% 71.01/71.10  0 [] c_Lambda_OdB_OAbs(V_dB)!=c_Lambda_OdB_OAbs(V_dB_H)|V_dB=V_dB_H.
% 71.01/71.10  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)).
% 71.01/71.10  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.
% 71.01/71.10  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.
% 71.01/71.10  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)).
% 71.01/71.10  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)).
% 71.01/71.10  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)).
% 71.01/71.10  0 [] -hBOOL(hAPP(hAPP(c_Lambda_Obeta,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)),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))).
% 71.01/71.10  0 [] class_Orderings_Opreorder(tc_fun(T_2,T_1))| -class_Orderings_Opreorder(T_1).
% 71.01/71.10  0 [] class_Orderings_Oorder(tc_fun(T_2,T_1))| -class_Orderings_Oorder(T_1).
% 71.01/71.10  0 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 71.01/71.10  0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 71.01/71.10  0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 71.01/71.10  0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 71.01/71.10  0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 71.01/71.10  0 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 71.01/71.10  0 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 71.01/71.10  0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 71.01/71.10  0 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 71.01/71.10  0 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 71.01/71.10  0 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 71.01/71.10  0 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 71.01/71.10  0 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 71.01/71.10  0 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 71.01/71.10  0 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 71.01/71.10  0 [] class_OrderedGroup_Omonoid__mult(tc_nat).
% 71.01/71.10  0 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 71.01/71.10  0 [] class_Nat_Osemiring__char__0(tc_nat).
% 71.01/71.10  0 [] class_Orderings_Opreorder(tc_nat).
% 71.01/71.10  0 [] class_Orderings_Olinorder(tc_nat).
% 71.01/71.10  0 [] class_Orderings_Oorder(tc_nat).
% 71.01/71.10  0 [] class_Power_Opower(tc_nat).
% 71.01/71.10  0 [] class_Orderings_Opreorder(tc_bool).
% 71.01/71.10  0 [] class_Orderings_Oorder(tc_bool).
% 71.01/71.10  0 [] hBOOL(hAPP(hAPP(c_fe_qual(T_a),V_x),V_x)).
% 71.01/71.10  0 [] V_X=V_Y| -hBOOL(hAPP(hAPP(c_fe_qual(T_a),V_X),V_Y)).
% 71.01/71.10  end_of_list.
% 71.01/71.10  
% 71.01/71.10  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 71.01/71.10  
% 71.01/71.10  This ia a non-Horn set with equality.  The strategy will be
% 71.01/71.10  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 71.01/71.10  deletion, with positive clauses in sos and nonpositive
% 71.01/71.10  clauses in usable.
% 71.01/71.10  
% 71.01/71.10     dependent: set(knuth_bendix).
% 71.01/71.10     dependent: set(anl_eq).
% 71.01/71.10     dependent: set(para_from).
% 71.01/71.10     dependent: set(para_into).
% 71.01/71.10     dependent: clear(para_from_right).
% 71.01/71.10     dependent: clear(para_into_right).
% 71.01/71.10     dependent: set(para_from_vars).
% 71.01/71.10     dependent: set(eq_units_both_ways).
% 71.01/71.10     dependent: set(dynamic_demod_all).
% 71.01/71.10     dependent: set(dynamic_demod).
% 71.01/71.10     dependent: set(order_eq).
% 71.01/71.10     dependent: set(back_demod).
% 71.01/71.10     dependent: set(lrpo).
% 71.01/71.10     dependent: set(hyper_res).
% 71.01/71.10     dependent: set(unit_deletion).
% 71.01/71.10     dependent: set(factor).
% 71.01/71.10  
% 71.01/71.10  ------------> process usable:
% 71.01/71.10  ** KEPT (pick-wt=35): 2 [copy,1,flip.1,flip.2] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,A),B),C,tc_Lambda_OdB,tc_Lambda_OdB)!=A|c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,A),B),c_List_Oappend(C,c_List_Olist_OCons(B,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=hAPP(hAPP(c_Lambda_OdB_OApp,A),B).
% 71.01/71.10  ** KEPT (pick-wt=15): 3 [] hBOOL(hAPP(c_Wellfounded_Oaccp(c_ListOrder_Ostep1(A,B),tc_List_Olist(B)),C))| -c_List_Olistsp(c_Wellfounded_Oaccp(A,B),C,B).
% 71.01/71.10  ** KEPT (pick-wt=21): 4 [] 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).
% 71.01/71.10  ** KEPT (pick-wt=13): 5 [] 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).
% 71.01/71.10  ** KEPT (pick-wt=13): 6 [] 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).
% 71.01/71.10  ** KEPT (pick-wt=13): 7 [] 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).
% 71.01/71.10    Following clause subsumed by 5 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).
% 71.01/71.10    Following clause subsumed by 6 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).
% 71.01/71.10  ** KEPT (pick-wt=10): 8 [] c_List_Orotate1(A,B)!=c_List_Olist_ONil(B)|A=c_List_Olist_ONil(B).
% 71.01/71.10  ** KEPT (pick-wt=12): 9 [] c_List_Oreplicate(A,B,C)!=c_List_Oreplicate(D,E,C)|A=D.
% 71.01/71.10  ** KEPT (pick-wt=11): 10 [] c_List_Olistsp(A,B,C)| -c_List_Olistsp(A,c_List_Oappend(D,B,C),C).
% 71.01/71.10  ** KEPT (pick-wt=11): 11 [] c_List_Olistsp(A,B,C)| -c_List_Olistsp(A,c_List_Oappend(B,D,C),C).
% 71.01/71.10  ** KEPT (pick-wt=14): 12 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=14): 13 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=10): 14 [] c_List_Orev(A,B)!=c_List_Olist_ONil(B)|A=c_List_Olist_ONil(B).
% 71.01/71.10  ** KEPT (pick-wt=10): 15 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat__aux(B,c_HOL_Ozero__class_Ozero(tc_nat),C,A)=C.
% 71.01/71.10  ** KEPT (pick-wt=6): 16 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 71.01/71.10  ** KEPT (pick-wt=5): 17 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 71.01/71.10    Following clause subsumed by 17 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 71.01/71.10  ** KEPT (pick-wt=16): 18 [] c_List_Oreplicate(A,B,C)!=c_List_Oreplicate(D,E,C)|B=E|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 71.01/71.10  ** KEPT (pick-wt=14): 19 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)),A).
% 71.01/71.10  ** KEPT (pick-wt=30): 21 [copy,20,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_Oappend(c_ListApplication_Osko__ListApplication__XApp__e_q__foldl__conv__1__1(A,B,C,D),c_List_Olist_OCons(B,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB)=D|D=c_List_Olist_ONil(tc_Lambda_OdB).
% 71.01/71.10  ** KEPT (pick-wt=15): 22 [] c_List_Olistsp(c_Wellfounded_Oaccp(A,B),C,B)| -hBOOL(hAPP(c_Wellfounded_Oaccp(c_ListOrder_Ostep1(A,B),tc_List_Olist(B)),C)).
% 71.01/71.10  ** KEPT (pick-wt=4): 23 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 71.01/71.10    Following clause subsumed by 23 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 71.01/71.10  ** KEPT (pick-wt=6): 24 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 71.01/71.10  ** KEPT (pick-wt=6): 25 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 71.01/71.10  ** KEPT (pick-wt=6): 26 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 71.01/71.10  ** KEPT (pick-wt=13): 27 [] -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.
% 71.01/71.10  ** KEPT (pick-wt=13): 28 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(C,B,A)|c_HOL_Oord__class_Oless(B,C,A).
% 71.01/71.10    Following clause subsumed by 28 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.
% 71.01/71.10    Following clause subsumed by 28 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).
% 71.01/71.10    Following clause subsumed by 28 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).
% 71.01/71.10  ** KEPT (pick-wt=24): 29 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=22): 30 [] 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).
% 71.01/71.10  ** KEPT (pick-wt=14): 31 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=14): 32 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=10): 33 [] c_List_Orev(A,B)!=c_List_Orev(C,B)|A=C.
% 71.01/71.10  ** KEPT (pick-wt=15): 34 [] c_List_Olistsp(A,c_List_Oappend(B,C,D),D)| -c_List_Olistsp(A,C,D)| -c_List_Olistsp(A,B,D).
% 71.01/71.10  ** KEPT (pick-wt=15): 35 [] hAPP(c_Type_Oshift(A,B,C,D),E)=hAPP(A,E)| -c_HOL_Oord__class_Oless(E,B,tc_nat).
% 71.01/71.10  ** KEPT (pick-wt=10): 36 [] c_List_Olist_ONil(A)!=c_List_Orev(B,A)|B=c_List_Olist_ONil(A).
% 71.01/71.10  ** KEPT (pick-wt=15): 37 [] c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xex__least__nat__less__1__1(A,B),B,tc_nat)| -hBOOL(hAPP(A,B))|hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 71.01/71.10  ** KEPT (pick-wt=21): 38 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A).
% 71.01/71.10  ** KEPT (pick-wt=21): 39 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A).
% 71.01/71.10    Following clause subsumed by 38 during input processing: 0 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A)| -c_HOL_Oord__class_Oless(C,D,tc_nat).
% 71.01/71.10    Following clause subsumed by 39 during input processing: 0 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A).
% 71.01/71.10  ** KEPT (pick-wt=9): 40 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat).
% 71.01/71.10  ** KEPT (pick-wt=9): 41 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat).
% 71.01/71.10  ** KEPT (pick-wt=10): 42 [] c_Type_Otype_OFun(A,B)!=c_Type_Otype_OFun(C,D)|B=D.
% 71.01/71.10  ** KEPT (pick-wt=10): 43 [] c_Type_Otype_OFun(A,B)!=c_Type_Otype_OFun(C,D)|A=C.
% 71.01/71.10  ** KEPT (pick-wt=20): 44 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=20): 45 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=20): 46 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=20): 47 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=20): 48 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=20): 49 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=18): 50 [] 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).
% 71.01/71.10  ** KEPT (pick-wt=18): 51 [] 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).
% 71.01/71.10  ** KEPT (pick-wt=18): 52 [] 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).
% 71.01/71.10  ** KEPT (pick-wt=10): 53 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 71.01/71.10  ** KEPT (pick-wt=10): 54 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 71.01/71.10  ** KEPT (pick-wt=10): 55 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 71.01/71.10    Following clause subsumed by 55 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 71.01/71.10  ** KEPT (pick-wt=14): 56 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=14): 57 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=26): 58 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(D,C,tc_nat).
% 71.01/71.10  ** KEPT (pick-wt=20): 59 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A).
% 71.01/71.10  ** KEPT (pick-wt=17): 60 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=17): 61 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=22): 62 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=17): 63 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=17): 64 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=17): 65 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=17): 66 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=22): 67 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=20): 68 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=8): 69 [] -class_Ring__and__Field_Oordered__semidom(A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A).
% 71.01/71.10  ** KEPT (pick-wt=8): 70 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A).
% 71.01/71.10  ** KEPT (pick-wt=12): 71 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)),A).
% 71.01/71.10  ** KEPT (pick-wt=9): 72 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=15): 73 [] -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).
% 71.01/71.10  ** KEPT (pick-wt=15): 74 [] c_List_Otake(A,B,C)!=c_List_Olist_ONil(C)|B=c_List_Olist_ONil(C)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 71.01/71.10  ** KEPT (pick-wt=11): 75 [] c_List_Oreplicate(A,B,C)!=c_List_Olist_ONil(C)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 71.01/71.10  ** KEPT (pick-wt=11): 76 [] c_List_Olist_ONil(A)!=c_List_Oreplicate(B,C,A)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 71.01/71.10  ** KEPT (pick-wt=16): 77 [] c_List_Olist_OCons(A,c_List_Olist_ONil(B),B)!=c_List_Orev(C,B)|C=c_List_Olist_OCons(A,c_List_Olist_ONil(B),B).
% 71.01/71.10  ** KEPT (pick-wt=16): 78 [] c_List_Orev(A,B)!=c_List_Olist_OCons(C,c_List_Olist_ONil(B),B)|A=c_List_Olist_OCons(C,c_List_Olist_ONil(B),B).
% 71.01/71.10    Following clause subsumed by 6 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).
% 71.01/71.10    Following clause subsumed by 5 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).
% 71.01/71.10  ** KEPT (pick-wt=20): 79 [] 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).
% 71.01/71.10  ** KEPT (pick-wt=26): 80 [] c_List_Oappend(A,B,C)!=c_List_Olist_OCons(D,E,C)|c_List_Oappend(c_List_Osko__List__Xappend__e_q__Cons__conv__1__1(D,E,A,B,C),B,C)=E|B=c_List_Olist_OCons(D,E,C).
% 71.01/71.10  ** KEPT (pick-wt=26): 81 [] c_List_Olist_OCons(A,B,C)!=c_List_Oappend(D,E,C)|c_List_Olist_OCons(A,c_List_Osko__List__XCons__e_q__append__conv__1__1(A,B,D,E,C),C)=D|c_List_Olist_OCons(A,B,C)=E.
% 71.01/71.10  ** KEPT (pick-wt=26): 83 [copy,82,flip.2] c_List_Oappend(A,B,C)!=c_List_Olist_OCons(D,E,C)|c_List_Olist_OCons(D,c_List_Osko__List__Xappend__e_q__Cons__conv__1__1(D,E,A,B,C),C)=A|B=c_List_Olist_OCons(D,E,C).
% 71.01/71.10  ** KEPT (pick-wt=26): 85 [copy,84,flip.2] c_List_Olist_OCons(A,B,C)!=c_List_Oappend(D,E,C)|c_List_Oappend(c_List_Osko__List__XCons__e_q__append__conv__1__1(A,B,D,E,C),E,C)=B|c_List_Olist_OCons(A,B,C)=E.
% 71.01/71.10  ** KEPT (pick-wt=19): 86 [] -class_Ring__and__Field_Oordered__semidom(A)|c_Power_Opower__class_Opower(B,C,A)!=c_Power_Opower__class_Opower(B,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A)|C=D.
% 71.01/71.10  ** KEPT (pick-wt=18): 87 [] c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),D)| -c_Type_Otyping(A,C,E)| -c_Type_Otyping(A,B,c_Type_Otype_OFun(E,D)).
% 71.01/71.10  ** KEPT (pick-wt=15): 88 [] 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).
% 71.01/71.10  ** KEPT (pick-wt=13): 89 [] 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).
% 71.01/71.10  ** KEPT (pick-wt=12): 90 [] c_Lambda_Oliftn(A,c_Lambda_OdB_OVar(B),C)=c_Lambda_OdB_OVar(B)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 71.01/71.10  ** KEPT (pick-wt=24): 92 [copy,91,flip.2] c_List_Olist_OCons(A,B,C)!=c_List_Oappend(D,E,C)|c_List_Oappend(c_List_Osko__List__XCons__e_q__append__conv__1__1(A,B,D,E,C),E,C)=B|D=c_List_Olist_ONil(C).
% 71.01/71.10  ** KEPT (pick-wt=24): 94 [copy,93,flip.2] c_List_Oappend(A,B,C)!=c_List_Olist_OCons(D,E,C)|c_List_Olist_OCons(D,c_List_Osko__List__Xappend__e_q__Cons__conv__1__1(D,E,A,B,C),C)=A|A=c_List_Olist_ONil(C).
% 71.01/71.10  ** KEPT (pick-wt=24): 95 [] c_List_Oappend(A,B,C)!=c_List_Olist_OCons(D,E,C)|c_List_Oappend(c_List_Osko__List__Xappend__e_q__Cons__conv__1__1(D,E,A,B,C),B,C)=E|A=c_List_Olist_ONil(C).
% 71.01/71.10  ** KEPT (pick-wt=24): 96 [] c_List_Olist_OCons(A,B,C)!=c_List_Oappend(D,E,C)|c_List_Olist_OCons(A,c_List_Osko__List__XCons__e_q__append__conv__1__1(A,B,D,E,C),C)=D|D=c_List_Olist_ONil(C).
% 71.01/71.10  ** KEPT (pick-wt=20): 97 [] c_List_Orev(A,B)!=c_List_Olist_OCons(C,D,B)|A=c_List_Oappend(c_List_Orev(D,B),c_List_Olist_OCons(C,c_List_Olist_ONil(B),B),B).
% 71.01/71.10  ** KEPT (pick-wt=21): 98 [] hBOOL(hAPP(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xex__least__nat__less__1__1(A,B)),c_HOL_Oone__class_Oone(tc_nat))))| -hBOOL(hAPP(A,B))|hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 71.01/71.10  ** KEPT (pick-wt=27): 99 [] hBOOL(hAPP(c_Wellfounded_Oaccp(c_ListOrder_Ostep1(A,B),tc_List_Olist(B)),c_List_Olist_OCons(C,D,B)))| -hBOOL(hAPP(c_Wellfounded_Oaccp(c_ListOrder_Ostep1(A,B),tc_List_Olist(B)),D))| -hBOOL(hAPP(c_Wellfounded_Oaccp(A,B),C)).
% 71.01/71.10  ** KEPT (pick-wt=14): 100 [] 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).
% 71.01/71.10  ** KEPT (pick-wt=43): 101 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),D)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),D)),hAPP(hAPP(c_Lambda_Olift,B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)))| -c_HOL_Oord__class_Oless(D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 71.01/71.10  ** KEPT (pick-wt=43): 102 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),D)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,B),D)),C)| -c_HOL_Oord__class_Oless(C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 71.01/71.10  ** KEPT (pick-wt=16): 103 [] c_Type_Otyping(A,c_Lambda_OdB_OAbs(B),c_Type_Otype_OFun(C,D))| -c_Type_Otyping(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),C,tc_Type_Otype),B,D).
% 71.01/71.10  ** KEPT (pick-wt=19): 104 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(B,A)=c_Nat_Osemiring__1__class_Oof__nat__aux(c_COMBC(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A),A,A,A),B,c_HOL_Ozero__class_Ozero(A),A).
% 71.01/71.10  ** KEPT (pick-wt=21): 105 [] c_Type_Otypings(c_Type_Oshift(A,B,C,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,B,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),D,tc_Lambda_OdB,tc_Lambda_OdB),E)| -c_Type_Otypings(A,D,E).
% 71.01/71.10  ** KEPT (pick-wt=35): 107 [copy,106,flip.1] c_Type_Otype_OFun(A,B)!=v_T____|hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,C),D),E)))| -c_Type_Otyping(F,D,B)| -hBOOL(hAPP(c_InductTermi_OIT,D))| -c_Type_Otyping(c_Type_Oshift(F,E,B,tc_Type_Otype),C,G)| -hBOOL(hAPP(c_InductTermi_OIT,C)).
% 71.01/71.10  ** KEPT (pick-wt=35): 109 [copy,108,flip.1] c_Type_Otype_OFun(A,B)!=v_T____|hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,C),D),E)))| -c_Type_Otyping(F,D,A)| -hBOOL(hAPP(c_InductTermi_OIT,D))| -c_Type_Otyping(c_Type_Oshift(F,E,A,tc_Type_Otype),C,G)| -hBOOL(hAPP(c_InductTermi_OIT,C)).
% 71.01/71.10  ** KEPT (pick-wt=18): 110 [] 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).
% 71.01/71.10  ** KEPT (pick-wt=45): 112 [copy,111,flip.1,flip.2,flip.3] c_List_Olist_OCons(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(A,B,C),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(A,B,C),tc_Lambda_OdB)=B|c_List_Ofoldl(c_Lambda_OdB_OApp,A,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(A,B,C),tc_Lambda_OdB,tc_Lambda_OdB)=C|c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(A,B,C),B,tc_Lambda_OdB,tc_Lambda_OdB)=C| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 71.01/71.10  ** KEPT (pick-wt=43): 114 [copy,113,flip.1,flip.2] c_List_Olist_OCons(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(A,B,C),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(A,B,C),tc_Lambda_OdB)=B|c_List_Ofoldl(c_Lambda_OdB_OApp,A,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(A,B,C),tc_Lambda_OdB,tc_Lambda_OdB)=C|hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(A,B,C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 71.01/71.10  ** KEPT (pick-wt=32): 115 [] c_Type_Otypings(A,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,B,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),C,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),D,tc_Lambda_OdB,tc_Lambda_OdB),E)| -c_Type_Otypings(c_Type_Oshift(A,C,F,tc_Type_Otype),D,E)| -c_Type_Otyping(A,B,F).
% 71.01/71.10  ** KEPT (pick-wt=43): 117 [copy,116,flip.1] c_List_Olist_OCons(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(A,B,C),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(A,B,C),tc_Lambda_OdB)=B|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),B),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(A,B,C)))|hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(A,B,C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 71.01/71.11  ** KEPT (pick-wt=45): 119 [copy,118,flip.1,flip.3] c_List_Olist_OCons(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(A,B,C),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(A,B,C),tc_Lambda_OdB)=B|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),B),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(A,B,C)))|c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(A,B,C),B,tc_Lambda_OdB,tc_Lambda_OdB)=C| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 71.01/71.11  ** KEPT (pick-wt=9): 120 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 71.01/71.11  ** KEPT (pick-wt=19): 121 [] 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)).
% 71.01/71.11  ** KEPT (pick-wt=19): 122 [] 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)).
% 71.01/71.11  ** KEPT (pick-wt=36): 123 [] hBOOL(hAPP(hAPP(A,B),C))|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(A,D),E),F))| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(A,D),c_List_Oappend(E,c_List_Olist_OCons(B,c_List_Olist_ONil(D),D),D)),c_List_Oappend(F,c_List_Olist_OCons(C,c_List_Olist_ONil(D),D),D))).
% 71.01/71.11  ** KEPT (pick-wt=16): 124 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)|B=C.
% 71.01/71.11  ** KEPT (pick-wt=16): 125 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B)|A=C.
% 71.01/71.11    Following clause subsumed by 124 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.
% 71.01/71.11  ** KEPT (pick-wt=20): 126 [] -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.
% 71.01/71.11  ** KEPT (pick-wt=18): 127 [] -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.
% 71.01/71.11  ** KEPT (pick-wt=18): 128 [] -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.
% 71.01/71.11  ** KEPT (pick-wt=18): 129 [] -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.
% 71.01/71.11  ** KEPT (pick-wt=7): 130 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 71.01/71.11    Following clause subsumed by 130 during input processing: 0 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 71.01/71.11  ** KEPT (pick-wt=23): 131 [] A=B|hBOOL(hAPP(hAPP(C,B),A))| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(C,D),c_List_Olist_OCons(B,E,D)),c_List_Olist_OCons(A,F,D))).
% 71.01/71.11  ** KEPT (pick-wt=35): 132 [] -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)).
% 71.01/71.11  ** KEPT (pick-wt=16): 133 [] 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)).
% 71.01/71.11  ** KEPT (pick-wt=6): 134 [] c_List_Olist_OCons(A,B,C)!=B.
% 71.01/71.11    Following clause subsumed by 134 during input processing: 0 [flip.1] c_List_Olist_OCons(B,A,C)!=A.
% 71.01/71.11  ** KEPT (pick-wt=13): 135 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,A),c_Lambda_OdB_OVar(B))))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 71.01/71.11  ** KEPT (pick-wt=22): 136 [] -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).
% 71.01/71.11  ** KEPT (pick-wt=33): 137 [] A=B|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(C,D),A),B))| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(C,D),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))).
% 71.01/71.11  ** KEPT (pick-wt=11): 138 [] hAPP(hAPP(A,B),C)=B| -c_OrderedGroup_Omonoid__add(C,A,D).
% 71.01/71.11  ** KEPT (pick-wt=11): 139 [] hAPP(hAPP(A,B),C)=C| -c_OrderedGroup_Omonoid__add(B,A,D).
% 71.01/71.11  ** KEPT (pick-wt=57): 141 [copy,140,flip.1,flip.3] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(A,B,C)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(A,B,C)),c_HOL_Ozero__class_Ozero(tc_nat)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(A,B,C),tc_Lambda_OdB,tc_Lambda_OdB)=C|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),B),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(A,B,C)))|c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(A,B,C),B,tc_Lambda_OdB,tc_Lambda_OdB)=C| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 71.01/71.11  ** KEPT (pick-wt=55): 143 [copy,142,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(A,B,C)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(A,B,C)),c_HOL_Ozero__class_Ozero(tc_nat)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(A,B,C),tc_Lambda_OdB,tc_Lambda_OdB)=C|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),B),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(A,B,C)))|hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(A,B,C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 71.01/71.11  ** KEPT (pick-wt=19): 144 [] -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).
% 71.01/71.11  ** KEPT (pick-wt=13): 145 [] -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).
% 71.01/71.11  ** KEPT (pick-wt=7): 147 [copy,146,flip.2] -class_Ring__and__Field_Ozero__ne_q__one(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Oone__class_Oone(A).
% 71.01/71.11  ** KEPT (pick-wt=15): 148 [] -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).
% 71.01/71.11  ** KEPT (pick-wt=16): 150 [copy,149,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).
% 71.01/71.11  ** KEPT (pick-wt=13): 151 [] -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).
% 71.01/71.11    Following clause subsumed by 147 during input processing: 0 [] -class_Ring__and__Field_Ozero__ne_q__one(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Oone__class_Oone(A).
% 71.01/71.11  ** KEPT (pick-wt=11): 152 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 71.01/71.11  ** KEPT (pick-wt=11): 153 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 71.01/71.11  ** KEPT (pick-wt=13): 155 [copy,154,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.
% 71.01/71.11  ** KEPT (pick-wt=11): 156 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 71.01/71.11  ** KEPT (pick-wt=11): 157 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 71.01/71.11  ** KEPT (pick-wt=11): 158 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 71.01/71.11  ** KEPT (pick-wt=11): 159 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 71.01/71.11    Following clause subsumed by 152 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.
% 71.01/71.11  ** KEPT (pick-wt=13): 160 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 71.01/71.11  ** KEPT (pick-wt=13): 161 [] 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).
% 71.01/71.11  ** KEPT (pick-wt=13): 162 [] 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).
% 71.01/71.11  ** KEPT (pick-wt=12): 164 [copy,163,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 71.01/71.11    Following clause subsumed by 164 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 71.01/71.11  ** KEPT (pick-wt=21): 165 [] -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))).
% 71.01/71.11    Following clause subsumed by 165 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))).
% 71.01/71.11  ** KEPT (pick-wt=8): 166 [] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 71.01/71.11  ** KEPT (pick-wt=10): 167 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A)=c_HOL_Oone__class_Oone(A).
% 71.01/71.11  ** KEPT (pick-wt=28): 168 [] -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.
% 71.01/71.11  ** KEPT (pick-wt=15): 169 [] hBOOL(hAPP(hAPP(A,B),C))| -hBOOL(hAPP(hAPP(c_Predicate_Oconversep(A,D,E),C),B)).
% 71.01/71.11  ** KEPT (pick-wt=15): 170 [] hBOOL(hAPP(hAPP(c_Predicate_Oconversep(A,B,C),D),E))| -hBOOL(hAPP(hAPP(A,E),D)).
% 71.01/71.11    Following clause subsumed by 169 during input processing: 0 [] hBOOL(hAPP(hAPP(A,B),C))| -hBOOL(hAPP(hAPP(c_Predicate_Oconversep(A,D,E),C),B)).
% 71.01/71.11    Following clause subsumed by 170 during input processing: 0 [] hBOOL(hAPP(hAPP(c_Predicate_Oconversep(A,B,C),D),E))| -hBOOL(hAPP(hAPP(A,E),D)).
% 71.01/71.11  ** KEPT (pick-wt=25): 171 [] -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)).
% 71.01/71.11  ** KEPT (pick-wt=25): 172 [] -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)).
% 71.01/71.11  ** KEPT (pick-wt=25): 173 [] -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).
% 71.01/71.11    Following clause subsumed by 171 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)).
% 71.01/71.11  ** KEPT (pick-wt=25): 174 [] -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)).
% 71.01/71.11  ** KEPT (pick-wt=25): 175 [] -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)).
% 71.01/71.11  ** KEPT (pick-wt=25): 176 [] -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)).
% 71.01/71.11  ** KEPT (pick-wt=25): 177 [] -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)).
% 71.01/71.11    Following clause subsumed by 171 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)).
% 71.01/71.11  ** KEPT (pick-wt=22): 178 [] -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(A,B),C),D))|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(A,B),c_List_Oappend(C,E,B)),c_List_Oappend(D,E,B))).
% 71.01/71.11  ** KEPT (pick-wt=22): 179 [] hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(A,B),c_List_Oappend(C,D,B)),c_List_Oappend(C,E,B)))| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(A,B),D),E)).
% 71.01/71.11  ** KEPT (pick-wt=20): 180 [] A=B|C=D| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(E,F),c_List_Olist_OCons(B,D,F)),c_List_Olist_OCons(A,C,F))).
% 71.01/71.11  ** KEPT (pick-wt=20): 181 [] -hBOOL(hAPP(hAPP(A,B),C))|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(A,D),c_List_Olist_OCons(B,E,D)),c_List_Olist_OCons(C,E,D))).
% 71.01/71.11  ** KEPT (pick-wt=12): 182 [] c_List_Oappend(A,B,C)!=c_List_Oappend(D,B,C)|A=D.
% 71.01/71.11  ** KEPT (pick-wt=12): 183 [] c_List_Oappend(A,B,C)!=c_List_Oappend(A,D,C)|B=D.
% 71.01/71.11  ** KEPT (pick-wt=20): 184 [] hBOOL(hAPP(c_Wellfounded_Oaccp(A,B),C))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(c_Wellfounded_Oaccp(A,B),D)).
% 71.01/71.11    Following clause subsumed by 184 during input processing: 0 [] hBOOL(hAPP(c_Wellfounded_Oaccp(A,B),C))| -hBOOL(hAPP(c_Wellfounded_Oaccp(A,B),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D)).
% 71.01/71.11  ** KEPT (pick-wt=24): 185 [] 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)).
% 71.01/71.11  ** KEPT (pick-wt=13): 186 [] hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),A))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 71.01/71.11  ** KEPT (pick-wt=13): 187 [] hBOOL(hAPP(c_InductTermi_OIT,A))| -hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),A)).
% 71.01/71.11  ** KEPT (pick-wt=15): 188 [] -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).
% 71.01/71.11  ** KEPT (pick-wt=15): 189 [] -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).
% 71.01/71.11    Following clause subsumed by 188 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).
% 71.01/71.11  ** KEPT (pick-wt=31): 190 [] hBOOL(hAPP(hAPP(A,B),C))|B=C| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(A,D),c_List_Oappend(E,c_List_Olist_OCons(B,c_List_Olist_ONil(D),D),D)),c_List_Oappend(F,c_List_Olist_OCons(C,c_List_Olist_ONil(D),D),D))).
% 71.01/71.11  ** KEPT (pick-wt=12): 191 [] -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.
% 71.01/71.11  ** KEPT (pick-wt=10): 192 [] hAPP(A,B)=C| -c_Type_Otyping(A,c_Lambda_OdB_OVar(B),C).
% 71.01/71.11  ** KEPT (pick-wt=12): 193 [] c_List_Olist_ONil(A)!=c_List_Omap(B,C,D,A)|C=c_List_Olist_ONil(D).
% 71.01/71.11  ** KEPT (pick-wt=9): 194 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A)=B.
% 71.01/71.11  ** KEPT (pick-wt=9): 195 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A)=B.
% 71.01/71.11  ** KEPT (pick-wt=14): 196 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(A,C),D)).
% 71.01/71.11  ** KEPT (pick-wt=9): 197 [] -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(A,B),c_List_Olist_ONil(B)),C)).
% 71.01/71.11  ** KEPT (pick-wt=9): 198 [] -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(A,B),C),c_List_Olist_ONil(B))).
% 71.01/71.11  ** KEPT (pick-wt=12): 199 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,A),B)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 71.01/71.11  ** KEPT (pick-wt=11): 200 [] c_List_Olist_ONil(A)!=c_List_Oappend(B,C,A)|B=c_List_Olist_ONil(A).
% 71.01/71.11  ** KEPT (pick-wt=11): 201 [] c_List_Olist_ONil(A)!=c_List_Oappend(B,C,A)|C=c_List_Olist_ONil(A).
% 71.01/71.11  ** KEPT (pick-wt=11): 202 [] c_List_Oappend(A,B,C)!=c_List_Olist_ONil(C)|A=c_List_Olist_ONil(C).
% 71.01/71.11  ** KEPT (pick-wt=11): 203 [] c_List_Oappend(A,B,C)!=c_List_Olist_ONil(C)|B=c_List_Olist_ONil(C).
% 71.01/71.11  ** KEPT (pick-wt=24): 204 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,A),B)),hAPP(hAPP(c_Lambda_Olift,C),B)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),C)).
% 71.01/71.11  ** KEPT (pick-wt=25): 205 [] hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(A,B),C),D))|D=C| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(A,B),c_List_Olist_OCons(E,C,B)),c_List_Olist_OCons(F,D,B))).
% 71.01/71.11  ** KEPT (pick-wt=22): 206 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_OrderedGroup_Osemigroup__add(A,E).
% 71.01/71.11  ** KEPT (pick-wt=7): 207 [] c_List_Olist_ONil(A)!=c_List_Olist_OCons(B,C,A).
% 71.01/71.11  ** KEPT (pick-wt=28): 208 [] A=B|C=D| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(E,F),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))).
% 71.01/71.11  ** KEPT (pick-wt=10): 209 [] -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 71.01/71.11  ** KEPT (pick-wt=10): 210 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 71.01/71.11  ** KEPT (pick-wt=6): 211 [] -class_OrderedGroup_Osemigroup__add(A)|c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(A),A).
% 71.01/71.11  ** KEPT (pick-wt=15): 212 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),c_Lambda_OdB_OVar(B)),C)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 71.01/71.11  ** KEPT (pick-wt=10): 213 [] c_List_Oappend(A,B,C)!=A|B=c_List_Olist_ONil(C).
% 71.01/71.11    Following clause subsumed by 213 during input processing: 0 [flip.1] c_List_Oappend(A,B,C)!=A|B=c_List_Olist_ONil(C).
% 71.01/71.11  ** KEPT (pick-wt=10): 214 [] c_List_Oappend(A,B,C)!=B|A=c_List_Olist_ONil(C).
% 71.01/71.11    Following clause subsumed by 214 during input processing: 0 [flip.1] c_List_Oappend(B,A,C)!=A|B=c_List_Olist_ONil(C).
% 71.01/71.11  ** KEPT (pick-wt=12): 215 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_OCons(D,E,C)|A=D.
% 71.01/71.11  ** KEPT (pick-wt=12): 216 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_OCons(D,E,C)|B=E.
% 71.01/71.11  ** KEPT (pick-wt=28): 217 [] hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(A,B),C),D))|hBOOL(hAPP(hAPP(A,E),F))| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(A,B),c_List_Olist_OCons(E,C,B)),c_List_Olist_OCons(F,D,B))).
% 71.01/71.11  ** KEPT (pick-wt=22): 218 [] hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(A,B),c_List_Olist_OCons(C,D,B)),c_List_Olist_OCons(C,E,B)))| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(A,B),D),E)).
% 71.01/71.11  ** KEPT (pick-wt=16): 219 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OVar(E),t_a)))|hBOOL(hAPP(A,hAPP(B,E))).
% 71.01/71.11    Following clause subsumed by 219 during input processing: 0 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OVar(E),t_a)))|hBOOL(hAPP(A,hAPP(B,E))).
% 71.01/71.11  ** KEPT (pick-wt=8): 220 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OVar(B)|A=B.
% 71.01/71.11  ** KEPT (pick-wt=21): 221 [] -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)).
% 71.01/71.11  ** KEPT (pick-wt=12): 222 [] c_List_Omap(A,B,C,D)!=c_List_Olist_ONil(D)|B=c_List_Olist_ONil(C).
% 71.01/71.11  ** KEPT (pick-wt=20): 223 [] 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.
% 71.01/71.11  ** KEPT (pick-wt=20): 224 [] 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.
% 71.01/71.11  ** KEPT (pick-wt=26): 225 [] 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).
% 71.01/71.11  ** KEPT (pick-wt=16): 226 [] 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).
% 71.01/71.11  ** KEPT (pick-wt=22): 227 [] 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)).
% 71.01/71.11  ** KEPT (pick-wt=22): 228 [] 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)).
% 71.01/71.11  ** KEPT (pick-wt=18): 229 [] hBOOL(hAPP(c_Wellfounded_Oaccp(A,B),C))| -hBOOL(hAPP(hAPP(A,C),D))| -hBOOL(hAPP(c_Wellfounded_Oaccp(A,B),D)).
% 71.01/71.11    Following clause subsumed by 229 during input processing: 0 [] hBOOL(hAPP(c_Wellfounded_Oaccp(A,B),C))| -hBOOL(hAPP(hAPP(A,C),D))| -hBOOL(hAPP(c_Wellfounded_Oaccp(A,B),D)).
% 71.01/71.11  ** KEPT (pick-wt=8): 230 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 71.01/71.11  ** KEPT (pick-wt=36): 232 [copy,231,flip.1,flip.3] hAPP(hAPP(c_Lambda_OdB_OApp,A),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(A,B,C))=C|hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),c_Lambda_Osko__Lambda__Xbeta__cases__3__2(A,B,C)))|c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__3__1(A,B,C))=A| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),C)).
% 71.01/71.11  ** KEPT (pick-wt=36): 234 [copy,233,flip.2,flip.3] hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(B,A,C)))|hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osko__Lambda__Xbeta__cases__3__2(B,A,C)),A)=C|c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__3__1(B,A,C))=B| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,B),A)),C)).
% 71.01/71.11  ** KEPT (pick-wt=37): 236 [copy,235,flip.1,flip.2,flip.3] hAPP(hAPP(c_Lambda_OdB_OApp,A),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(A,B,C))=C|hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osko__Lambda__Xbeta__cases__3__2(A,B,C)),B)=C|c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__3__1(A,B,C))=A| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),C)).
% 71.01/71.11  ** KEPT (pick-wt=35): 238 [copy,237,flip.3] hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(B,A,C)))|hBOOL(hAPP(hAPP(c_Lambda_Obeta,B),c_Lambda_Osko__Lambda__Xbeta__cases__3__2(B,A,C)))|c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__3__1(B,A,C))=B| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,B),A)),C)).
% 71.01/71.11  ** KEPT (pick-wt=14): 239 [] c_Type_Otyping(A,B,C)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,D),B))| -c_Type_Otyping(A,D,C).
% 71.01/71.11  ** KEPT (pick-wt=7): 240 [] -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(A)),B)).
% 71.01/71.11  ** KEPT (pick-wt=20): 241 [] 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)).
% 71.01/71.11  ** KEPT (pick-wt=55): 243 [copy,242,flip.1,flip.2] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(A,B,C)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(A,B,C)),c_HOL_Ozero__class_Ozero(tc_nat)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(A,B,C),tc_Lambda_OdB,tc_Lambda_OdB)=C|c_List_Ofoldl(c_Lambda_OdB_OApp,A,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(A,B,C),tc_Lambda_OdB,tc_Lambda_OdB)=C|hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(A,B,C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 71.01/71.11  ** KEPT (pick-wt=57): 245 [copy,244,flip.1,flip.2,flip.3] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(A,B,C)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(A,B,C)),c_HOL_Ozero__class_Ozero(tc_nat)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(A,B,C),tc_Lambda_OdB,tc_Lambda_OdB)=C|c_List_Ofoldl(c_Lambda_OdB_OApp,A,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(A,B,C),tc_Lambda_OdB,tc_Lambda_OdB)=C|c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(A,B,C),B,tc_Lambda_OdB,tc_Lambda_OdB)=C| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 71.01/71.11  ** KEPT (pick-wt=5): 246 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 71.01/71.11  ** KEPT (pick-wt=16): 247 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OAbs(E),t_a)))|hBOOL(hAPP(A,hAPP(D,E))).
% 71.01/71.11    Following clause subsumed by 247 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))).
% 71.01/71.11  ** KEPT (pick-wt=5): 248 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 71.01/71.11  ** KEPT (pick-wt=9): 249 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(A)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 71.01/71.11  ** KEPT (pick-wt=38): 251 [copy,250,flip.1] c_Lambda_OdB_OAbs(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(A,B,C))=A|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),B),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(A,B,C)))|hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(A,B,C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 71.01/71.11  ** KEPT (pick-wt=40): 253 [copy,252,flip.1,flip.3] c_Lambda_OdB_OAbs(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(A,B,C))=A|hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),B),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(A,B,C)))|c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(A,B,C),B,tc_Lambda_OdB,tc_Lambda_OdB)=C| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 71.01/71.11  ** KEPT (pick-wt=23): 254 [] hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),A),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(B,A,C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(B),A,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 71.01/71.11  ** KEPT (pick-wt=23): 255 [] 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).
% 71.01/71.11  ** KEPT (pick-wt=28): 257 [copy,256,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).
% 71.01/71.11  ** KEPT (pick-wt=13): 258 [] 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).
% 71.01/71.11  ** KEPT (pick-wt=24): 260 [copy,259,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).
% 71.01/71.11  ** KEPT (pick-wt=27): 262 [copy,261,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).
% 71.01/71.11  ** KEPT (pick-wt=21): 263 [] 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).
% 71.01/71.11  ** KEPT (pick-wt=42): 265 [copy,264,flip.2,flip.3] hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(B,A,C)))|hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osko__Lambda__Xbeta__cases__3__2(B,A,C)),A)=C|hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Osko__Lambda__Xbeta__cases__3__1(B,A,C)),A),c_HOL_Ozero__class_Ozero(tc_nat))=C| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,B),A)),C)).
% 71.01/71.11  ** KEPT (pick-wt=42): 267 [copy,266,flip.1,flip.3] hAPP(hAPP(c_Lambda_OdB_OApp,A),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(A,B,C))=C|hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),c_Lambda_Osko__Lambda__Xbeta__cases__3__2(A,B,C)))|hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Osko__Lambda__Xbeta__cases__3__1(A,B,C)),B),c_HOL_Ozero__class_Ozero(tc_nat))=C| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),C)).
% 71.01/71.11  ** KEPT (pick-wt=41): 269 [copy,268,flip.3] hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(B,A,C)))|hBOOL(hAPP(hAPP(c_Lambda_Obeta,B),c_Lambda_Osko__Lambda__Xbeta__cases__3__2(B,A,C)))|hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Osko__Lambda__Xbeta__cases__3__1(B,A,C)),A),c_HOL_Ozero__class_Ozero(tc_nat))=C| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,B),A)),C)).
% 71.01/71.11  ** KEPT (pick-wt=43): 271 [copy,270,flip.1,flip.2,flip.3] hAPP(hAPP(c_Lambda_OdB_OApp,A),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(A,B,C))=C|hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osko__Lambda__Xbeta__cases__3__2(A,B,C)),B)=C|hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Osko__Lambda__Xbeta__cases__3__1(A,B,C)),B),c_HOL_Ozero__class_Ozero(tc_nat))=C| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),C)).
% 71.01/71.11  ** KEPT (pick-wt=40): 273 [copy,272,flip.1,flip.2,flip.3] c_Lambda_OdB_OAbs(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(A,B,C))=A|c_List_Ofoldl(c_Lambda_OdB_OApp,A,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(A,B,C),tc_Lambda_OdB,tc_Lambda_OdB)=C|c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(A,B,C),B,tc_Lambda_OdB,tc_Lambda_OdB)=C| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 71.01/71.11  ** KEPT (pick-wt=38): 275 [copy,274,flip.1,flip.2] c_Lambda_OdB_OAbs(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(A,B,C))=A|c_List_Ofoldl(c_Lambda_OdB_OApp,A,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(A,B,C),tc_Lambda_OdB,tc_Lambda_OdB)=C|hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(A,B,C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 71.01/71.11  ** KEPT (pick-wt=24): 277 [copy,276,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(A,B,C),tc_Lambda_OdB,tc_Lambda_OdB)=C| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 71.01/71.11  ** KEPT (pick-wt=20): 278 [] -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).
% 71.01/71.11  ** KEPT (pick-wt=16): 279 [] -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).
% 71.01/71.11  ** KEPT (pick-wt=16): 280 [] -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).
% 71.01/71.11  ** KEPT (pick-wt=9): 281 [] -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).
% 71.01/71.11  ** KEPT (pick-wt=23): 282 [] -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).
% 71.01/71.11  ** KEPT (pick-wt=24): 283 [] 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)).
% 71.01/71.11  ** KEPT (pick-wt=24): 284 [] 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)).
% 71.01/71.11  ** KEPT (pick-wt=32): 285 [] 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)).
% 71.01/71.11  ** KEPT (pick-wt=15): 286 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),c_Lambda_Osko__Lambda__Xbeta__cases__2__1(A,B)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(A)),B)).
% 71.01/71.11  ** KEPT (pick-wt=18): 287 [] 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)).
% 71.01/71.11  ** KEPT (pick-wt=13): 289 [copy,288,flip.1] c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(A,B))=B| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(A)),B)).
% 71.01/71.12  ** KEPT (pick-wt=18): 290 [] 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.
% 71.01/71.12  ** KEPT (pick-wt=18): 291 [] 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.
% 71.01/71.12  ** KEPT (pick-wt=20): 292 [] 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.
% 71.01/71.12  ** KEPT (pick-wt=13): 293 [] 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.
% 71.01/71.12  ** KEPT (pick-wt=28): 294 [] 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)).
% 71.01/71.12  ** KEPT (pick-wt=28): 295 [] 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)).
% 71.01/71.12  ** KEPT (pick-wt=26): 296 [] 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)).
% 71.01/71.12  ** KEPT (pick-wt=50): 297 [] 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).
% 71.01/71.12  ** KEPT (pick-wt=49): 298 [] -hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,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)))| -hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),B))|hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,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))).
% 71.01/71.12  ** KEPT (pick-wt=26): 299 [] 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)).
% 71.01/71.12  ** KEPT (pick-wt=24): 300 [] 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)))| -hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),B),C)).
% 71.01/71.12  ** KEPT (pick-wt=13): 301 [] 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).
% 71.01/71.12  ** KEPT (pick-wt=15): 302 [] 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).
% 71.01/71.12  ** KEPT (pick-wt=13): 303 [] 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).
% 71.01/71.12  ** KEPT (pick-wt=14): 304 [] 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).
% 71.01/71.12  ** KEPT (pick-wt=34): 305 [] 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))).
% 71.01/71.12  ** KEPT (pick-wt=8): 306 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 71.01/71.12  ** KEPT (pick-wt=8): 307 [] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 71.01/71.12  ** KEPT (pick-wt=13): 308 [] 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).
% 71.01/71.12  ** KEPT (pick-wt=18): 309 [] 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.
% 71.01/71.12  ** KEPT (pick-wt=18): 310 [] 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.
% 71.01/71.12  ** KEPT (pick-wt=14): 311 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|A=C.
% 71.01/71.12  ** KEPT (pick-wt=14): 312 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|B=D.
% 71.01/71.12  ** KEPT (pick-wt=22): 313 [] 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)).
% 71.01/71.12  ** KEPT (pick-wt=8): 314 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OAbs(B)|A=B.
% 71.01/71.12  ** KEPT (pick-wt=24): 315 [] 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)).
% 71.01/71.12  ** KEPT (pick-wt=13): 316 [] 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.
% 71.01/71.12  ** KEPT (pick-wt=16): 317 [] 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.
% 71.01/71.12  ** KEPT (pick-wt=20): 318 [] 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)).
% 71.01/71.12  ** KEPT (pick-wt=20): 319 [] 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)).
% 71.01/71.12  ** KEPT (pick-wt=14): 320 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(A)),c_Lambda_OdB_OAbs(B)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),B)).
% 71.01/71.12  ** KEPT (pick-wt=28): 321 [] -hBOOL(hAPP(hAPP(c_Lambda_Obeta,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)),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))).
% 71.01/71.12  ** KEPT (pick-wt=6): 322 [] class_Orderings_Opreorder(tc_fun(A,B))| -class_Orderings_Opreorder(B).
% 71.01/71.12  ** KEPT (pick-wt=6): 323 [] class_Orderings_Oorder(tc_fun(A,B))| -class_Orderings_Oorder(B).
% 71.01/71.12  ** KEPT (pick-wt=10): 324 [] A=B| -hBOOL(hAPP(hAPP(c_fe_qual(C),A),B)).
% 71.01/71.12  17 back subsumes 16.
% 71.01/71.12    Following clause subsumed by 207 during input processing: 0 [copy,130,flip.1] c_List_Olist_ONil(A)!=c_List_Olist_OCons(B,C,A).
% 71.01/71.12    Following clause subsumed by 230 during input processing: 0 [copy,166,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 71.01/71.12    Following clause subsumed by 130 during input processing: 0 [copy,207,flip.1] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 71.01/71.12  209 back subsumes 160.
% 71.01/71.12    Following clause subsumed by 166 during input processing: 0 [copy,230,flip.1] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 71.01/71.12    Following clause subsumed by 248 during input processing: 0 [copy,246,flip.1] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 71.01/71.12    Following clause subsumed by 246 during input processing: 0 [copy,248,flip.1] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 71.01/71.12  ** KEPT (pick-wt=15): 344 [copy,302,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).
% 71.01/71.12  ** KEPT (pick-wt=14): 345 [copy,304,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).
% 71.01/71.12    Following clause subsumed by 307 during input processing: 0 [copy,306,flip.1] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 71.01/71.12    Following clause subsumed by 306 during input processing: 0 [copy,307,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 71.01/71.12    Following clause subsumed by 302 during input processing: 0 [copy,344,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).
% 71.01/71.12    Following clause subsumed by 304 during input processing: 0 [copy,345,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).
% 71.01/71.12  
% 71.01/71.12  ------------> process sos:
% 71.01/71.12  ** KEPT (pick-wt=3): 346 [] A=A.
% 71.01/71.12  ** KEPT (pick-wt=24): 347 [] hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)=c_List_Ofoldl(c_Lambda_OdB_OApp,A,c_List_Oappend(B,c_List_Olist_OCons(C,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 71.01/71.12    Following clause subsumed by 347 during input processing: 0 [] c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB)=c_List_Olist_ONil(tc_Lambda_OdB)|hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,C,A,tc_Lambda_OdB,tc_Lambda_OdB)),B)=c_List_Ofoldl(c_Lambda_OdB_OApp,C,c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 71.01/71.12  ** KEPT (pick-wt=11): 348 [] c_List_Orev(c_List_Oreplicate(A,B,C),C)=c_List_Oreplicate(A,B,C).
% 71.01/71.12  ---> New Demodulator: 349 [new_demod,348] c_List_Orev(c_List_Oreplicate(A,B,C),C)=c_List_Oreplicate(A,B,C).
% 71.01/71.12  ** KEPT (pick-wt=15): 350 [] c_List_Omap(A,c_List_Oreplicate(B,C,D),D,E)=c_List_Oreplicate(B,hAPP(A,C),E).
% 71.01/71.12  ** KEPT (pick-wt=7): 351 [] c_List_Orev(c_List_Orev(A,B),B)=A.
% 71.01/71.12  ---> New Demodulator: 352 [new_demod,351] c_List_Orev(c_List_Orev(A,B),B)=A.
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,352] A=A.
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,352] A=A.
% 71.01/71.12  ** KEPT (pick-wt=8): 353 [] c_List_Otake(A,c_List_Olist_ONil(B),B)=c_List_Olist_ONil(B).
% 71.01/71.12  ---> New Demodulator: 354 [new_demod,353] c_List_Otake(A,c_List_Olist_ONil(B),B)=c_List_Olist_ONil(B).
% 71.01/71.12  ** KEPT (pick-wt=5): 355 [] c_List_Olistsp(A,c_List_Olist_ONil(B),B).
% 71.01/71.12  ** KEPT (pick-wt=15): 356 [] c_List_Orev(c_List_Omap(A,B,C,D),D)=c_List_Omap(A,c_List_Orev(B,C),C,D).
% 71.01/71.12  ---> New Demodulator: 357 [new_demod,356] c_List_Orev(c_List_Omap(A,B,C,D),D)=c_List_Omap(A,c_List_Orev(B,C),C,D).
% 71.01/71.12  ** KEPT (pick-wt=7): 358 [] c_List_Orotate1(c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 71.01/71.12  ---> New Demodulator: 359 [new_demod,358] c_List_Orotate1(c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 71.01/71.12  ** KEPT (pick-wt=4): 360 [] hBOOL(hAPP(c_InductTermi_OIT,v_ua______)).
% 71.01/71.12  ** KEPT (pick-wt=17): 361 [] c_List_Otake(A,c_List_Omap(B,C,D,E),E)=c_List_Omap(B,c_List_Otake(A,C,D),D,E).
% 71.01/71.12  ---> New Demodulator: 362 [new_demod,361] c_List_Otake(A,c_List_Omap(B,C,D,E),E)=c_List_Omap(B,c_List_Otake(A,C,D),D,E).
% 71.01/71.12  ** KEPT (pick-wt=12): 363 [] c_List_Olast(c_List_Oreplicate(A,B,C),C)=B|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=4): 364 [] hBOOL(hAPP(c_InductTermi_OIT,v_u____)).
% 71.01/71.12  ** KEPT (pick-wt=7): 365 [] c_List_Orev(c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 71.01/71.12  ---> New Demodulator: 366 [new_demod,365] c_List_Orev(c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 71.01/71.12  ** KEPT (pick-wt=15): 367 [] c_List_Orev(c_List_Oappend(A,B,C),C)=c_List_Oappend(c_List_Orev(B,C),c_List_Orev(A,C),C).
% 71.01/71.12  ---> New Demodulator: 368 [new_demod,367] c_List_Orev(c_List_Oappend(A,B,C),C)=c_List_Oappend(c_List_Orev(B,C),c_List_Orev(A,C),C).
% 71.01/71.12  ** KEPT (pick-wt=9): 369 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=11): 370 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),C,B).
% 71.01/71.12  ** KEPT (pick-wt=15): 371 [] 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).
% 71.01/71.12  ** KEPT (pick-wt=11): 372 [] c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(A,B,C),C)=c_List_Olist_ONil(C).
% 71.01/71.12  ** KEPT (pick-wt=11): 373 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 71.01/71.12    Following clause subsumed by 373 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).
% 71.01/71.12    Following clause subsumed by 373 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 71.01/71.12  ** KEPT (pick-wt=21): 374 [] 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).
% 71.01/71.12  ** KEPT (pick-wt=7): 375 [] c_List_Obutlast(c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 71.01/71.12  ---> New Demodulator: 376 [new_demod,375] c_List_Obutlast(c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,366] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 71.01/71.12  ** KEPT (pick-wt=18): 377 [] c_List_Oappend(c_List_Obutlast(A,B),c_List_Olist_OCons(c_List_Olast(A,B),c_List_Olist_ONil(B),B),B)=A|A=c_List_Olist_ONil(B).
% 71.01/71.12  ** KEPT (pick-wt=8): 378 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Olist_ONil(B).
% 71.01/71.12  ** KEPT (pick-wt=8): 379 [] c_List_Olist_ONil(A)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),B,A).
% 71.01/71.12  ** KEPT (pick-wt=8): 380 [] c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Olist_ONil(B).
% 71.01/71.12  ** KEPT (pick-wt=13): 382 [copy,381,flip.1] c_List_Orev(c_List_Olist_OCons(A,c_List_Olist_ONil(B),B),B)=c_List_Olist_OCons(A,c_List_Olist_ONil(B),B).
% 71.01/71.12  ---> New Demodulator: 383 [new_demod,382] c_List_Orev(c_List_Olist_OCons(A,c_List_Olist_ONil(B),B),B)=c_List_Olist_OCons(A,c_List_Olist_ONil(B),B).
% 71.01/71.12  ** KEPT (pick-wt=14): 384 [] c_List_Olast(c_List_Olist_OCons(A,B,C),C)=c_List_Olast(B,C)|B=c_List_Olist_ONil(C).
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,383] c_List_Olist_OCons(A,c_List_Olist_ONil(B),B)=c_List_Olist_OCons(A,c_List_Olist_ONil(B),B).
% 71.01/71.12  ** KEPT (pick-wt=10): 385 [] c_List_Obutlast(c_List_Olist_OCons(A,c_List_Olist_ONil(B),B),B)=c_List_Olist_ONil(B).
% 71.01/71.12  ---> New Demodulator: 386 [new_demod,385] c_List_Obutlast(c_List_Olist_OCons(A,c_List_Olist_ONil(B),B),B)=c_List_Olist_ONil(B).
% 71.01/71.12  ** KEPT (pick-wt=9): 387 [] c_List_Olast(c_List_Olist_OCons(A,c_List_Olist_ONil(B),B),B)=A.
% 71.01/71.12  ---> New Demodulator: 388 [new_demod,387] c_List_Olast(c_List_Olist_OCons(A,c_List_Olist_ONil(B),B),B)=A.
% 71.01/71.12  ** KEPT (pick-wt=17): 389 [] c_List_Obutlast(c_List_Olist_OCons(A,B,C),C)=c_List_Olist_OCons(A,c_List_Obutlast(B,C),C)|B=c_List_Olist_ONil(C).
% 71.01/71.12  ** KEPT (pick-wt=21): 391 [copy,390,flip.1] c_List_Olist_OCons(A,c_List_Oappend(c_List_Oreplicate(B,A,C),D,C),C)=c_List_Oappend(c_List_Oreplicate(B,A,C),c_List_Olist_OCons(A,D,C),C).
% 71.01/71.12  ---> New Demodulator: 392 [new_demod,391] c_List_Olist_OCons(A,c_List_Oappend(c_List_Oreplicate(B,A,C),D,C),C)=c_List_Oappend(c_List_Oreplicate(B,A,C),c_List_Olist_OCons(A,D,C),C).
% 71.01/71.12  ** KEPT (pick-wt=11): 393 [] c_List_Obutlast(c_List_Oappend(A,c_List_Olist_ONil(B),B),B)=c_List_Obutlast(A,B).
% 71.01/71.12  ---> New Demodulator: 394 [new_demod,393] c_List_Obutlast(c_List_Oappend(A,c_List_Olist_ONil(B),B),B)=c_List_Obutlast(A,B).
% 71.01/71.12  ** KEPT (pick-wt=14): 395 [] c_List_Olast(c_List_Oappend(A,B,C),C)=c_List_Olast(B,C)|B=c_List_Olist_ONil(C).
% 71.01/71.12  ** KEPT (pick-wt=11): 396 [] c_List_Olast(c_List_Oappend(A,c_List_Olist_ONil(B),B),B)=c_List_Olast(A,B).
% 71.01/71.12  ---> New Demodulator: 397 [new_demod,396] c_List_Olast(c_List_Oappend(A,c_List_Olist_ONil(B),B),B)=c_List_Olast(A,B).
% 71.01/71.12  ** KEPT (pick-wt=17): 398 [] c_List_Obutlast(c_List_Oappend(A,B,C),C)=c_List_Oappend(A,c_List_Obutlast(B,C),C)|B=c_List_Olist_ONil(C).
% 71.01/71.12  ** KEPT (pick-wt=20): 399 [] 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).
% 71.01/71.12  ---> New Demodulator: 400 [new_demod,399] 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).
% 71.01/71.12  ** KEPT (pick-wt=10): 402 [copy,401,unit_del,23] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),A)=B.
% 71.01/71.12  ---> New Demodulator: 403 [new_demod,402] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),A)=B.
% 71.01/71.12  ** KEPT (pick-wt=18): 404 [] 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).
% 71.01/71.12  ** KEPT (pick-wt=12): 405 [] c_List_Olast(c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C),C)=B.
% 71.01/71.12  ---> New Demodulator: 406 [new_demod,405] c_List_Olast(c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C),C)=B.
% 71.01/71.12  ** KEPT (pick-wt=12): 407 [] c_List_Obutlast(c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C),C)=A.
% 71.01/71.12  ---> New Demodulator: 408 [new_demod,407] c_List_Obutlast(c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C),C)=A.
% 71.01/71.12  ** KEPT (pick-wt=17): 409 [] c_List_Orev(c_List_Olist_OCons(A,B,C),C)=c_List_Oappend(c_List_Orev(B,C),c_List_Olist_OCons(A,c_List_Olist_ONil(C),C),C).
% 71.01/71.12  ** KEPT (pick-wt=13): 411 [copy,410,demod,368,383,352] c_List_Oappend(c_List_Olist_OCons(A,c_List_Olist_ONil(B),B),C,B)=c_List_Olist_OCons(A,C,B).
% 71.01/71.12  ** KEPT (pick-wt=15): 412 [] c_List_Orotate1(c_List_Olist_OCons(A,B,C),C)=c_List_Oappend(B,c_List_Olist_OCons(A,c_List_Olist_ONil(C),C),C).
% 71.01/71.12  ** KEPT (pick-wt=19): 413 [] 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).
% 71.01/71.12  ** KEPT (pick-wt=14): 414 [] c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(A,B,C),C)=c_List_Olist_OCons(A,c_List_Olist_ONil(C),C).
% 71.01/71.12  ** KEPT (pick-wt=17): 415 [] 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).
% 71.01/71.12  ** KEPT (pick-wt=19): 416 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(A)),B)=c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)))|c_HOL_Oord__class_Oless(A,B,tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=4): 417 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 71.01/71.12  ** KEPT (pick-wt=4): 418 [] c_Type_Otyping(v_ea______,v_ua______,v_T____).
% 71.01/71.12  ** KEPT (pick-wt=11): 420 [copy,419,unit_del,23] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 71.01/71.12  ---> New Demodulator: 421 [new_demod,420] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 71.01/71.12  ** KEPT (pick-wt=14): 422 [] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 71.01/71.12  ** KEPT (pick-wt=9): 423 [] c_List_Omap(A,c_List_Olist_ONil(B),B,C)=c_List_Olist_ONil(C).
% 71.01/71.12  ** KEPT (pick-wt=7): 424 [] c_Type_Otyping(A,c_Lambda_OdB_OVar(B),hAPP(A,B)).
% 71.01/71.12  ** KEPT (pick-wt=15): 426 [copy,425,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).
% 71.01/71.12  ---> New Demodulator: 427 [new_demod,426] c_List_Olist_OCons(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,427] c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C)=c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C).
% 71.01/71.12  ** KEPT (pick-wt=19): 429 [copy,428,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).
% 71.01/71.12  ---> New Demodulator: 430 [new_demod,429] 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).
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,430] 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).
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,430] 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).
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,427] c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,427] c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 71.01/71.12  ** KEPT (pick-wt=13): 432 [copy,431,flip.1] c_List_Oappend(c_List_Olist_ONil(A),c_List_Olist_OCons(B,C,A),A)=c_List_Olist_OCons(B,C,A).
% 71.01/71.12  ---> New Demodulator: 433 [new_demod,432] c_List_Oappend(c_List_Olist_ONil(A),c_List_Olist_OCons(B,C,A),A)=c_List_Olist_OCons(B,C,A).
% 71.01/71.12  ** KEPT (pick-wt=9): 434 [] c_List_Olist_ONil(A)=c_List_Omap(B,c_List_Olist_ONil(C),C,A).
% 71.01/71.12  ** KEPT (pick-wt=9): 436 [copy,435,flip.1] c_List_Oappend(c_List_Olist_ONil(A),c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 71.01/71.12  ---> New Demodulator: 437 [new_demod,436] c_List_Oappend(c_List_Olist_ONil(A),c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 71.01/71.12  ** KEPT (pick-wt=9): 438 [] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(A,B),B)=c_Transitive__Closure_Ortranclp(A,B).
% 71.01/71.12  ---> New Demodulator: 439 [new_demod,438] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(A,B),B)=c_Transitive__Closure_Ortranclp(A,B).
% 71.01/71.12  ** KEPT (pick-wt=7): 440 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 71.01/71.12  ---> New Demodulator: 441 [new_demod,440] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 71.01/71.12  ** KEPT (pick-wt=11): 442 [] 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).
% 71.01/71.12  ---> New Demodulator: 443 [new_demod,442] 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).
% 71.01/71.12  ** KEPT (pick-wt=9): 445 [copy,444,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 71.01/71.12  ---> New Demodulator: 446 [new_demod,445] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 71.01/71.12  ** KEPT (pick-wt=9): 447 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 71.01/71.12  ---> New Demodulator: 448 [new_demod,447] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,446] A=A.
% 71.01/71.12  ** KEPT (pick-wt=11): 449 [] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 71.01/71.12  ** KEPT (pick-wt=23): 450 [] 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)).
% 71.01/71.12  ---> New Demodulator: 451 [new_demod,450] 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)).
% 71.01/71.12  ** KEPT (pick-wt=23): 452 [] 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)).
% 71.01/71.12  ** KEPT (pick-wt=8): 453 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),C)).
% 71.01/71.12    Following clause subsumed by 453 during input processing: 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),C)).
% 71.01/71.12  ** KEPT (pick-wt=7): 454 [] c_List_Oappend(A,c_List_Olist_ONil(B),B)=A.
% 71.01/71.12  ---> New Demodulator: 455 [new_demod,454] c_List_Oappend(A,c_List_Olist_ONil(B),B)=A.
% 71.01/71.12  ** KEPT (pick-wt=7): 457 [copy,456,flip.1] c_List_Oappend(c_List_Olist_ONil(A),B,A)=B.
% 71.01/71.12  ---> New Demodulator: 458 [new_demod,457] c_List_Oappend(c_List_Olist_ONil(A),B,A)=B.
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,455] A=A.
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,458] B=B.
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,458] A=A.
% 71.01/71.12  ** KEPT (pick-wt=17): 460 [copy,459,flip.1] c_Lambda_OdB_OAbs(c_Lambda_Osubstn(A,B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=c_Lambda_Osubstn(c_Lambda_OdB_OAbs(A),B,C).
% 71.01/71.12  ---> New Demodulator: 461 [new_demod,460] c_Lambda_OdB_OAbs(c_Lambda_Osubstn(A,B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=c_Lambda_Osubstn(c_Lambda_OdB_OAbs(A),B,C).
% 71.01/71.12  ** KEPT (pick-wt=13): 462 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 71.01/71.12  ** KEPT (pick-wt=5): 463 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(A))).
% 71.01/71.12  ** KEPT (pick-wt=9): 464 [] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 71.01/71.12  ---> New Demodulator: 465 [new_demod,464] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 71.01/71.12  ** KEPT (pick-wt=8): 466 [] c_Predicate_Oconversep(c_fe_qual(A),A,A)=c_fe_qual(A).
% 71.01/71.12  ---> New Demodulator: 467 [new_demod,466] c_Predicate_Oconversep(c_fe_qual(A),A,A)=c_fe_qual(A).
% 71.01/71.12  ** KEPT (pick-wt=11): 468 [] c_Lambda_OdB_OdB__rec(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 71.01/71.12  ** KEPT (pick-wt=17): 470 [copy,469,flip.1] c_Lambda_OdB_OAbs(c_Lambda_Oliftn(A,B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=c_Lambda_Oliftn(A,c_Lambda_OdB_OAbs(B),C).
% 71.01/71.12  ---> New Demodulator: 471 [new_demod,470] c_Lambda_OdB_OAbs(c_Lambda_Oliftn(A,B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=c_Lambda_Oliftn(A,c_Lambda_OdB_OAbs(B),C).
% 71.01/71.12  ** KEPT (pick-wt=21): 473 [copy,472,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).
% 71.01/71.12  ---> New Demodulator: 474 [new_demod,473] 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).
% 71.01/71.12  ** KEPT (pick-wt=30): 475 [] 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).
% 71.01/71.12  ---> New Demodulator: 476 [new_demod,475] 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).
% 71.01/71.12  ** KEPT (pick-wt=9): 477 [] c_Predicate_Oconversep(c_Predicate_Oconversep(A,B,C),C,B)=A.
% 71.01/71.12  ---> New Demodulator: 478 [new_demod,477] c_Predicate_Oconversep(c_Predicate_Oconversep(A,B,C),C,B)=A.
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,458] c_List_Olist_OCons(B,C,A)=c_List_Olist_OCons(B,C,A).
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,455] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 71.01/71.12  ** KEPT (pick-wt=19): 480 [copy,479,flip.1] c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(A)),B).
% 71.01/71.12  ---> New Demodulator: 481 [new_demod,480] c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(A)),B).
% 71.01/71.12  ** KEPT (pick-wt=15): 482 [] c_List_Oappend(c_List_Oappend(A,B,C),D,C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 71.01/71.12  ---> New Demodulator: 483 [new_demod,482] c_List_Oappend(c_List_Oappend(A,B,C),D,C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,483] c_List_Oappend(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(A,c_List_Oappend(B,C,D),D).
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,483] c_List_Oappend(A,c_List_Oappend(B,D,C),C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,483] c_List_Oappend(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(A,c_List_Oappend(B,C,D),D).
% 71.01/71.12  ** KEPT (pick-wt=23): 484 [] 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)).
% 71.01/71.12  ** KEPT (pick-wt=16): 485 [] c_Lambda_OdB_OdB__case(A,B,C,hAPP(hAPP(c_Lambda_OdB_OApp,D),E),F)=hAPP(hAPP(B,D),E).
% 71.01/71.12  ** KEPT (pick-wt=30): 487 [copy,486,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).
% 71.01/71.12  ---> New Demodulator: 488 [new_demod,487] 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).
% 71.01/71.12  ** KEPT (pick-wt=20): 490 [copy,489,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).
% 71.01/71.12  ---> New Demodulator: 491 [new_demod,490] 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).
% 71.01/71.12  ** KEPT (pick-wt=20): 493 [copy,492,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).
% 71.01/71.12  ---> New Demodulator: 494 [new_demod,493] 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).
% 71.01/71.12  ** KEPT (pick-wt=16): 496 [copy,495,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).
% 71.01/71.12  ---> New Demodulator: 497 [new_demod,496] 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).
% 71.01/71.12  ** KEPT (pick-wt=28): 499 [copy,498,flip.1] c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,A),hAPP(hAPP(c_Lambda_Olift,B),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(A)),B),C).
% 71.01/71.12  ---> New Demodulator: 500 [new_demod,499] c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,A),hAPP(hAPP(c_Lambda_Olift,B),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(A)),B),C).
% 71.01/71.12  ** KEPT (pick-wt=18): 501 [] 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)).
% 71.01/71.12  ** KEPT (pick-wt=11): 502 [] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(C,D).
% 71.01/71.12  ** KEPT (pick-wt=11): 504 [copy,503,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).
% 71.01/71.12  ---> New Demodulator: 505 [new_demod,504] 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).
% 71.01/71.12  ** KEPT (pick-wt=10): 507 [copy,506,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.
% 71.01/71.12  ---> New Demodulator: 508 [new_demod,507] 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.
% 71.01/71.12  ** KEPT (pick-wt=9): 509 [] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 71.01/71.12  ---> New Demodulator: 510 [new_demod,509] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 71.01/71.12  ** KEPT (pick-wt=20): 511 [] 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).
% 71.01/71.12  ** KEPT (pick-wt=21): 512 [] 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).
% 71.01/71.12  ** KEPT (pick-wt=41): 513 [] 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).
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,403] B=B.
% 71.01/71.12  ** KEPT (pick-wt=13): 514 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),B)),C),B)=A.
% 71.01/71.12  ---> New Demodulator: 515 [new_demod,514] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),B)),C),B)=A.
% 71.01/71.12  ** KEPT (pick-wt=18): 516 [] c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,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_Ha______).
% 71.01/71.12  ** KEPT (pick-wt=18): 517 [] 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____).
% 71.01/71.12  ** KEPT (pick-wt=4): 518 [] hBOOL(hAPP(c_InductTermi_OIT,v_a____)).
% 71.01/71.12  ** KEPT (pick-wt=14): 520 [copy,519,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)).
% 71.01/71.12  ---> New Demodulator: 521 [new_demod,520] 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)).
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,510] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)=hAPP(hAPP(c_Lambda_OdB_OApp,A),B).
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,510] c_Lambda_OdB_OAbs(A)=c_Lambda_OdB_OAbs(A).
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [demod,510] c_Lambda_OdB_OAbs(A)=c_Lambda_OdB_OAbs(A).
% 71.01/71.12  ** KEPT (pick-wt=13): 523 [copy,522,demod,521] 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))).
% 71.01/71.12  ** KEPT (pick-wt=29): 524 [] 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)).
% 71.01/71.12  ** KEPT (pick-wt=15): 526 [copy,525,demod,521] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B)),c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)))).
% 71.01/71.12  ** KEPT (pick-wt=2): 527 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 528 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 529 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 530 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 531 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 532 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 533 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 534 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 535 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 536 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 537 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 538 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 539 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 540 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 541 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 542 [] class_OrderedGroup_Omonoid__mult(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 543 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 544 [] class_Nat_Osemiring__char__0(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 545 [] class_Orderings_Opreorder(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 546 [] class_Orderings_Olinorder(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 547 [] class_Orderings_Oorder(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 548 [] class_Power_Opower(tc_nat).
% 71.01/71.12  ** KEPT (pick-wt=2): 549 [] class_Orderings_Opreorder(tc_bool).
% 71.01/71.12  ** KEPT (pick-wt=2): 550 [] class_Orderings_Oorder(tc_bool).
% 71.01/71.12  ** KEPT (pick-wt=7): 551 [] hBOOL(hAPP(hAPP(c_fe_qual(A),B),B)).
% 71.01/71.12    Following clause subsumed by 346 during input processing: 0 [copy,346,flip.1] A=A.
% 71.01/71.12  346 back subsumes 342.
% 71.01/71.12  346 back subsumes 327.
% 71.01/71.12  346 back subsumes 326.
% 71.01/71.12  ** KEPT (pick-wt=24): 552 [copy,347,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,A,c_List_Oappend(B,c_List_Olist_OCons(C,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C).
% 71.01/71.13  >>>> Starting back demodulation with 349.
% 71.01/71.13  ** KEPT (pick-wt=15): 553 [copy,350,flip.1] c_List_Oreplicate(A,hAPP(B,C),D)=c_List_Omap(B,c_List_Oreplicate(A,C,E),E,D).
% 71.01/71.13  >>>> Starting back demodulation with 352.
% 71.01/71.13  >>>> Starting back demodulation with 354.
% 71.01/71.13  >>>> Starting back demodulation with 357.
% 71.01/71.13  >>>> Starting back demodulation with 359.
% 71.01/71.13  >>>> Starting back demodulation with 362.
% 71.01/71.13  >>>> Starting back demodulation with 366.
% 71.01/71.13  >>>> Starting back demodulation with 368.
% 71.01/71.13    Following clause subsumed by 370 during input processing: 0 [copy,370,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).
% 71.01/71.13  ** KEPT (pick-wt=11): 554 [copy,372,flip.1] c_List_Olist_ONil(A)=c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(B,C,A),A).
% 71.01/71.13    Following clause subsumed by 374 during input processing: 0 [copy,374,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).
% 71.01/71.13  >>>> Starting back demodulation with 376.
% 71.01/71.13    Following clause subsumed by 379 during input processing: 0 [copy,378,flip.1] c_List_Olist_ONil(A)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),B,A).
% 71.01/71.13    Following clause subsumed by 378 during input processing: 0 [copy,379,flip.1] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Olist_ONil(B).
% 71.01/71.13  ** KEPT (pick-wt=8): 555 [copy,380,flip.1] c_List_Olist_ONil(A)=c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),B,A).
% 71.01/71.13  380 back subsumes 372.
% 71.01/71.13  >>>> Starting back demodulation with 383.
% 71.01/71.13  >>>> Starting back demodulation with 386.
% 71.01/71.13  >>>> Starting back demodulation with 388.
% 71.01/71.13  >>>> Starting back demodulation with 392.
% 71.01/71.13  >>>> Starting back demodulation with 394.
% 71.01/71.13  >>>> Starting back demodulation with 397.
% 71.01/71.13  >>>> Starting back demodulation with 400.
% 71.01/71.13  >>>> Starting back demodulation with 403.
% 71.01/71.13  >>>> Starting back demodulation with 406.
% 71.01/71.13  >>>> Starting back demodulation with 408.
% 71.01/71.13  ** KEPT (pick-wt=17): 556 [copy,409,flip.1] c_List_Oappend(c_List_Orev(A,B),c_List_Olist_OCons(C,c_List_Olist_ONil(B),B),B)=c_List_Orev(c_List_Olist_OCons(C,A,B),B).
% 71.01/71.13  ** KEPT (pick-wt=13): 557 [copy,411,flip.1] c_List_Olist_OCons(A,B,C)=c_List_Oappend(c_List_Olist_OCons(A,c_List_Olist_ONil(C),C),B,C).
% 71.01/71.13  ** KEPT (pick-wt=15): 558 [copy,412,flip.1] c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C)=c_List_Orotate1(c_List_Olist_OCons(B,A,C),C).
% 71.01/71.13  ** KEPT (pick-wt=19): 559 [copy,413,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).
% 71.01/71.13  ** KEPT (pick-wt=14): 560 [copy,414,flip.1] c_List_Olist_OCons(A,c_List_Olist_ONil(B),B)=c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(A,C,B),B).
% 71.01/71.13  >>>> Starting back demodulation with 421.
% 71.01/71.13  ** KEPT (pick-wt=14): 561 [copy,422,flip.1] hAPP(hAPP(A,B),C)=hAPP(c_COMBC(A,C,D,E,F),B).
% 71.01/71.13    Following clause subsumed by 434 during input processing: 0 [copy,423,flip.1] c_List_Olist_ONil(A)=c_List_Omap(B,c_List_Olist_ONil(C),C,A).
% 71.01/71.13  >>>> Starting back demodulation with 427.
% 71.01/71.13      >> back demodulating 391 with 427.
% 71.01/71.13  >>>> Starting back demodulation with 430.
% 71.01/71.13  >>>> Starting back demodulation with 433.
% 71.01/71.13    Following clause subsumed by 423 during input processing: 0 [copy,434,flip.1] c_List_Omap(A,c_List_Olist_ONil(B),B,C)=c_List_Olist_ONil(C).
% 71.01/71.13  >>>> Starting back demodulation with 437.
% 71.01/71.13  >>>> Starting back demodulation with 439.
% 71.01/71.13  >>>> Starting back demodulation with 441.
% 71.01/71.13  >>>> Starting back demodulation with 443.
% 71.01/71.13  >>>> Starting back demodulation with 446.
% 71.01/71.13      >> back demodulating 442 with 446.
% 71.01/71.13  >>>> Starting back demodulation with 448.
% 71.01/71.13  ** KEPT (pick-wt=11): 563 [copy,449,flip.1] hAPP(A,B)=c_Lambda_OdB_OdB__case(A,C,D,c_Lambda_OdB_OVar(B),E).
% 71.01/71.13  >>>> Starting back demodulation with 451.
% 71.01/71.13    Following clause subsumed by 452 during input processing: 0 [copy,452,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)).
% 71.01/71.13  >>>> Starting back demodulation with 455.
% 71.01/71.13      >> back demodulating 436 with 455.
% 71.01/71.13      >> back demodulating 396 with 455.
% 71.01/71.13      >> back demodulating 393 with 455.
% 71.01/71.13  >>>> Starting back demodulation with 458.
% 71.01/71.13      >> back demodulating 432 with 458.
% 71.01/71.13  >>>> Starting back demodulation with 461.
% 71.01/71.13    Following clause subsumed by 462 during input processing: 0 [copy,462,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 71.01/71.13  >>>> Starting back demodulation with 465.
% 71.01/71.13  >>>> Starting back demodulation with 467.
% 71.01/71.13  ** KEPT (pick-wt=11): 564 [copy,468,flip.1] hAPP(A,B)=c_Lambda_OdB_OdB__rec(A,C,D,c_Lambda_OdB_OVar(B),E).
% 71.01/71.13  >>>> Starting back demodulation with 471.
% 71.01/71.13  >>>> Starting back demodulation with 474.
% 71.01/71.13  >>>> Starting back demodulation with 476.
% 71.01/71.13  >>>> Starting back demodulation with 478.
% 71.01/71.13  >>>> Starting back demodulation with 481.
% 71.01/71.13  >>>> Starting back demodulation with 483.
% 71.01/71.13  ** KEPT (pick-wt=23): 565 [copy,484,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).
% 71.01/71.13  ** KEPT (pick-wt=16): 566 [copy,485,flip.1] hAPP(hAPP(A,B),C)=c_Lambda_OdB_OdB__case(D,A,E,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),F).
% 71.01/71.13  >>>> Starting back demodulation with 488.
% 71.01/71.13  >>>> Starting back demodulation with 491.
% 71.01/71.13  >>>> Starting back demodulation with 494.
% 71.01/71.13  >>>> Starting back demodulation with 497.
% 71.01/71.13  >>>> Starting back demodulation with 500.
% 71.01/71.13  ** KEPT (pick-wt=18): 567 [copy,501,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).
% 71.01/71.13  ** KEPT (pick-wt=11): 568 [copy,502,flip.1] hAPP(A,B)=c_Lambda_OdB_OdB__case(C,D,A,c_Lambda_OdB_OAbs(B),E).
% 71.01/71.13  >>>> Starting back demodulation with 505.
% 71.01/71.13  >>>> Starting back demodulation with 508.
% 71.01/71.13  >>>> Starting back demodulation with 510.
% 71.01/71.13      >> back demodulating 504 with 510.
% 71.01/71.13      >> back demodulating 292 with 510.
% 71.01/71.13  ** KEPT (pick-wt=20): 569 [copy,511,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).
% 71.01/71.13  ** KEPT (pick-wt=21): 570 [copy,512,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).
% 71.01/71.13  ** KEPT (pick-wt=41): 571 [copy,513,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).
% 71.01/71.13  >>>> Starting back demodulation with 515.
% 71.01/71.13  >>>> Starting back demodulation with 521.
% 71.01/71.13      >> back demodulating 321 with 521.
% 71.01/71.13      >> back demodulating 305 with 521.
% 71.01/71.13      >> back demodulating 298 with 521.
% 71.01/71.13      >> back demodulating 297 with 521.
% 71.01/71.13      >> back demodulating 271 with 521.
% 71.01/71.13      >> back demodulating 269 with 521.
% 71.01/71.13      >> back demodulating 267 with 521.
% 71.01/71.13      >> back demodulating 265 with 521.
% 71.01/71.13      >> back demodulating 245 with 521.
% 71.01/71.13      >> back demodulating 243 with 521.
% 71.01/71.13      >> back demodulating 143 with 521.
% 71.01/71.13      >> back demodulating 141 with 521.
% 71.01/71.13  ** KEPT (pick-wt=29): 584 [copy,524,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).
% 71.01/71.13    Following clause subsumed by 347 during input processing: 0 [copy,552,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)=c_List_Ofoldl(c_Lambda_OdB_OApp,A,c_List_Oappend(B,c_List_Olist_OCons(C,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 71.01/71.13    Following clause subsumed by 350 during input processing: 0 [copy,553,flip.1] c_List_Omap(A,c_List_Oreplicate(B,C,D),D,E)=c_List_Oreplicate(B,hAPP(A,C),E).
% 71.01/71.13    Following clause subsumed by 380 during input processing: 0 [copy,554,flip.1] c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(A,B,C),C)=c_List_Olist_ONil(C).
% 72.04/72.12    Following clause subsumed by 380 during input processing: 0 [copy,555,flip.1] c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Olist_ONil(B).
% 72.04/72.12  555 back subsumes 554.
% 72.04/72.12    Following clause subsumed by 409 during input processing: 0 [copy,556,flip.1] c_List_Orev(c_List_Olist_OCons(A,B,C),C)=c_List_Oappend(c_List_Orev(B,C),c_List_Olist_OCons(A,c_List_Olist_ONil(C),C),C).
% 72.04/72.12    Following clause subsumed by 411 during input processing: 0 [copy,557,flip.1] c_List_Oappend(c_List_Olist_OCons(A,c_List_Olist_ONil(B),B),C,B)=c_List_Olist_OCons(A,C,B).
% 72.04/72.12    Following clause subsumed by 412 during input processing: 0 [copy,558,flip.1] c_List_Orotate1(c_List_Olist_OCons(A,B,C),C)=c_List_Oappend(B,c_List_Olist_OCons(A,c_List_Olist_ONil(C),C),C).
% 72.04/72.12    Following clause subsumed by 413 during input processing: 0 [copy,559,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).
% 72.04/72.12    Following clause subsumed by 414 during input processing: 0 [copy,560,flip.1] c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(A,B,C),C)=c_List_Olist_OCons(A,c_List_Olist_ONil(C),C).
% 72.04/72.12    Following clause subsumed by 422 during input processing: 0 [copy,561,flip.1] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 72.04/72.12  ** KEPT (pick-wt=21): 585 [copy,562,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).
% 72.04/72.12    Following clause subsumed by 449 during input processing: 0 [copy,563,flip.1] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 72.04/72.12    Following clause subsumed by 468 during input processing: 0 [copy,564,flip.1] c_Lambda_OdB_OdB__rec(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 72.04/72.12    Following clause subsumed by 484 during input processing: 0 [copy,565,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)).
% 72.04/72.12    Following clause subsumed by 485 during input processing: 0 [copy,566,flip.1] c_Lambda_OdB_OdB__case(A,B,C,hAPP(hAPP(c_Lambda_OdB_OApp,D),E),F)=hAPP(hAPP(B,D),E).
% 72.04/72.12    Following clause subsumed by 501 during input processing: 0 [copy,567,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)).
% 72.04/72.12    Following clause subsumed by 502 during input processing: 0 [copy,568,flip.1] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(C,D).
% 72.04/72.12    Following clause subsumed by 511 during input processing: 0 [copy,569,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).
% 72.04/72.12    Following clause subsumed by 512 during input processing: 0 [copy,570,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).
% 72.04/72.12    Following clause subsumed by 513 during input processing: 0 [copy,571,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).
% 72.04/72.12    Following clause subsumed by 524 during input processing: 0 [copy,584,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)).
% 72.04/72.12    Following clause subsumed by 562 during input processing: 0 [copy,585,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).
% 72.04/72.12  
% 72.04/72.12  ======= end of input processing =======
% 72.04/72.12  
% 72.04/72.12  =========== start of search ===========
% 72.04/72.12  
% 72.04/72.12  
% 72.04/72.12  Resetting weight limit to 2.
% 72.04/72.12  
% 72.04/72.12  
% 72.04/72.12  Resetting weight limit to 2.
% 72.04/72.12  
% 72.04/72.12  sos_size=154
% 72.04/72.12  
% 72.04/72.12  Search stopped because sos empty.
% 72.04/72.12  
% 72.04/72.12  
% 72.04/72.12  Search stopped because sos empty.
% 72.04/72.12  
% 72.04/72.12  ============ end of search ============
% 72.04/72.12  
% 72.04/72.12  -------------- statistics -------------
% 72.04/72.12  clauses given                155
% 72.04/72.12  clauses generated         102460
% 72.04/72.12  clauses kept                 472
% 72.04/72.12  clauses forward subsumed     106
% 72.04/72.12  clauses back subsumed          7
% 72.04/72.12  Kbytes malloced            11718
% 72.04/72.12  
% 72.04/72.12  ----------- times (seconds) -----------
% 72.04/72.12  user CPU time          1.06          (0 hr, 0 min, 1 sec)
% 72.04/72.12  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 72.04/72.12  wall-clock time       72             (0 hr, 1 min, 12 sec)
% 72.04/72.12  
% 72.04/72.12  Process 3949 finished Wed Jul 27 09:20:50 2022
% 72.04/72.12  Otter interrupted
% 72.04/72.12  PROOF NOT FOUND
%------------------------------------------------------------------------------