TSTP Solution File: LCL762-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL762-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 13:05:19 EDT 2022
% Result : Unsatisfiable 48.27s 48.34s
% Output : Refutation 48.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 5 ( 5 unt; 0 nHn; 4 RR)
% Number of literals : 5 ( 1 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-5 aty)
% Number of variables : 4 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(289,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_n))),
file('LCL762-1.p',unknown),
[] ).
cnf(478,axiom,
c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C) = B,
file('LCL762-1.p',unknown),
[] ).
cnf(479,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('LCL762-1.p',unknown),
[] ).
cnf(480,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_n))),
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[479]),478]),
[iquote('copy,479,demod,478')] ).
cnf(481,plain,
$false,
inference(binary,[status(thm)],[480,289]),
[iquote('binary,480.1,289.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL762-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 09:09:40 EDT 2022
% 0.14/0.34 % CPUTime :
% 48.27/48.32 ----- Otter 3.3f, August 2004 -----
% 48.27/48.32 The process was started by sandbox on n011.cluster.edu,
% 48.27/48.32 Wed Jul 27 09:09:40 2022
% 48.27/48.32 The command was "./otter". The process ID is 28085.
% 48.27/48.32
% 48.27/48.32 set(prolog_style_variables).
% 48.27/48.32 set(auto).
% 48.27/48.32 dependent: set(auto1).
% 48.27/48.32 dependent: set(process_input).
% 48.27/48.32 dependent: clear(print_kept).
% 48.27/48.32 dependent: clear(print_new_demod).
% 48.27/48.32 dependent: clear(print_back_demod).
% 48.27/48.32 dependent: clear(print_back_sub).
% 48.27/48.32 dependent: set(control_memory).
% 48.27/48.32 dependent: assign(max_mem, 12000).
% 48.27/48.32 dependent: assign(pick_given_ratio, 4).
% 48.27/48.32 dependent: assign(stats_level, 1).
% 48.27/48.32 dependent: assign(max_seconds, 10800).
% 48.27/48.32 clear(print_given).
% 48.27/48.32
% 48.27/48.32 list(usable).
% 48.27/48.32 0 [] A=A.
% 48.27/48.32 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_a,V_xs,T_a,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a)).
% 48.27/48.32 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_xs,T_a,T_a)=c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a).
% 48.27/48.32 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).
% 48.27/48.32 0 [] c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a)=V_a.
% 48.27/48.32 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)),tc_nat).
% 48.27/48.32 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).
% 48.27/48.32 0 [] c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 48.27/48.32 0 [] c_Nat_Osize__class_Osize(c_List_Olist__update(V_xs,V_i,V_x,T_a),tc_List_Olist(T_a))=c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)).
% 48.27/48.32 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).
% 48.27/48.32 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat)|V_xs=c_List_Olist_ONil(T_a).
% 48.27/48.32 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)).
% 48.27/48.32 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)).
% 48.27/48.32 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)).
% 48.27/48.32 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)).
% 48.27/48.32 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)).
% 48.27/48.32 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)).
% 48.27/48.32 0 [] -c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 48.27/48.32 0 [] -c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 0 [] c_List_Oreplicate(V_m,V_x,T_a)!=c_List_Oreplicate(V_n,V_y,T_a)|V_m=V_n.
% 48.27/48.32 0 [] c_Wellfounded_Oaccp(V_r,V_b,T_a)| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a))| -c_Wellfounded_Oaccp(V_r,V_a,T_a).
% 48.27/48.32 0 [] c_Wellfounded_Oaccp(V_r,V_b,T_a)| -c_Wellfounded_Oaccp(V_r,V_a,T_a)| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a)).
% 48.27/48.32 0 [] c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 48.27/48.32 0 [] c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 48.27/48.32 0 [] hBOOL(hAPP(c_InductTermi_OIT,V_r))| -c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_r,tc_Lambda_OdB).
% 48.27/48.32 0 [] c_Nat_Osize__class_Osize(c_List_Oremdups(V_xs,T_a),tc_List_Olist(T_a))!=c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a))|c_List_Oremdups(V_xs,T_a)=V_xs.
% 48.27/48.32 0 [] c_List_Oremdups(V_xs,T_a)!=V_xs|c_Nat_Osize__class_Osize(c_List_Oremdups(V_xs,T_a),tc_List_Olist(T_a))=c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)).
% 48.27/48.32 0 [] c_Nat_Osize__class_Osize(c_List_Omap(V_f,V_xs,T_b,T_a),tc_List_Olist(T_a))=c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_b)).
% 48.27/48.32 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).
% 48.27/48.32 0 [] c_List_Orev(c_List_Oreplicate(V_n,V_x,T_a),T_a)=c_List_Oreplicate(V_n,V_x,T_a).
% 48.27/48.32 0 [] c_List_Ofoldr(V_f,c_List_Oappend(V_xs,V_ys,T_b),V_a,T_b,T_a)=c_List_Ofoldr(V_f,V_xs,c_List_Ofoldr(V_f,V_ys,V_a,T_b,T_a),T_b,T_a).
% 48.27/48.32 0 [] c_List_Ofilter(V_P,c_List_Oreplicate(V_n,V_x,T_a),T_a)=c_List_Oreplicate(V_n,V_x,T_a)| -hBOOL(hAPP(V_P,V_x)).
% 48.27/48.32 0 [] c_List_Omap(V_f,V_xs,T_b,T_a)!=c_List_Omap(V_f,V_ys,T_b,T_a)|c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_b))=c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b)).
% 48.27/48.32 0 [] c_Predicate_Oconversep(c_fe_qual(T_a),T_a,T_a)=c_fe_qual(T_a).
% 48.27/48.32 0 [] c_List_Olist__update(c_List_Oappend(V_xs,V_ys,T_a),V_n,V_x,T_a)=c_List_Oappend(c_List_Olist__update(V_xs,V_n,V_x,T_a),V_ys,T_a)| -c_HOL_Oord__class_Oless(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat).
% 48.27/48.32 0 [] c_List_Olist__update(c_List_Oappend(V_xs,V_ys,T_a),V_i,V_x,T_a)=c_List_Oappend(c_List_Olist__update(V_xs,V_i,V_x,T_a),V_ys,T_a)| -c_HOL_Oord__class_Oless(V_i,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat).
% 48.27/48.32 0 [] c_Nat_Osize__class_Osize(c_List_Orotate(V_n,V_xs,T_a),tc_List_Olist(T_a))=c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)).
% 48.27/48.32 0 [] -c_HOL_Oord__class_Oless(V_x,V_x,tc_nat).
% 48.27/48.32 0 [] -c_HOL_Oord__class_Oless(V_n,V_n,tc_nat).
% 48.27/48.32 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 48.27/48.32 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 48.27/48.32 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 48.27/48.32 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.
% 48.27/48.32 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).
% 48.27/48.32 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.
% 48.27/48.32 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).
% 48.27/48.32 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.
% 48.27/48.32 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.
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 48.27/48.32 0 [] c_Nat_Osize__class_Osize(c_List_Oreplicate(V_n,V_x,T_a),tc_List_Olist(T_a))=V_n.
% 48.27/48.32 0 [] c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a)=hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a)).
% 48.27/48.32 0 [] c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a)=V_r.
% 48.27/48.32 0 [] hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2)!=hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H)|V_type2=V_type2_H.
% 48.27/48.32 0 [] hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2)!=hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H)|V_type1=V_type1_H.
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 0 [] c_Nat_Osize__class_Osize(c_List_Orev(V_xs,T_a),tc_List_Olist(T_a))=c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 0 [] c_Wellfounded_Oaccp(V_r,V_y,T_a)| -hBOOL(hAPP(hAPP(V_r,V_y),V_a))| -c_Wellfounded_Oaccp(V_r,V_a,T_a).
% 48.27/48.32 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).
% 48.27/48.32 0 [] c_Wellfounded_Oaccp(V_r,V_a,T_a)| -hBOOL(hAPP(hAPP(V_r,V_a),V_b))| -c_Wellfounded_Oaccp(V_r,V_b,T_a).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 0 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a)=c_List_Olist_ONil(T_a).
% 48.27/48.32 0 [] c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a))=c_HOL_Ozero__class_Ozero(tc_nat).
% 48.27/48.32 0 [] c_List_Olist_ONil(T_a)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 0 [] c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a))!=c_HOL_Ozero__class_Ozero(tc_nat)|V_xs=c_List_Olist_ONil(T_a).
% 48.27/48.32 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).
% 48.27/48.32 0 [] -class_OrderedGroup_Oab__semigroup__add(T_a)|c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,V_a,T_a,T_a)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_a,V_xs,T_a,T_a).
% 48.27/48.32 0 [] c_List_Ofilter(V_P,c_List_Oreplicate(V_n,V_x,T_a),T_a)=c_List_Olist_ONil(T_a)|hBOOL(hAPP(V_P,V_x)).
% 48.27/48.32 0 [] c_Type_Otyping(V_env,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_U)| -c_Type_Otyping(V_env,V_t,V_T)| -c_Type_Otyping(V_env,V_s,hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U)).
% 48.27/48.32 0 [] c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)|c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x)=V_s.
% 48.27/48.32 0 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(V_i),V_s,V_k)=c_Lambda_OdB_OVar(V_i)|V_i=V_k|c_HOL_Oord__class_Oless(V_k,V_i,tc_nat).
% 48.27/48.32 0 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(V_j),V_u,V_i)=c_Lambda_OdB_OVar(V_j)| -c_HOL_Oord__class_Oless(V_j,V_i,tc_nat).
% 48.27/48.32 0 [] c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T)| -c_Type_Otypings(V_e,V_ts,V_Ts)| -c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,V_T,tc_Type_Otype,tc_Type_Otype)).
% 48.27/48.32 0 [] c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a))!=c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))|c_Map_Omap__upds(V_m,c_List_Oappend(V_xs,V_zs,T_a),V_ys,T_a,T_b)=c_Map_Omap__upds(V_m,V_xs,V_ys,T_a,T_b).
% 48.27/48.32 0 [] c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a))!=c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))|c_Map_Omap__upds(V_m,V_xs,c_List_Oappend(V_ys,V_zs,T_b),T_a,T_b)=c_Map_Omap__upds(V_m,V_xs,V_ys,T_a,T_b).
% 48.27/48.32 0 [] c_Lambda_Olift(c_Lambda_OdB_OVar(V_i),V_k)=c_Lambda_OdB_OVar(V_i)| -c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 0 [] -hBOOL(hAPP(V_P,V_x))|hBOOL(hAPP(V_P,c_List_Osko__List__XCons__e_q__filter__iff__1__3(V_P,V_xa,T_a)))|c_List_Olist_OCons(V_x,c_List_Ofilter(V_P,V_xb,T_a),T_a)=c_List_Ofilter(V_P,c_List_Oappend(V_xa,c_List_Olist_OCons(V_x,V_xb,T_a),T_a),T_a).
% 48.27/48.32 0 [] -hBOOL(hAPP(V_P,V_x))|hBOOL(hAPP(V_P,c_List_Osko__List__Xfilter__e_q__Cons__iff__1__3(V_P,V_xa,T_a)))|c_List_Ofilter(V_P,c_List_Oappend(V_xa,c_List_Olist_OCons(V_x,V_xb,T_a),T_a),T_a)=c_List_Olist_OCons(V_x,c_List_Ofilter(V_P,V_xb,T_a),T_a).
% 48.27/48.32 0 [] -c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(V_r,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)| -c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_s,tc_Lambda_OdB)|c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r)),V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB).
% 48.27/48.32 0 [] c_List_Olist__update(c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,V_ys,T_a),T_a),c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_y,T_a)=c_List_Oappend(V_xs,c_List_Olist_OCons(V_y,V_ys,T_a),T_a).
% 48.27/48.32 0 [] c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T,V_e,V_i,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 48.27/48.32 0 [] V_U=c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(V_T,V_U,V_e,V_us),V_T,tc_Type_Otype,tc_Type_Otype)| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_U)| -c_Type_Otypings(V_e,V_ts,V_Ts)| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_us,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 48.27/48.32 0 [] hBOOL(hAPP(V_P,V_list))| -hBOOL(hAPP(V_P,c_List_Olist_OCons(v_sko__List__Xconcat__Xinduct__1(V_P),v_sko__List__Xconcat__Xinduct__2(V_P),t_a)))| -hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))).
% 48.27/48.32 0 [] hBOOL(hAPP(V_P,V_list))| -hBOOL(hAPP(V_P,c_List_Olist_OCons(v_sko__List__Xtake__Xinduct__1(V_P),v_sko__List__Xtake__Xinduct__2(V_P),t_a)))| -hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))).
% 48.27/48.32 0 [] hBOOL(hAPP(V_P,V_list))| -hBOOL(hAPP(V_P,c_List_Olist_OCons(v_sko__List__Xmap__Xinduct__1(V_P),v_sko__List__Xmap__Xinduct__2(V_P),t_a)))| -hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))).
% 48.27/48.32 0 [] hBOOL(hAPP(V_P,V_list))| -hBOOL(hAPP(V_P,c_List_Olist_OCons(v_sko__List__Xlist__Xinduct__1(V_P),v_sko__List__Xlist__Xinduct__2(V_P),t_a)))| -hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))).
% 48.27/48.32 0 [] hBOOL(hAPP(V_P,V_list))| -hBOOL(hAPP(V_P,c_List_Olist_OCons(v_sko__List__XdropWhile__Xinduct__1(V_P),v_sko__List__XdropWhile__Xinduct__2(V_P),t_a)))| -hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))).
% 48.27/48.32 0 [] hBOOL(hAPP(V_P,V_list))| -hBOOL(hAPP(V_P,c_List_Olist_OCons(v_sko__List__Xremove1__Xinduct__1(V_P),v_sko__List__Xremove1__Xinduct__2(V_P),t_a)))| -hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))).
% 48.27/48.32 0 [] hBOOL(hAPP(V_P,V_list))| -hBOOL(hAPP(V_P,c_List_Olist_OCons(v_sko__List__Xdistinct__Xinduct__1(V_P),v_sko__List__Xdistinct__Xinduct__2(V_P),t_a)))| -hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))).
% 48.27/48.32 0 [] c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 48.27/48.32 0 [] c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeE__1__1(V_T,V_e,V_t,V_ts))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 48.27/48.32 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)).
% 48.27/48.32 0 [] V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(V_a))),v_sko__InductTermi__XIT__Xcases__5(V_a)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 48.27/48.32 0 [] V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(V_a))),v_sko__InductTermi__XIT__Xcases__5(V_a)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)|V_a=c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 48.27/48.32 0 [] c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xtypes__snocE__1__1(V_Ts,V_e,V_t,V_ts))| -c_Type_Otypings(V_e,c_List_Oappend(V_ts,c_List_Olist_OCons(V_t,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),V_Ts).
% 48.27/48.32 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(V_a),v_sko__InductTermi__XIT__Xcases__5(V_a),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 48.27/48.32 0 [] V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(V_a))),v_sko__InductTermi__XIT__Xcases__5(V_a)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)|V_a=c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))|V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 48.27/48.32 0 [] V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(V_a))),v_sko__InductTermi__XIT__Xcases__5(V_a)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))|V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 48.27/48.32 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(V_a),v_sko__InductTermi__XIT__Xcases__5(V_a),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)))|V_a=c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 48.27/48.32 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(V_a),v_sko__InductTermi__XIT__Xcases__5(V_a),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))|V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 48.27/48.32 0 [] c_Type_Otyping(V_e,V_t,c_Type_Osko__Type__Xtypes__snocE__1__2(V_Ts,V_e,V_t,V_ts))| -c_Type_Otypings(V_e,c_List_Oappend(V_ts,c_List_Olist_OCons(V_t,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),V_Ts).
% 48.27/48.32 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(V_a),v_sko__InductTermi__XIT__Xcases__5(V_a),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)))|V_a=c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))|V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 48.27/48.32 0 [] -hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(V_P)),c_ListApplication_Osko__ListApplication__Xlem__1__4(V_P),tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(V_P)),c_ListApplication_Osko__ListApplication__Xlem__1__2(V_P),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(V_P,V_t)).
% 48.27/48.32 0 [] hBOOL(hAPP(V_P,V_t))| -hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(V_P)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(V_P),tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(V_P)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(V_P),tc_Lambda_OdB,tc_Lambda_OdB))).
% 48.27/48.32 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)).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 0 [] c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_OCons(V_a,V_list,T_b),T_a,T_b)=hAPP(hAPP(V_f2,V_a),V_list).
% 48.27/48.32 0 [] c_List_Oremove1(V_x,c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=V_xs.
% 48.27/48.32 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.
% 48.27/48.32 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.
% 48.27/48.32 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.
% 48.27/48.32 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.
% 48.27/48.32 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).
% 48.27/48.32 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).
% 48.27/48.32 0 [] V_x=V_y|hBOOL(hAPP(hAPP(V_r,V_y),V_x))| -c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a).
% 48.27/48.32 0 [] -class_Orderings_Olinorder(T_a)|c_List_Olinorder__class_Osorted(V_xs,T_a)| -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(V_x,V_xs,T_a),T_a).
% 48.27/48.32 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)).
% 48.27/48.32 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)).
% 48.27/48.32 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).
% 48.27/48.32 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)).
% 48.27/48.33 0 [] c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k)=V_t.
% 48.27/48.33 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(V_r,V_i)),c_Lambda_Olift(V_s,V_i)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)).
% 48.27/48.33 0 [] c_List_Olist_OCons(V_x,V_t,T_a)!=V_t.
% 48.27/48.33 0 [] V_xs!=c_List_Olist_OCons(V_x,V_xs,T_a).
% 48.27/48.33 0 [] c_List_Olist__update(c_List_Olist_OCons(V_x,V_xs,T_a),c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a)=c_List_Olist_OCons(V_y,V_xs,T_a).
% 48.27/48.33 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).
% 48.27/48.33 0 [] c_List_Omap(V_f,c_List_Olist__update(V_xs,V_k,V_y,T_b),T_b,T_a)=c_List_Olist__update(c_List_Omap(V_f,V_xs,T_b,T_a),V_k,hAPP(V_f,V_y),T_a).
% 48.27/48.33 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).
% 48.27/48.33 0 [] V_ys=V_xs|c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)| -c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a).
% 48.27/48.33 0 [] -class_Orderings_Olinorder(T_a)|c_List_Olinorder__class_Osorted(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a).
% 48.27/48.33 0 [] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a)=c_Transitive__Closure_Ortranclp(V_r,T_a).
% 48.27/48.33 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.
% 48.27/48.33 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.
% 48.27/48.33 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)).
% 48.27/48.33 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.
% 48.27/48.33 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.
% 48.27/48.33 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.
% 48.27/48.33 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.
% 48.27/48.33 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.
% 48.27/48.33 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)).
% 48.27/48.33 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).
% 48.27/48.33 0 [] hAPP(hAPP(V_plus,V_a),V_zero)=V_a| -c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a).
% 48.27/48.33 0 [] hAPP(hAPP(V_plus,V_zero),V_a)=V_a| -c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a).
% 48.27/48.33 0 [] c_List_Ofilter(V_P,c_List_Oappend(V_xs,V_ys,T_a),T_a)=c_List_Oappend(c_List_Ofilter(V_P,V_xs,T_a),c_List_Ofilter(V_P,V_ys,T_a),T_a).
% 48.27/48.33 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(V_a)))|V_a=c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))|V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 48.27/48.33 0 [] c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 48.27/48.33 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).
% 48.27/48.33 0 [] c_List_Olist_ONil(T_a)=c_List_Orev(c_List_Olist_ONil(T_a),T_a).
% 48.27/48.33 0 [] c_List_Olist_ONil(T_a)=c_List_Oremdups(c_List_Olist_ONil(T_a),T_a).
% 48.27/48.33 0 [] V_ys!=c_List_Oappend(V_xs,V_ys,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=V_ys|V_xs=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] V_xs!=c_List_Oappend(V_xs,V_ys,T_a)|V_ys=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=V_xs|V_ys=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] c_List_Oremdups(V_x,T_a)!=c_List_Olist_ONil(T_a)|V_x=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] c_List_Orotate(V_n,V_xs,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] c_List_Olist_ONil(T_a)!=c_List_Orev(V_xs,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] c_List_Olist_ONil(T_a)!=c_List_Olist_OCons(V_a_H,V_list_H,T_a).
% 48.27/48.33 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Olist_ONil(T_a)|V_ys=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] c_List_Olist_ONil(T_a)!=c_List_Oappend(V_xs,V_ys,T_a)|V_ys=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] c_List_Olist_ONil(T_a)!=c_List_Oappend(V_xs,V_ys,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] -c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a).
% 48.27/48.33 0 [] -c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a).
% 48.27/48.33 0 [] c_List_Oremdups(c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 48.27/48.33 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).
% 48.27/48.33 0 [] V_ys=c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a).
% 48.27/48.33 0 [] c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a)=V_ys.
% 48.27/48.33 0 [] V_xs=c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a).
% 48.27/48.33 0 [] V_x=c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a).
% 48.27/48.33 0 [] c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a)=V_xs.
% 48.27/48.33 0 [] c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a).
% 48.27/48.33 0 [] -hBOOL(hAPP(V_P,c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_ONil(t_b),t_a,t_b)))|hBOOL(hAPP(V_P,V_f1)).
% 48.27/48.33 0 [] c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a)=c_List_Olist_ONil(T_a).
% 48.27/48.33 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)).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 0 [] -class_Orderings_Olinorder(T_a)|c_List_Olinorder__class_Osorted(c_List_Olist_OCons(V_y,V_zs,T_a),T_a)| -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(V_x,c_List_Olist_OCons(V_y,V_zs,T_a),T_a),T_a).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 0 [] hBOOL(hAPP(hAPP(V_r,V_y),V_x))|c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)| -c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a).
% 48.27/48.33 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).
% 48.27/48.33 0 [] c_List_Olist_OCons(V_x,V_xs,T_a)!=c_List_Ofilter(V_P,V_ys,T_a)|hBOOL(hAPP(V_P,V_x)).
% 48.27/48.33 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.
% 48.27/48.33 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)).
% 48.27/48.33 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)).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 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)).
% 48.27/48.33 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)).
% 48.27/48.33 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)).
% 48.27/48.33 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)).
% 48.27/48.33 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).
% 48.27/48.33 0 [] c_List_Oremdups(c_List_Ofilter(V_P,V_xs,T_a),T_a)=c_List_Ofilter(V_P,c_List_Oremdups(V_xs,T_a),T_a).
% 48.27/48.33 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).
% 48.27/48.33 0 [] c_List_Ofilter(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olist_OCons(V_x,c_List_Ofilter(V_P,V_xs,T_a),T_a)| -hBOOL(hAPP(V_P,V_x)).
% 48.27/48.33 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).
% 48.27/48.33 0 [] c_Lambda_Osubstn(V_t,V_s,V_n)=c_Lambda_Osubst(V_t,c_Lambda_Oliftn(V_n,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),V_n).
% 48.27/48.33 0 [] -c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)|c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,V_x,T_a),c_List_Oappend(V_xs,V_x,T_a),T_a).
% 48.27/48.33 0 [] c_ListOrder_Ostep1(V_r,c_List_Oappend(V_x,V_vs,T_a),c_List_Oappend(V_x,V_us,T_a),T_a)| -c_ListOrder_Ostep1(V_r,V_vs,V_us,T_a).
% 48.27/48.33 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)).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(V_r,V_t,V_i)),c_Lambda_Osubst(V_s,V_t,V_i)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)).
% 48.27/48.33 0 [] V_x=V_y|V_xs=V_ys| -c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a).
% 48.27/48.33 0 [] -hBOOL(hAPP(hAPP(V_r,V_y),V_xa))|c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_x,T_a),c_List_Olist_OCons(V_xa,V_x,T_a),T_a).
% 48.27/48.33 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).
% 48.27/48.33 0 [] c_List_Oappend(V_ys,V_xs,T_a)!=c_List_Oappend(V_zs,V_xs,T_a)|V_ys=V_zs.
% 48.27/48.33 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Oappend(V_xs,V_zs,T_a)|V_ys=V_zs.
% 48.27/48.33 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)).
% 48.27/48.33 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)).
% 48.27/48.33 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)).
% 48.27/48.33 0 [] c_List_Ofilter(V_P,V_ys,T_a)!=c_List_Olist_OCons(V_x,V_xs,T_a)|hBOOL(hAPP(V_P,V_x)).
% 48.27/48.33 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(V_a)))|V_a=c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 48.27/48.33 0 [] c_List_Orotate(V_n,c_List_Omap(V_f,V_xs,T_b,T_a),T_a)=c_List_Omap(V_f,c_List_Orotate(V_n,V_xs,T_b),T_b,T_a).
% 48.27/48.33 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(V_t,V_r,V_i)),c_Lambda_Osubst(V_t,V_s,V_i)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)).
% 48.27/48.33 0 [] V_xs=c_List_Orev(c_List_Orev(V_xs,T_a),T_a).
% 48.27/48.33 0 [] c_List_Orev(c_List_Orev(V_ys,T_a),T_a)=V_ys.
% 48.27/48.33 0 [] c_List_Orev(c_List_Orev(V_xs,T_a),T_a)=V_xs.
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 0 [] hBOOL(hAPP(hAPP(V_r,V_y),V_x))|V_y=V_x| -c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(V_r,V_t,V_i)),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)).
% 48.27/48.33 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(V_t,V_r,V_i)),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)).
% 48.27/48.33 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).
% 48.27/48.33 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)).
% 48.27/48.33 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).
% 48.27/48.33 0 [] c_List_Olistrelp(V_r,c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_a),T_a)| -c_List_Olistrelp(V_r,V_xs,V_ys,T_a)| -hBOOL(hAPP(hAPP(V_r,V_x),V_y)).
% 48.27/48.33 0 [] c_Lambda_OdB_OAbs(V_dB)!=c_Lambda_OdB_OAbs(V_dB_H)|V_dB=V_dB_H.
% 48.27/48.33 0 [] c_List_Oremove1(V_x,c_List_Olist_OCons(V_y,V_xs,T_a),T_a)=c_List_Olist_OCons(V_y,c_List_Oremove1(V_x,V_xs,T_a),T_a)|V_x=V_y.
% 48.27/48.33 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(V_a)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 48.27/48.33 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),c_Lambda_Osubst(V_s,V_t,c_HOL_Ozero__class_Ozero(tc_nat)))).
% 48.27/48.33 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(V_r,V_i)),c_Lambda_Olift(V_s,V_i)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)).
% 48.27/48.33 0 [] c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)|V_xs=V_ys| -c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 0 [] c_List_Oremove1(V_x,c_List_Ofilter(V_P,V_xs,T_a),T_a)=c_List_Ofilter(V_P,V_xs,T_a)|hBOOL(hAPP(V_P,V_x)).
% 48.27/48.33 0 [] c_List_Orev(V_xs,T_a)!=c_List_Orev(V_ys,T_a)|V_xs=V_ys.
% 48.27/48.33 0 [] V_ys=V_xs|V_y=V_x| -c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a).
% 48.27/48.33 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).
% 48.27/48.33 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)).
% 48.27/48.33 0 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k)=V_t.
% 48.27/48.33 0 [] -class_OrderedGroup_Osemigroup__add(T_a)|c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(T_a),T_a).
% 48.27/48.33 0 [] c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubst(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)).
% 48.27/48.33 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))).
% 48.27/48.33 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))).
% 48.27/48.33 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).
% 48.27/48.33 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.
% 48.27/48.33 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.
% 48.27/48.33 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).
% 48.27/48.33 0 [] c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)|hBOOL(hAPP(hAPP(V_r,V_y),V_x))| -c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a).
% 48.27/48.33 0 [] c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_x,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)| -c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a).
% 48.27/48.33 0 [] -class_Orderings_Olinorder(T_a)|c_List_Olinorder__class_Osorted(V_xs,T_a)| -c_List_Olinorder__class_Osorted(c_List_Oappend(V_xs,V_ys,T_a),T_a).
% 48.27/48.33 0 [] -class_Orderings_Olinorder(T_a)|c_List_Olinorder__class_Osorted(V_ys,T_a)| -c_List_Olinorder__class_Osorted(c_List_Oappend(V_xs,V_ys,T_a),T_a).
% 48.27/48.33 0 [] c_List_Olist__update(c_List_Olist__update(V_xs,V_i,V_x,T_a),V_i_H,V_x_H,T_a)=c_List_Olist__update(c_List_Olist__update(V_xs,V_i_H,V_x_H,T_a),V_i,V_x,T_a)|V_i=V_i_H.
% 48.27/48.33 0 [] -class_Orderings_Olinorder(T_a)|c_List_Olinorder__class_Osorted(c_List_Oremdups(V_l,T_a),T_a)| -c_List_Olinorder__class_Osorted(V_l,T_a).
% 48.27/48.33 0 [] c_List_Ofilter(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Ofilter(V_P,V_xs,T_a)|hBOOL(hAPP(V_P,V_x)).
% 48.27/48.33 0 [] c_List_Orev(c_List_Ofilter(V_P,V_xs,T_a),T_a)=c_List_Ofilter(V_P,c_List_Orev(V_xs,T_a),T_a).
% 48.27/48.33 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.
% 48.27/48.33 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.
% 48.27/48.33 0 [] -hBOOL(hAPP(V_P,c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_OCons(V_a,V_list,t_b),t_a,t_b)))|hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_a),V_list))).
% 48.27/48.33 0 [] -hBOOL(hAPP(V_P,c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_OCons(V_xa,V_xb,t_b),t_a,t_b)))|hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_xa),V_xb))).
% 48.27/48.33 0 [] c_List_Olist__update(c_List_Olist__update(V_xs,V_i,V_x,T_a),V_i,V_y,T_a)=c_List_Olist__update(V_xs,V_i,V_y,T_a).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 0 [] -class_Orderings_Olinorder(T_a)|c_List_Olinorder__class_Osorted(c_List_Oremove1(V_a,V_xs,T_a),T_a)| -c_List_Olinorder__class_Osorted(V_xs,T_a).
% 48.27/48.33 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)).
% 48.27/48.33 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)).
% 48.27/48.33 0 [] hBOOL(hAPP(V_P,V_list))|hBOOL(hAPP(V_P,v_sko__List__XdropWhile__Xinduct__2(V_P)))| -hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))).
% 48.27/48.33 0 [] hBOOL(hAPP(V_P,V_list))|hBOOL(hAPP(V_P,v_sko__List__Xtake__Xinduct__2(V_P)))| -hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))).
% 48.27/48.33 0 [] -class_Orderings_Olinorder(T_a)|c_List_Olinorder__class_Osorted(c_List_Olist_ONil(T_a),T_a).
% 48.27/48.33 0 [] c_List_Ofiltermap(V_f,c_List_Olist_ONil(T_b),T_b,T_a)=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] c_List_Olist_ONil(T_a)!=c_List_Oremdups(V_x,T_a)|V_x=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] c_List_Ofilter(V_P,c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] c_List_Olist__update(c_List_Olist_ONil(T_a),V_k,V_x,T_a)=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] c_List_Olist__update(c_List_Olist_ONil(T_a),V_i,V_y,T_a)=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] c_List_Olist__update(c_List_Olist_ONil(T_a),V_i,V_v,T_a)=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] hBOOL(hAPP(V_P,V_list))|hBOOL(hAPP(V_P,v_sko__List__Xconcat__Xinduct__2(V_P)))| -hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))).
% 48.27/48.33 0 [] c_List_Olist_OCons(V_x,V_xa,T_a)!=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] c_List_Olist_OCons(V_a_H,V_list_H,T_a)!=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] c_List_Oremove1(V_x,c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] hBOOL(hAPP(V_P,V_list))|hBOOL(hAPP(V_P,v_sko__List__Xdistinct__Xinduct__2(V_P)))| -hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))).
% 48.27/48.33 0 [] c_Map_Omap__upds(V_m,V_as,c_List_Olist_ONil(T_b),T_a,T_b)=V_m.
% 48.27/48.33 0 [] c_Map_Omap__upds(V_m,c_List_Olist_ONil(T_a),V_bs,T_a,T_b)=V_m.
% 48.27/48.33 0 [] hBOOL(hAPP(V_P,V_list))|hBOOL(hAPP(V_P,v_sko__List__Xremove1__Xinduct__2(V_P)))| -hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))).
% 48.27/48.33 0 [] c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_ONil(T_b),T_a,T_b)=V_f1.
% 48.27/48.33 0 [] c_List_Orev(V_xs,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] c_List_Orotate(V_n,c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] hBOOL(hAPP(V_P,V_list))|hBOOL(hAPP(V_P,v_sko__List__Xlist__Xinduct__2(V_P)))| -hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))).
% 48.27/48.33 0 [] c_List_Olist_ONil(T_a)=c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a).
% 48.27/48.33 0 [] c_List_Olist_ONil(T_a)=c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a).
% 48.27/48.33 0 [] c_List_Olistrelp(V_r,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a).
% 48.27/48.33 0 [] hBOOL(hAPP(V_P,V_list))|hBOOL(hAPP(V_P,v_sko__List__Xmap__Xinduct__2(V_P)))| -hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))).
% 48.27/48.33 0 [] c_List_Orev(c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] c_List_Olist__update(V_xs,V_k,V_x,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_a).
% 48.27/48.33 0 [] c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(V_t,V_s,V_k)),c_Lambda_Osubst(V_u,V_s,V_k)).
% 48.27/48.33 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=c_Lambda_OdB_OAbs(V_dB_H).
% 48.27/48.33 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2).
% 48.27/48.33 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))).
% 48.27/48.33 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))).
% 48.27/48.33 0 [] c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(V_s,V_k)),c_Lambda_Olift(V_t,V_k)).
% 48.27/48.33 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).
% 48.27/48.33 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)).
% 48.27/48.33 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)).
% 48.27/48.33 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)).
% 48.27/48.33 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)).
% 48.27/48.33 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)).
% 48.27/48.33 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)).
% 48.27/48.33 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)))| -c_ListOrder_Ostep1(c_Lambda_Obeta,V_rs,V_ss,tc_Lambda_OdB).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 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)).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 0 [] hBOOL(hAPP(V_P,c_ListApplication_Osko__ListApplication__Xlem__1__3(V_P)))| -hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(V_P)),c_ListApplication_Osko__ListApplication__Xlem__1__2(V_P),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(V_P,V_t)).
% 48.27/48.33 0 [] c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T,V_e,V_i,V_ts))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 48.27/48.33 0 [] hBOOL(hAPP(V_P,V_t))|hBOOL(hAPP(V_P,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(V_P)))| -hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(V_P)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(V_P),tc_Lambda_OdB,tc_Lambda_OdB))).
% 48.27/48.33 0 [] c_Type_Otypings(V_e,V_us,c_Type_Osko__Type__Xvar__app__types__1__1(V_T,V_U,V_e,V_us))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_U)| -c_Type_Otypings(V_e,V_ts,V_Ts)| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_us,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 48.27/48.33 0 [] c_ListOrder_Ostep1(c_Lambda_Obeta,V_rs,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(V_n,V_rs,V_v),tc_Lambda_OdB)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_v)).
% 48.27/48.33 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,c_Lambda_Osubst(V_r,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))).
% 48.27/48.33 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(V_a)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))|V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 48.27/48.33 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=c_Lambda_OdB_OVar(V_nat).
% 48.27/48.33 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))).
% 48.27/48.33 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))).
% 48.27/48.33 0 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k)=V_u.
% 48.27/48.33 0 [] -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)).
% 48.27/48.33 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).
% 48.27/48.33 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OAbs(V_dB_H).
% 48.27/48.33 0 [] hAPP(V_e,V_i)=V_T| -c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T).
% 48.27/48.33 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).
% 48.27/48.33 0 [] c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)).
% 48.27/48.33 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).
% 48.27/48.33 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(V_t,V_i)))| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 48.27/48.33 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r)))| -hBOOL(hAPP(c_InductTermi_OIT,V_r)).
% 48.27/48.33 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)).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 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.
% 48.27/48.33 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.
% 48.27/48.33 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)).
% 48.27/48.33 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.
% 48.27/48.33 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)))| -hBOOL(hAPP(c_InductTermi_OIT,V_r)).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 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).
% 48.27/48.33 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OVar(V_nat_H)|V_nat=V_nat_H.
% 48.27/48.33 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.
% 48.27/48.33 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.
% 48.27/48.33 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.
% 48.27/48.33 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.
% 48.27/48.33 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.
% 48.27/48.33 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.
% 48.27/48.33 0 [] c_Lambda_OdB_OVar(V_nat)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H).
% 48.27/48.33 0 [] c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b)=V_a.
% 48.27/48.33 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).
% 48.27/48.33 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.
% 48.27/48.33 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).
% 48.27/48.33 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)!=c_Lambda_OdB_OVar(V_nat).
% 48.27/48.33 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))).
% 48.27/48.33 0 [] -hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_n))).
% 48.27/48.33 0 [] class_Orderings_Opreorder(tc_fun(T_2,T_1))| -class_Orderings_Opreorder(T_1).
% 48.27/48.33 0 [] class_Orderings_Oorder(tc_fun(T_2,T_1))| -class_Orderings_Oorder(T_1).
% 48.27/48.33 0 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 48.27/48.33 0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 48.27/48.33 0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 48.27/48.33 0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 48.27/48.33 0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 48.27/48.33 0 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 48.27/48.33 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 48.27/48.33 0 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 48.27/48.33 0 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 48.27/48.33 0 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 48.27/48.33 0 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 48.27/48.33 0 [] class_Orderings_Opreorder(tc_nat).
% 48.27/48.33 0 [] class_Orderings_Olinorder(tc_nat).
% 48.27/48.33 0 [] class_Orderings_Oorder(tc_nat).
% 48.27/48.33 0 [] class_Orderings_Opreorder(tc_bool).
% 48.27/48.33 0 [] class_Orderings_Oorder(tc_bool).
% 48.27/48.33 0 [] hBOOL(hAPP(hAPP(c_fe_qual(T_a),V_x),V_x)).
% 48.27/48.33 0 [] V_X=V_Y| -hBOOL(hAPP(hAPP(c_fe_qual(T_a),V_X),V_Y)).
% 48.27/48.33 end_of_list.
% 48.27/48.33
% 48.27/48.33 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 48.27/48.33
% 48.27/48.33 This ia a non-Horn set with equality. The strategy will be
% 48.27/48.33 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 48.27/48.33 deletion, with positive clauses in sos and nonpositive
% 48.27/48.33 clauses in usable.
% 48.27/48.33
% 48.27/48.33 dependent: set(knuth_bendix).
% 48.27/48.33 dependent: set(anl_eq).
% 48.27/48.33 dependent: set(para_from).
% 48.27/48.33 dependent: set(para_into).
% 48.27/48.33 dependent: clear(para_from_right).
% 48.27/48.33 dependent: clear(para_into_right).
% 48.27/48.33 dependent: set(para_from_vars).
% 48.27/48.33 dependent: set(eq_units_both_ways).
% 48.27/48.33 dependent: set(dynamic_demod_all).
% 48.27/48.33 dependent: set(dynamic_demod).
% 48.27/48.33 dependent: set(order_eq).
% 48.27/48.33 dependent: set(back_demod).
% 48.27/48.33 dependent: set(lrpo).
% 48.27/48.33 dependent: set(hyper_res).
% 48.27/48.33 dependent: set(unit_deletion).
% 48.27/48.33 dependent: set(factor).
% 48.27/48.33
% 48.27/48.33 ------------> process usable:
% 48.27/48.33 ** KEPT (pick-wt=23): 2 [copy,1,flip.2] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),C,c_HOL_Ozero__class_Ozero(A),A,A))=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A).
% 48.27/48.33 ** KEPT (pick-wt=19): 4 [copy,3,flip.2] -class_OrderedGroup_Omonoid__add(A)|c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,c_HOL_Ozero__class_Ozero(A),A,A)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),B,A,A).
% 48.27/48.33 ** KEPT (pick-wt=9): 5 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(c_List_Olist_ONil(A),tc_List_Olist(A)),tc_nat).
% 48.27/48.33 ** KEPT (pick-wt=16): 6 [] c_List_Oreplicate(A,B,C)!=c_List_Oreplicate(D,E,C)|B=E|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 48.27/48.33 ** KEPT (pick-wt=22): 7 [] c_Type_Otyping(A,B,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(C,A,B,D),C,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,B,D,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 48.27/48.33 ** KEPT (pick-wt=19): 8 [] 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)).
% 48.27/48.33 ** KEPT (pick-wt=19): 9 [] 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)).
% 48.27/48.33 ** KEPT (pick-wt=15): 10 [] hBOOL(hAPP(hAPP(A,B),C))| -hBOOL(hAPP(hAPP(c_Predicate_Oconversep(A,D,E),C),B)).
% 48.27/48.33 ** KEPT (pick-wt=15): 11 [] hBOOL(hAPP(hAPP(c_Predicate_Oconversep(A,B,C),D),E))| -hBOOL(hAPP(hAPP(A,E),D)).
% 48.27/48.33 Following clause subsumed by 10 during input processing: 0 [] hBOOL(hAPP(hAPP(A,B),C))| -hBOOL(hAPP(hAPP(c_Predicate_Oconversep(A,D,E),C),B)).
% 48.27/48.33 Following clause subsumed by 11 during input processing: 0 [] hBOOL(hAPP(hAPP(c_Predicate_Oconversep(A,B,C),D),E))| -hBOOL(hAPP(hAPP(A,E),D)).
% 48.27/48.33 ** KEPT (pick-wt=5): 12 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 48.27/48.33 Following clause subsumed by 12 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 48.27/48.33 ** 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).
% 48.27/48.33 ** KEPT (pick-wt=14): 14 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=12): 15 [] c_List_Oreplicate(A,B,C)!=c_List_Oreplicate(D,E,C)|A=D.
% 48.27/48.33 ** KEPT (pick-wt=16): 16 [] c_Wellfounded_Oaccp(A,B,C)| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,C),B),D))| -c_Wellfounded_Oaccp(A,D,C).
% 48.27/48.33 Following clause subsumed by 16 during input processing: 0 [] c_Wellfounded_Oaccp(A,B,C)| -c_Wellfounded_Oaccp(A,D,C)| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,C),B),D)).
% 48.27/48.33 ** KEPT (pick-wt=22): 17 [] c_Type_Otyping(A,B,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(C,A,B,D),C,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,B,D,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 48.27/48.33 ** KEPT (pick-wt=11): 18 [] c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),A,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 48.27/48.33 ** KEPT (pick-wt=11): 19 [] hBOOL(hAPP(c_InductTermi_OIT,A))| -c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),A,tc_Lambda_OdB).
% 48.27/48.33 ** KEPT (pick-wt=16): 20 [] c_Nat_Osize__class_Osize(c_List_Oremdups(A,B),tc_List_Olist(B))!=c_Nat_Osize__class_Osize(A,tc_List_Olist(B))|c_List_Oremdups(A,B)=A.
% 48.27/48.33 ** KEPT (pick-wt=16): 21 [] c_List_Oremdups(A,B)!=A|c_Nat_Osize__class_Osize(c_List_Oremdups(A,B),tc_List_Olist(B))=c_Nat_Osize__class_Osize(A,tc_List_Olist(B)).
% 48.27/48.33 ** KEPT (pick-wt=16): 22 [] c_List_Ofilter(A,c_List_Oreplicate(B,C,D),D)=c_List_Oreplicate(B,C,D)| -hBOOL(hAPP(A,C)).
% 48.27/48.33 ** KEPT (pick-wt=20): 23 [] c_List_Omap(A,B,C,D)!=c_List_Omap(A,E,C,D)|c_Nat_Osize__class_Osize(B,tc_List_Olist(C))=c_Nat_Osize__class_Osize(E,tc_List_Olist(C)).
% 48.27/48.33 ** KEPT (pick-wt=24): 25 [copy,24,flip.1] c_List_Oappend(c_List_Olist__update(A,B,C,D),E,D)=c_List_Olist__update(c_List_Oappend(A,E,D),B,C,D)| -c_HOL_Oord__class_Oless(B,c_Nat_Osize__class_Osize(A,tc_List_Olist(D)),tc_nat).
% 48.27/48.33 Following clause subsumed by 25 during input processing: 0 [flip.1] c_List_Oappend(c_List_Olist__update(A,D,E,C),B,C)=c_List_Olist__update(c_List_Oappend(A,B,C),D,E,C)| -c_HOL_Oord__class_Oless(D,c_Nat_Osize__class_Osize(A,tc_List_Olist(C)),tc_nat).
% 48.27/48.33 ** KEPT (pick-wt=4): 26 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 48.27/48.33 Following clause subsumed by 26 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 48.27/48.33 ** KEPT (pick-wt=6): 27 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 48.27/48.33 ** KEPT (pick-wt=6): 28 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 48.27/48.33 ** KEPT (pick-wt=6): 29 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 48.27/48.33 ** KEPT (pick-wt=13): 30 [] -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.
% 48.27/48.33 ** KEPT (pick-wt=13): 31 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(C,B,A)|c_HOL_Oord__class_Oless(B,C,A).
% 48.27/48.33 Following clause subsumed by 31 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.
% 48.27/48.33 Following clause subsumed by 31 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).
% 48.27/48.33 Following clause subsumed by 31 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).
% 48.27/48.33 ** KEPT (pick-wt=24): 32 [] -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).
% 48.27/48.33 Following clause subsumed by 26 during input processing: 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 48.27/48.33 ** KEPT (pick-wt=14): 33 [] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=hAPP(hAPP(c_Type_Otype_OFun,C),D)|B=D.
% 48.27/48.33 ** KEPT (pick-wt=14): 34 [] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=hAPP(hAPP(c_Type_Otype_OFun,C),D)|A=C.
% 48.27/48.33 ** KEPT (pick-wt=20): 35 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=20): 36 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=20): 37 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=20): 38 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=20): 39 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=20): 40 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=10): 41 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 48.27/48.33 ** KEPT (pick-wt=10): 42 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 48.27/48.33 ** KEPT (pick-wt=14): 43 [] c_Wellfounded_Oaccp(A,B,C)| -hBOOL(hAPP(hAPP(A,B),D))| -c_Wellfounded_Oaccp(A,D,C).
% 48.27/48.33 ** KEPT (pick-wt=10): 44 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 48.27/48.33 Following clause subsumed by 43 during input processing: 0 [] c_Wellfounded_Oaccp(A,B,C)| -hBOOL(hAPP(hAPP(A,B),D))| -c_Wellfounded_Oaccp(A,D,C).
% 48.27/48.33 Following clause subsumed by 44 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 48.27/48.33 ** KEPT (pick-wt=17): 45 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=17): 46 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=22): 47 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=17): 48 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=17): 49 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=17): 50 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=17): 51 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=22): 52 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=20): 53 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=11): 54 [] c_List_Oreplicate(A,B,C)!=c_List_Olist_ONil(C)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 48.27/48.33 ** KEPT (pick-wt=11): 55 [] c_List_Olist_ONil(A)!=c_List_Oreplicate(B,C,A)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 48.27/48.33 ** KEPT (pick-wt=11): 56 [] c_Nat_Osize__class_Osize(A,tc_List_Olist(B))!=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_List_Olist_ONil(B).
% 48.27/48.33 ** KEPT (pick-wt=17): 57 [] -class_OrderedGroup_Oab__semigroup__add(A)|c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,C,A,A)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,B,A,A).
% 48.27/48.33 ** KEPT (pick-wt=20): 58 [] c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),D)| -c_Type_Otyping(A,C,E)| -c_Type_Otyping(A,B,hAPP(hAPP(c_Type_Otype_OFun,E),D)).
% 48.27/48.33 ** KEPT (pick-wt=12): 59 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,C)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 48.27/48.33 ** KEPT (pick-wt=22): 60 [] c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,B,C,tc_Lambda_OdB,tc_Lambda_OdB),D)| -c_Type_Otypings(A,C,E)| -c_Type_Otyping(A,B,c_List_Ofoldr(c_Type_Otype_OFun,E,D,tc_Type_Otype,tc_Type_Otype)).
% 48.27/48.33 ** KEPT (pick-wt=25): 61 [] c_Nat_Osize__class_Osize(A,tc_List_Olist(B))!=c_Nat_Osize__class_Osize(C,tc_List_Olist(D))|c_Map_Omap__upds(E,c_List_Oappend(A,F,B),C,B,D)=c_Map_Omap__upds(E,A,C,B,D).
% 48.27/48.33 ** KEPT (pick-wt=25): 62 [] c_Nat_Osize__class_Osize(A,tc_List_Olist(B))!=c_Nat_Osize__class_Osize(C,tc_List_Olist(D))|c_Map_Omap__upds(E,A,c_List_Oappend(C,F,D),B,D)=c_Map_Omap__upds(E,A,C,B,D).
% 48.27/48.33 ** KEPT (pick-wt=11): 63 [] c_Lambda_Olift(c_Lambda_OdB_OVar(A),B)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 48.27/48.33 ** KEPT (pick-wt=12): 64 [] c_Lambda_Oliftn(A,c_Lambda_OdB_OVar(B),C)=c_Lambda_OdB_OVar(B)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 48.27/48.33 ** KEPT (pick-wt=29): 65 [] -hBOOL(hAPP(A,B))|hBOOL(hAPP(A,c_List_Osko__List__XCons__e_q__filter__iff__1__3(A,C,D)))|c_List_Olist_OCons(B,c_List_Ofilter(A,E,D),D)=c_List_Ofilter(A,c_List_Oappend(C,c_List_Olist_OCons(B,E,D),D),D).
% 48.27/48.33 ** KEPT (pick-wt=29): 66 [] -hBOOL(hAPP(A,B))|hBOOL(hAPP(A,c_List_Osko__List__Xfilter__e_q__Cons__iff__1__3(A,C,D)))|c_List_Ofilter(A,c_List_Oappend(C,c_List_Olist_OCons(B,E,D),D),D)=c_List_Olist_OCons(B,c_List_Ofilter(A,E,D),D).
% 48.27/48.33 ** KEPT (pick-wt=40): 67 [] -c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)| -c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),B,tc_Lambda_OdB)|c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B),C,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB).
% 48.27/48.33 ** KEPT (pick-wt=24): 68 [] c_Type_Otyping(A,c_Lambda_OdB_OVar(B),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(C,A,B,D),C,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(B),D,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 48.27/48.33 ** KEPT (pick-wt=41): 70 [copy,69,flip.1] c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(A,B,C,D),A,tc_Type_Otype,tc_Type_Otype)=B| -c_Type_Otyping(C,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(E),F,tc_Lambda_OdB,tc_Lambda_OdB),B)| -c_Type_Otypings(C,F,G)| -c_Type_Otyping(C,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(E),F,tc_Lambda_OdB,tc_Lambda_OdB),D,tc_Lambda_OdB,tc_Lambda_OdB),A).
% 48.27/48.33 ** KEPT (pick-wt=18): 71 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_List_Olist_OCons(v_sko__List__Xconcat__Xinduct__1(A),v_sko__List__Xconcat__Xinduct__2(A),t_a)))| -hBOOL(hAPP(A,c_List_Olist_ONil(t_a))).
% 48.27/48.33 ** KEPT (pick-wt=18): 72 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_List_Olist_OCons(v_sko__List__Xtake__Xinduct__1(A),v_sko__List__Xtake__Xinduct__2(A),t_a)))| -hBOOL(hAPP(A,c_List_Olist_ONil(t_a))).
% 48.27/48.33 ** KEPT (pick-wt=18): 73 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_List_Olist_OCons(v_sko__List__Xmap__Xinduct__1(A),v_sko__List__Xmap__Xinduct__2(A),t_a)))| -hBOOL(hAPP(A,c_List_Olist_ONil(t_a))).
% 48.27/48.33 ** KEPT (pick-wt=18): 74 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_List_Olist_OCons(v_sko__List__Xlist__Xinduct__1(A),v_sko__List__Xlist__Xinduct__2(A),t_a)))| -hBOOL(hAPP(A,c_List_Olist_ONil(t_a))).
% 48.27/48.33 ** KEPT (pick-wt=18): 75 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_List_Olist_OCons(v_sko__List__XdropWhile__Xinduct__1(A),v_sko__List__XdropWhile__Xinduct__2(A),t_a)))| -hBOOL(hAPP(A,c_List_Olist_ONil(t_a))).
% 48.27/48.33 ** KEPT (pick-wt=18): 76 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_List_Olist_OCons(v_sko__List__Xremove1__Xinduct__1(A),v_sko__List__Xremove1__Xinduct__2(A),t_a)))| -hBOOL(hAPP(A,c_List_Olist_ONil(t_a))).
% 48.27/48.33 ** KEPT (pick-wt=18): 77 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_List_Olist_OCons(v_sko__List__Xdistinct__Xinduct__1(A),v_sko__List__Xdistinct__Xinduct__2(A),t_a)))| -hBOOL(hAPP(A,c_List_Olist_ONil(t_a))).
% 48.27/48.33 ** KEPT (pick-wt=17): 78 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xlist__app__typeD__1__1(C,A,D,B))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,D,B,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 48.27/48.33 ** KEPT (pick-wt=17): 79 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xlist__app__typeE__1__1(C,A,D,B))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,D,B,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 48.27/48.33 ** KEPT (pick-wt=30): 81 [copy,80,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(A))),v_sko__InductTermi__XIT__Xcases__5(A)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)=A|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(A)))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 48.27/48.33 ** KEPT (pick-wt=30): 83 [copy,82,flip.1,flip.2] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(A))),v_sko__InductTermi__XIT__Xcases__5(A)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)=A|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(A))=A|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 48.27/48.33 ** KEPT (pick-wt=19): 84 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xtypes__snocE__1__1(C,A,D,B))| -c_Type_Otypings(A,c_List_Oappend(B,c_List_Olist_OCons(D,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),C).
% 48.27/48.33 ** KEPT (pick-wt=30): 85 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(A),v_sko__InductTermi__XIT__Xcases__5(A),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(A)))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 48.27/48.33 ** KEPT (pick-wt=36): 87 [copy,86,flip.1,flip.2,flip.3] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(A))),v_sko__InductTermi__XIT__Xcases__5(A)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)=A|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(A))=A|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(A)),v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 48.27/48.33 ** KEPT (pick-wt=36): 89 [copy,88,flip.1,flip.3] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(A))),v_sko__InductTermi__XIT__Xcases__5(A)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)=A|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(A)))|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(A)),v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 48.27/48.33 ** KEPT (pick-wt=30): 91 [copy,90,flip.2] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(A),v_sko__InductTermi__XIT__Xcases__5(A),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)))|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(A))=A|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 48.27/48.33 ** KEPT (pick-wt=36): 93 [copy,92,flip.3] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(A),v_sko__InductTermi__XIT__Xcases__5(A),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(A)))|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(A)),v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 48.27/48.33 ** KEPT (pick-wt=19): 94 [] c_Type_Otyping(A,B,c_Type_Osko__Type__Xtypes__snocE__1__2(C,A,B,D))| -c_Type_Otypings(A,c_List_Oappend(D,c_List_Olist_OCons(B,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),C).
% 48.27/48.33 ** KEPT (pick-wt=36): 96 [copy,95,flip.2,flip.3] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(A),v_sko__InductTermi__XIT__Xcases__5(A),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)))|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(A))=A|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(A)),v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 48.27/48.33 ** KEPT (pick-wt=28): 97 [] -hBOOL(hAPP(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(A)),c_ListApplication_Osko__ListApplication__Xlem__1__4(A),tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(A)),c_ListApplication_Osko__ListApplication__Xlem__1__2(A),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(A,B)).
% 48.27/48.33 ** KEPT (pick-wt=28): 98 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(A)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(A),tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(A)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(A),tc_Lambda_OdB,tc_Lambda_OdB))).
% 48.27/48.33 ** KEPT (pick-wt=24): 99 [] 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)).
% 48.27/48.33 ** KEPT (pick-wt=20): 100 [] -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.
% 48.27/48.33 ** KEPT (pick-wt=18): 101 [] -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.
% 48.27/48.33 ** KEPT (pick-wt=18): 102 [] -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.
% 48.27/48.33 ** KEPT (pick-wt=18): 103 [] -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.
% 48.27/48.33 ** KEPT (pick-wt=20): 104 [] A=B|hBOOL(hAPP(hAPP(C,B),A))| -c_ListOrder_Ostep1(C,c_List_Olist_OCons(B,D,E),c_List_Olist_OCons(A,F,E),E).
% 48.27/48.33 ** KEPT (pick-wt=11): 105 [] -class_Orderings_Olinorder(A)|c_List_Olinorder__class_Osorted(B,A)| -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(C,B,A),A).
% 48.27/48.33 ** KEPT (pick-wt=35): 106 [] -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)).
% 48.27/48.33 ** KEPT (pick-wt=32): 107 [] 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)).
% 48.27/48.33 ** KEPT (pick-wt=16): 108 [] 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)).
% 48.27/48.33 ** KEPT (pick-wt=16): 109 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(A,B)),c_Lambda_Olift(C,B)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),C)).
% 48.27/48.33 ** KEPT (pick-wt=6): 110 [] c_List_Olist_OCons(A,B,C)!=B.
% 48.27/48.33 Following clause subsumed by 110 during input processing: 0 [flip.1] c_List_Olist_OCons(B,A,C)!=A.
% 48.27/48.33 ** KEPT (pick-wt=27): 111 [] A=B|c_ListOrder_Ostep1(C,A,B,D)| -c_ListOrder_Ostep1(C,c_List_Oappend(A,c_List_Olist_OCons(E,c_List_Olist_ONil(D),D),D),c_List_Oappend(B,c_List_Olist_OCons(F,c_List_Olist_ONil(D),D),D),D).
% 48.27/48.33 ** KEPT (pick-wt=9): 112 [] -class_Orderings_Olinorder(A)|c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,c_List_Olist_ONil(A),A),A).
% 48.27/48.33 ** KEPT (pick-wt=11): 113 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 48.27/48.33 ** KEPT (pick-wt=11): 114 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 48.27/48.33 ** KEPT (pick-wt=13): 116 [copy,115,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.
% 48.27/48.33 ** KEPT (pick-wt=11): 117 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 48.27/48.33 ** KEPT (pick-wt=11): 118 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 48.27/48.33 ** KEPT (pick-wt=11): 119 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 48.27/48.33 ** KEPT (pick-wt=11): 120 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 48.27/48.33 Following clause subsumed by 113 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.
% 48.27/48.33 ** KEPT (pick-wt=14): 121 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(A)),c_Lambda_OdB_OAbs(B)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),B)).
% 48.27/48.33 ** KEPT (pick-wt=11): 122 [] hAPP(hAPP(A,B),C)=B| -c_OrderedGroup_Omonoid__add(C,A,D).
% 48.27/48.33 ** KEPT (pick-wt=11): 123 [] hAPP(hAPP(A,B),C)=C| -c_OrderedGroup_Omonoid__add(B,A,D).
% 48.27/48.33 ** KEPT (pick-wt=25): 125 [copy,124,flip.2,flip.3] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(A)))|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(A))=A|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(A)),v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 48.27/48.33 ** KEPT (pick-wt=12): 126 [] c_List_Omap(A,B,C,D)!=c_List_Olist_ONil(D)|B=c_List_Olist_ONil(C).
% 48.27/48.33 ** KEPT (pick-wt=10): 128 [copy,127,flip.1] c_List_Oappend(A,B,C)!=B|A=c_List_Olist_ONil(C).
% 48.27/48.33 Following clause subsumed by 128 during input processing: 0 [] c_List_Oappend(A,B,C)!=B|A=c_List_Olist_ONil(C).
% 48.27/48.33 ** KEPT (pick-wt=10): 130 [copy,129,flip.1] c_List_Oappend(A,B,C)!=A|B=c_List_Olist_ONil(C).
% 48.27/48.33 Following clause subsumed by 130 during input processing: 0 [] c_List_Oappend(A,B,C)!=A|B=c_List_Olist_ONil(C).
% 48.27/48.33 ** KEPT (pick-wt=10): 131 [] c_List_Oremdups(A,B)!=c_List_Olist_ONil(B)|A=c_List_Olist_ONil(B).
% 48.27/48.33 ** KEPT (pick-wt=11): 132 [] c_List_Orotate(A,B,C)!=c_List_Olist_ONil(C)|B=c_List_Olist_ONil(C).
% 48.27/48.33 ** KEPT (pick-wt=10): 133 [] c_List_Olist_ONil(A)!=c_List_Orev(B,A)|B=c_List_Olist_ONil(A).
% 48.27/48.33 ** KEPT (pick-wt=7): 134 [] c_List_Olist_ONil(A)!=c_List_Olist_OCons(B,C,A).
% 48.27/48.33 ** KEPT (pick-wt=11): 135 [] c_List_Oappend(A,B,C)!=c_List_Olist_ONil(C)|B=c_List_Olist_ONil(C).
% 48.27/48.33 ** KEPT (pick-wt=11): 136 [] c_List_Oappend(A,B,C)!=c_List_Olist_ONil(C)|A=c_List_Olist_ONil(C).
% 48.27/48.33 ** KEPT (pick-wt=11): 137 [] c_List_Olist_ONil(A)!=c_List_Oappend(B,C,A)|C=c_List_Olist_ONil(A).
% 48.27/48.33 ** KEPT (pick-wt=11): 138 [] c_List_Olist_ONil(A)!=c_List_Oappend(B,C,A)|B=c_List_Olist_ONil(A).
% 48.27/48.33 ** KEPT (pick-wt=6): 139 [] -c_ListOrder_Ostep1(A,B,c_List_Olist_ONil(C),C).
% 48.27/48.33 ** KEPT (pick-wt=6): 140 [] -c_ListOrder_Ostep1(A,c_List_Olist_ONil(B),C,B).
% 48.27/48.33 ** KEPT (pick-wt=12): 141 [] c_List_Olist_ONil(A)!=c_List_Omap(B,C,D,A)|C=c_List_Olist_ONil(D).
% 48.27/48.33 ** KEPT (pick-wt=14): 142 [] -hBOOL(hAPP(A,c_List_Olist_Olist__case(B,C,c_List_Olist_ONil(t_b),t_a,t_b)))|hBOOL(hAPP(A,B)).
% 48.27/48.33 ** KEPT (pick-wt=24): 143 [] 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)).
% 48.27/48.33 Following clause subsumed by 105 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,C,A),A)| -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(D,c_List_Olist_OCons(B,C,A),A),A).
% 48.27/48.33 ** KEPT (pick-wt=20): 144 [] 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).
% 48.27/48.33 ** KEPT (pick-wt=30): 145 [] hBOOL(hAPP(hAPP(A,B),C))|c_ListOrder_Ostep1(A,D,E,F)| -c_ListOrder_Ostep1(A,c_List_Oappend(D,c_List_Olist_OCons(B,c_List_Olist_ONil(F),F),F),c_List_Oappend(E,c_List_Olist_OCons(C,c_List_Olist_ONil(F),F),F),F).
% 48.27/48.33 ** KEPT (pick-wt=13): 146 [] c_List_Olist_OCons(A,B,C)!=c_List_Ofilter(D,E,C)|hBOOL(hAPP(D,A)).
% 48.27/48.33 ** KEPT (pick-wt=28): 147 [] -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.
% 48.27/48.33 ** KEPT (pick-wt=25): 148 [] -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)).
% 48.27/48.33 ** KEPT (pick-wt=25): 149 [] -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)).
% 48.27/48.33 ** KEPT (pick-wt=25): 150 [] -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).
% 48.27/48.33 Following clause subsumed by 148 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)).
% 48.27/48.33 ** KEPT (pick-wt=25): 151 [] -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)).
% 48.27/48.33 ** KEPT (pick-wt=25): 152 [] -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)).
% 48.27/48.33 ** KEPT (pick-wt=25): 153 [] -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)).
% 48.27/48.33 ** KEPT (pick-wt=25): 154 [] -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)).
% 48.27/48.33 Following clause subsumed by 148 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)).
% 48.27/48.33 ** KEPT (pick-wt=13): 155 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=19): 157 [copy,156,flip.1] c_List_Olist_OCons(A,c_List_Ofilter(B,C,D),D)=c_List_Ofilter(B,c_List_Olist_OCons(A,C,D),D)| -hBOOL(hAPP(B,A)).
% 48.27/48.33 ** KEPT (pick-wt=16): 158 [] 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).
% 48.27/48.33 ** KEPT (pick-wt=16): 159 [] -c_ListOrder_Ostep1(A,B,C,D)|c_ListOrder_Ostep1(A,c_List_Oappend(B,E,D),c_List_Oappend(C,E,D),D).
% 48.27/48.33 ** KEPT (pick-wt=16): 160 [] c_ListOrder_Ostep1(A,c_List_Oappend(B,C,D),c_List_Oappend(B,E,D),D)| -c_ListOrder_Ostep1(A,C,E,D).
% 48.27/48.33 ** KEPT (pick-wt=18): 161 [] 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)).
% 48.27/48.33 ** KEPT (pick-wt=11): 162 [] c_List_Olistsp(A,B,C)| -c_List_Olistsp(A,c_List_Oappend(B,D,C),C).
% 48.27/48.33 ** KEPT (pick-wt=11): 163 [] c_List_Olistsp(A,B,C)| -c_List_Olistsp(A,c_List_Oappend(D,B,C),C).
% 48.27/48.33 ** KEPT (pick-wt=18): 164 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(A,B,C)),c_Lambda_Osubst(D,B,C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),D)).
% 48.27/48.33 ** KEPT (pick-wt=17): 165 [] A=B|C=D| -c_ListOrder_Ostep1(E,c_List_Olist_OCons(B,D,F),c_List_Olist_OCons(A,C,F),F).
% 48.27/48.33 ** KEPT (pick-wt=17): 166 [] -hBOOL(hAPP(hAPP(A,B),C))|c_ListOrder_Ostep1(A,c_List_Olist_OCons(B,D,E),c_List_Olist_OCons(C,D,E),E).
% 48.27/48.33 ** KEPT (pick-wt=12): 167 [] c_List_Oappend(A,B,C)!=c_List_Oappend(D,B,C)|A=D.
% 48.27/48.33 ** KEPT (pick-wt=12): 168 [] c_List_Oappend(A,B,C)!=c_List_Oappend(A,D,C)|B=D.
% 48.27/48.33 ** KEPT (pick-wt=24): 169 [] 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)).
% 48.27/48.33 ** KEPT (pick-wt=13): 170 [] c_List_Ofilter(A,B,C)!=c_List_Olist_OCons(D,E,C)|hBOOL(hAPP(A,D)).
% 48.27/48.33 ** KEPT (pick-wt=19): 172 [copy,171,flip.2] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(A)))|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(A))=A|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 48.27/48.33 ** KEPT (pick-wt=20): 173 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(A,B,C)),c_Lambda_Osubst(A,D,C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,B),D)).
% 48.27/48.33 ** KEPT (pick-wt=15): 174 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=15): 175 [] -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).
% 48.27/48.33 Following clause subsumed by 174 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).
% 48.27/48.33 ** KEPT (pick-wt=28): 176 [] hBOOL(hAPP(hAPP(A,B),C))|B=C| -c_ListOrder_Ostep1(A,c_List_Oappend(D,c_List_Olist_OCons(B,c_List_Olist_ONil(E),E),E),c_List_Oappend(F,c_List_Olist_OCons(C,c_List_Olist_ONil(E),E),E),E).
% 48.27/48.33 ** KEPT (pick-wt=16): 177 [] 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).
% 48.27/48.33 ** KEPT (pick-wt=16): 179 [copy,178,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).
% 48.27/48.33 ** KEPT (pick-wt=22): 180 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(A,B,C)),c_Lambda_Osubst(D,B,C)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),D)).
% 48.27/48.33 ** KEPT (pick-wt=22): 181 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(A,B,C)),c_Lambda_Osubst(A,D,C)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),B),D)).
% 48.27/48.33 ** KEPT (pick-wt=15): 182 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=14): 183 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(A,C),D)).
% 48.27/48.33 ** KEPT (pick-wt=23): 184 [] -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).
% 48.27/48.33 ** KEPT (pick-wt=22): 185 [] c_List_Olistrelp(A,c_List_Olist_OCons(B,C,D),c_List_Olist_OCons(E,F,D),D)| -c_List_Olistrelp(A,C,F,D)| -hBOOL(hAPP(hAPP(A,B),E)).
% 48.27/48.33 ** KEPT (pick-wt=8): 186 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OAbs(B)|A=B.
% 48.27/48.33 ** KEPT (pick-wt=19): 187 [] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(A)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(A)))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 48.27/48.33 ** KEPT (pick-wt=20): 188 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(A,B)),c_Lambda_Olift(C,B)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),C)).
% 48.27/48.33 ** KEPT (pick-wt=19): 189 [] c_ListOrder_Ostep1(A,B,C,D)|C=B| -c_ListOrder_Ostep1(A,c_List_Olist_OCons(E,B,D),c_List_Olist_OCons(F,C,D),D).
% 48.27/48.33 ** KEPT (pick-wt=22): 190 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_OrderedGroup_Osemigroup__add(A,E).
% 48.27/48.33 ** KEPT (pick-wt=10): 191 [] c_List_Orev(A,B)!=c_List_Orev(C,B)|A=C.
% 48.27/48.33 ** KEPT (pick-wt=25): 192 [] A=B|C=D| -c_ListOrder_Ostep1(E,c_List_Oappend(A,c_List_Olist_OCons(C,c_List_Olist_ONil(F),F),F),c_List_Oappend(B,c_List_Olist_OCons(D,c_List_Olist_ONil(F),F),F),F).
% 48.27/48.33 ** KEPT (pick-wt=15): 193 [] c_List_Olistsp(A,c_List_Oappend(B,C,D),D)| -c_List_Olistsp(A,C,D)| -c_List_Olistsp(A,B,D).
% 48.27/48.33 ** KEPT (pick-wt=6): 194 [] -class_OrderedGroup_Osemigroup__add(A)|c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(A),A).
% 48.27/48.33 ** KEPT (pick-wt=16): 195 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OAbs(E),t_a)))|hBOOL(hAPP(A,hAPP(D,E))).
% 48.27/48.33 Following clause subsumed by 195 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))).
% 48.27/48.33 ** KEPT (pick-wt=12): 196 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_OCons(D,E,C)|A=D.
% 48.27/48.33 ** KEPT (pick-wt=12): 197 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_OCons(D,E,C)|B=E.
% 48.27/48.33 ** KEPT (pick-wt=14): 198 [] c_Type_Otyping(A,B,C)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,D),B))| -c_Type_Otyping(A,D,C).
% 48.27/48.33 ** KEPT (pick-wt=22): 199 [] c_ListOrder_Ostep1(A,B,C,D)|hBOOL(hAPP(hAPP(A,E),F))| -c_ListOrder_Ostep1(A,c_List_Olist_OCons(E,B,D),c_List_Olist_OCons(F,C,D),D).
% 48.27/48.33 ** KEPT (pick-wt=16): 200 [] c_ListOrder_Ostep1(A,c_List_Olist_OCons(B,C,D),c_List_Olist_OCons(B,E,D),D)| -c_ListOrder_Ostep1(A,C,E,D).
% 48.27/48.33 ** KEPT (pick-wt=11): 201 [] -class_Orderings_Olinorder(A)|c_List_Olinorder__class_Osorted(B,A)| -c_List_Olinorder__class_Osorted(c_List_Oappend(B,C,A),A).
% 48.27/48.33 ** KEPT (pick-wt=11): 202 [] -class_Orderings_Olinorder(A)|c_List_Olinorder__class_Osorted(B,A)| -c_List_Olinorder__class_Osorted(c_List_Oappend(C,B,A),A).
% 48.27/48.33 ** KEPT (pick-wt=10): 203 [] -class_Orderings_Olinorder(A)|c_List_Olinorder__class_Osorted(c_List_Oremdups(B,A),A)| -c_List_Olinorder__class_Osorted(B,A).
% 48.27/48.33 ** KEPT (pick-wt=20): 204 [] 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.
% 48.27/48.33 ** KEPT (pick-wt=20): 205 [] 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.
% 48.27/48.33 ** KEPT (pick-wt=20): 206 [] -hBOOL(hAPP(A,c_List_Olist_Olist__case(B,C,c_List_Olist_OCons(D,E,t_b),t_a,t_b)))|hBOOL(hAPP(A,hAPP(hAPP(C,D),E))).
% 48.27/48.33 Following clause subsumed by 206 during input processing: 0 [] -hBOOL(hAPP(A,c_List_Olist_Olist__case(B,C,c_List_Olist_OCons(D,E,t_b),t_a,t_b)))|hBOOL(hAPP(A,hAPP(hAPP(C,D),E))).
% 48.27/48.33 ** KEPT (pick-wt=11): 207 [] -class_Orderings_Olinorder(A)|c_List_Olinorder__class_Osorted(c_List_Oremove1(B,C,A),A)| -c_List_Olinorder__class_Osorted(C,A).
% 48.27/48.33 ** KEPT (pick-wt=22): 208 [] 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)).
% 48.27/48.33 ** KEPT (pick-wt=22): 209 [] 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)).
% 48.27/48.33 ** KEPT (pick-wt=10): 211 [copy,210,factor_simp] hBOOL(hAPP(A,v_sko__List__XdropWhile__Xinduct__2(A)))| -hBOOL(hAPP(A,c_List_Olist_ONil(t_a))).
% 48.27/48.33 ** KEPT (pick-wt=10): 213 [copy,212,factor_simp] hBOOL(hAPP(A,v_sko__List__Xtake__Xinduct__2(A)))| -hBOOL(hAPP(A,c_List_Olist_ONil(t_a))).
% 48.27/48.33 ** KEPT (pick-wt=6): 214 [] -class_Orderings_Olinorder(A)|c_List_Olinorder__class_Osorted(c_List_Olist_ONil(A),A).
% 48.27/48.33 ** KEPT (pick-wt=10): 215 [] c_List_Olist_ONil(A)!=c_List_Oremdups(B,A)|B=c_List_Olist_ONil(A).
% 48.27/48.33 ** KEPT (pick-wt=10): 217 [copy,216,factor_simp] hBOOL(hAPP(A,v_sko__List__Xconcat__Xinduct__2(A)))| -hBOOL(hAPP(A,c_List_Olist_ONil(t_a))).
% 48.27/48.33 ** KEPT (pick-wt=7): 218 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 48.27/48.33 Following clause subsumed by 218 during input processing: 0 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 48.27/48.33 ** KEPT (pick-wt=10): 220 [copy,219,factor_simp] hBOOL(hAPP(A,v_sko__List__Xdistinct__Xinduct__2(A)))| -hBOOL(hAPP(A,c_List_Olist_ONil(t_a))).
% 48.27/48.33 ** KEPT (pick-wt=10): 222 [copy,221,factor_simp] hBOOL(hAPP(A,v_sko__List__Xremove1__Xinduct__2(A)))| -hBOOL(hAPP(A,c_List_Olist_ONil(t_a))).
% 48.27/48.33 ** KEPT (pick-wt=10): 223 [] c_List_Orev(A,B)!=c_List_Olist_ONil(B)|A=c_List_Olist_ONil(B).
% 48.27/48.33 ** KEPT (pick-wt=10): 225 [copy,224,factor_simp] hBOOL(hAPP(A,v_sko__List__Xlist__Xinduct__2(A)))| -hBOOL(hAPP(A,c_List_Olist_ONil(t_a))).
% 48.27/48.33 ** KEPT (pick-wt=10): 227 [copy,226,factor_simp] hBOOL(hAPP(A,v_sko__List__Xmap__Xinduct__2(A)))| -hBOOL(hAPP(A,c_List_Olist_ONil(t_a))).
% 48.27/48.33 ** KEPT (pick-wt=12): 228 [] c_List_Olist__update(A,B,C,D)!=c_List_Olist_ONil(D)|A=c_List_Olist_ONil(D).
% 48.27/48.33 ** KEPT (pick-wt=8): 229 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 48.27/48.33 ** KEPT (pick-wt=8): 230 [] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 48.27/48.33 ** KEPT (pick-wt=21): 231 [] -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))).
% 48.27/48.33 Following clause subsumed by 231 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))).
% 48.27/48.33 ** KEPT (pick-wt=20): 232 [] 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)).
% 48.27/48.33 ** KEPT (pick-wt=20): 233 [] 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)).
% 48.27/48.33 ** KEPT (pick-wt=26): 234 [] 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)).
% 48.27/48.33 ** KEPT (pick-wt=21): 235 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,A,C,tc_Lambda_OdB,tc_Lambda_OdB)))| -c_ListOrder_Ostep1(c_Lambda_Obeta,B,C,tc_Lambda_OdB).
% 48.27/48.33 ** KEPT (pick-wt=24): 237 [copy,236,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).
% 48.27/48.33 ** KEPT (pick-wt=27): 239 [copy,238,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).
% 48.27/48.33 ** KEPT (pick-wt=21): 240 [] 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).
% 48.27/48.33 ** KEPT (pick-wt=17): 242 [copy,241,factor_simp] hBOOL(hAPP(A,c_ListApplication_Osko__ListApplication__Xlem__1__3(A)))| -hBOOL(hAPP(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(A)),c_ListApplication_Osko__ListApplication__Xlem__1__2(A),tc_Lambda_OdB,tc_Lambda_OdB))).
% 48.27/48.33 ** KEPT (pick-wt=18): 243 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xvar__app__typesE__1__1(C,A,D,B))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(D),B,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 48.27/48.33 ** KEPT (pick-wt=17): 245 [copy,244,factor_simp] hBOOL(hAPP(A,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(A)))| -hBOOL(hAPP(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(A)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(A),tc_Lambda_OdB,tc_Lambda_OdB))).
% 48.27/48.33 ** KEPT (pick-wt=37): 246 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xvar__app__types__1__1(C,D,A,B))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(E),F,tc_Lambda_OdB,tc_Lambda_OdB),D)| -c_Type_Otypings(A,F,G)| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(E),F,tc_Lambda_OdB,tc_Lambda_OdB),B,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 48.27/48.33 ** KEPT (pick-wt=20): 247 [] c_ListOrder_Ostep1(c_Lambda_Obeta,A,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(B,A,C),tc_Lambda_OdB)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(B),A,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 48.27/48.34 ** KEPT (pick-wt=31): 248 [] 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,c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_Lambda_OdB,tc_Lambda_OdB))).
% 48.27/48.34 ** KEPT (pick-wt=25): 250 [copy,249,flip.3] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(A)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(A)))|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(A)),v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 48.27/48.34 ** KEPT (pick-wt=5): 251 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 48.27/48.34 ** KEPT (pick-wt=16): 252 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OVar(E),t_a)))|hBOOL(hAPP(A,hAPP(B,E))).
% 48.27/48.34 Following clause subsumed by 252 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))).
% 48.27/48.34 ** KEPT (pick-wt=7): 253 [] -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(A)),B)).
% 48.27/48.34 ** KEPT (pick-wt=5): 254 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 48.27/48.34 ** KEPT (pick-wt=10): 255 [] hAPP(A,B)=C| -c_Type_Otyping(A,c_Lambda_OdB_OVar(B),C).
% 48.27/48.34 ** KEPT (pick-wt=30): 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_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).
% 48.27/48.34 ** KEPT (pick-wt=10): 258 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(A,B)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 48.27/48.34 ** KEPT (pick-wt=9): 259 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(A)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 48.27/48.34 ** KEPT (pick-wt=24): 261 [copy,260,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)).
% 48.27/48.34 ** KEPT (pick-wt=35): 263 [copy,262,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).
% 48.27/48.34 ** KEPT (pick-wt=13): 264 [] 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).
% 48.27/48.34 ** KEPT (pick-wt=18): 265 [] 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.
% 48.27/48.34 ** KEPT (pick-wt=18): 266 [] 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.
% 48.27/48.34 ** KEPT (pick-wt=22): 267 [] 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)).
% 48.27/48.34 ** KEPT (pick-wt=13): 268 [] 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.
% 48.27/48.34 ** KEPT (pick-wt=12): 269 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(A,c_Lambda_OdB_OVar(B),C)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 48.27/48.34 ** KEPT (pick-wt=23): 270 [] 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).
% 48.27/48.34 ** KEPT (pick-wt=15): 271 [] 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).
% 48.27/48.34 ** KEPT (pick-wt=14): 272 [] 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).
% 48.27/48.34 ** KEPT (pick-wt=13): 273 [] 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).
% 48.27/48.34 ** KEPT (pick-wt=28): 275 [copy,274,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).
% 48.27/48.34 ** KEPT (pick-wt=13): 276 [] 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).
% 48.27/48.34 ** KEPT (pick-wt=14): 277 [] 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).
% 48.27/48.34 ** KEPT (pick-wt=8): 278 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OVar(B)|A=B.
% 48.27/48.34 ** KEPT (pick-wt=18): 279 [] 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.
% 48.27/48.34 ** KEPT (pick-wt=18): 280 [] 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.
% 48.27/48.34 ** KEPT (pick-wt=20): 281 [] 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.
% 48.27/48.34 ** KEPT (pick-wt=14): 282 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|A=C.
% 48.27/48.34 ** KEPT (pick-wt=14): 283 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|B=D.
% 48.27/48.34 ** KEPT (pick-wt=13): 284 [] 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.
% 48.27/48.34 ** KEPT (pick-wt=8): 285 [] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 48.27/48.34 ** KEPT (pick-wt=16): 286 [] 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.
% 48.27/48.34 ** KEPT (pick-wt=13): 287 [] 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).
% 48.27/48.34 ** KEPT (pick-wt=8): 288 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 48.27/48.34 ** KEPT (pick-wt=5): 289 [] -hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_n))).
% 48.27/48.34 ** KEPT (pick-wt=6): 290 [] class_Orderings_Opreorder(tc_fun(A,B))| -class_Orderings_Opreorder(B).
% 48.27/48.34 ** KEPT (pick-wt=6): 291 [] class_Orderings_Oorder(tc_fun(A,B))| -class_Orderings_Oorder(B).
% 48.27/48.34 ** KEPT (pick-wt=10): 292 [] A=B| -hBOOL(hAPP(hAPP(c_fe_qual(C),A),B)).
% 48.27/48.34 Following clause subsumed by 218 during input processing: 0 [copy,134,flip.1] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 48.27/48.34 Following clause subsumed by 134 during input processing: 0 [copy,218,flip.1] c_List_Olist_ONil(A)!=c_List_Olist_OCons(B,C,A).
% 48.27/48.34 Following clause subsumed by 230 during input processing: 0 [copy,229,flip.1] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 48.27/48.34 Following clause subsumed by 229 during input processing: 0 [copy,230,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 48.27/48.34 Following clause subsumed by 254 during input processing: 0 [copy,251,flip.1] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 48.27/48.34 Following clause subsumed by 251 during input processing: 0 [copy,254,flip.1] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 48.27/48.34 ** KEPT (pick-wt=15): 305 [copy,271,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).
% 48.27/48.34 ** KEPT (pick-wt=14): 306 [copy,272,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).
% 48.27/48.34 Following clause subsumed by 288 during input processing: 0 [copy,285,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 48.27/48.34 Following clause subsumed by 285 during input processing: 0 [copy,288,flip.1] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 48.27/48.34 Following clause subsumed by 271 during input processing: 0 [copy,305,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).
% 48.27/48.34 Following clause subsumed by 272 during input processing: 0 [copy,306,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).
% 48.27/48.34
% 48.27/48.34 ------------> process sos:
% 48.27/48.34 ** KEPT (pick-wt=3): 307 [] A=A.
% 48.27/48.34 ** KEPT (pick-wt=15): 308 [] 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).
% 48.27/48.34 ** KEPT (pick-wt=9): 309 [] c_List_Ofoldr(A,c_List_Olist_ONil(B),C,B,D)=C.
% 48.27/48.34 ---> New Demodulator: 310 [new_demod,309] c_List_Ofoldr(A,c_List_Olist_ONil(B),C,B,D)=C.
% 48.27/48.34 ** KEPT (pick-wt=13): 311 [] c_Nat_Osize__class_Osize(c_List_Olist__update(A,B,C,D),tc_List_Olist(D))=c_Nat_Osize__class_Osize(A,tc_List_Olist(D)).
% 48.27/48.34 ---> New Demodulator: 312 [new_demod,311] c_Nat_Osize__class_Osize(c_List_Olist__update(A,B,C,D),tc_List_Olist(D))=c_Nat_Osize__class_Osize(A,tc_List_Olist(D)).
% 48.27/48.34 ** KEPT (pick-wt=11): 313 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),C,B).
% 48.27/48.34 ** KEPT (pick-wt=12): 314 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(A,tc_List_Olist(B)),tc_nat)|A=c_List_Olist_ONil(B).
% 48.27/48.34 ** KEPT (pick-wt=13): 315 [] c_Nat_Osize__class_Osize(c_List_Omap(A,B,C,D),tc_List_Olist(D))=c_Nat_Osize__class_Osize(B,tc_List_Olist(C)).
% 48.27/48.34 ** KEPT (pick-wt=15): 316 [] c_List_Omap(A,c_List_Oreplicate(B,C,D),D,E)=c_List_Oreplicate(B,hAPP(A,C),E).
% 48.27/48.34 ** KEPT (pick-wt=11): 317 [] c_List_Orev(c_List_Oreplicate(A,B,C),C)=c_List_Oreplicate(A,B,C).
% 48.27/48.34 ---> New Demodulator: 318 [new_demod,317] c_List_Orev(c_List_Oreplicate(A,B,C),C)=c_List_Oreplicate(A,B,C).
% 48.27/48.34 ** KEPT (pick-wt=21): 319 [] c_List_Ofoldr(A,c_List_Oappend(B,C,D),E,D,F)=c_List_Ofoldr(A,B,c_List_Ofoldr(A,C,E,D,F),D,F).
% 48.27/48.34 ---> New Demodulator: 320 [new_demod,319] c_List_Ofoldr(A,c_List_Oappend(B,C,D),E,D,F)=c_List_Ofoldr(A,B,c_List_Ofoldr(A,C,E,D,F),D,F).
% 48.27/48.34 ** KEPT (pick-wt=8): 321 [] c_Predicate_Oconversep(c_fe_qual(A),A,A)=c_fe_qual(A).
% 48.27/48.34 ---> New Demodulator: 322 [new_demod,321] c_Predicate_Oconversep(c_fe_qual(A),A,A)=c_fe_qual(A).
% 48.27/48.34 ** KEPT (pick-wt=12): 323 [] c_Nat_Osize__class_Osize(c_List_Orotate(A,B,C),tc_List_Olist(C))=c_Nat_Osize__class_Osize(B,tc_List_Olist(C)).
% 48.27/48.34 ---> New Demodulator: 324 [new_demod,323] c_Nat_Osize__class_Osize(c_List_Orotate(A,B,C),tc_List_Olist(C))=c_Nat_Osize__class_Osize(B,tc_List_Olist(C)).
% 48.27/48.34 ** KEPT (pick-wt=11): 325 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 48.27/48.34 Following clause subsumed by 325 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).
% 48.27/48.34 Following clause subsumed by 325 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 48.27/48.34 ** KEPT (pick-wt=21): 326 [] 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).
% 48.27/48.34 ** KEPT (pick-wt=9): 327 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 48.27/48.34 ** KEPT (pick-wt=9): 328 [] c_Nat_Osize__class_Osize(c_List_Oreplicate(A,B,C),tc_List_Olist(C))=A.
% 48.27/48.34 ---> New Demodulator: 329 [new_demod,328] c_Nat_Osize__class_Osize(c_List_Oreplicate(A,B,C),tc_List_Olist(C))=A.
% 48.27/48.34 ** KEPT (pick-wt=20): 331 [copy,330,flip.1] hAPP(hAPP(A,B),c_List_Ofoldr(A,C,D,E,F))=c_List_Ofoldr(A,c_List_Olist_OCons(B,C,E),D,E,F).
% 48.27/48.34 ---> New Demodulator: 332 [new_demod,331] hAPP(hAPP(A,B),c_List_Ofoldr(A,C,D,E,F))=c_List_Ofoldr(A,c_List_Olist_OCons(B,C,E),D,E,F).
% 48.27/48.34 ** KEPT (pick-wt=9): 333 [] c_Predicate_Oconversep(c_Predicate_Oconversep(A,B,C),C,B)=A.
% 48.27/48.34 ---> New Demodulator: 334 [new_demod,333] c_Predicate_Oconversep(c_Predicate_Oconversep(A,B,C),C,B)=A.
% 48.27/48.34 ** KEPT (pick-wt=11): 335 [] c_Nat_Osize__class_Osize(c_List_Orev(A,B),tc_List_Olist(B))=c_Nat_Osize__class_Osize(A,tc_List_Olist(B)).
% 48.27/48.34 ---> New Demodulator: 336 [new_demod,335] c_Nat_Osize__class_Osize(c_List_Orev(A,B),tc_List_Olist(B))=c_Nat_Osize__class_Osize(A,tc_List_Olist(B)).
% 48.27/48.34 ** KEPT (pick-wt=8): 337 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Olist_ONil(B).
% 48.27/48.34 ** KEPT (pick-wt=8): 338 [] c_Nat_Osize__class_Osize(c_List_Olist_ONil(A),tc_List_Olist(A))=c_HOL_Ozero__class_Ozero(tc_nat).
% 48.27/48.34 ---> New Demodulator: 339 [new_demod,338] c_Nat_Osize__class_Osize(c_List_Olist_ONil(A),tc_List_Olist(A))=c_HOL_Ozero__class_Ozero(tc_nat).
% 48.27/48.34 ** KEPT (pick-wt=8): 340 [] c_List_Olist_ONil(A)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),B,A).
% 48.27/48.34 ** KEPT (pick-wt=21): 342 [copy,341,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).
% 48.27/48.34 ---> New Demodulator: 343 [new_demod,342] 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).
% 48.27/48.34 ** KEPT (pick-wt=14): 344 [] c_List_Ofilter(A,c_List_Oreplicate(B,C,D),D)=c_List_Olist_ONil(D)|hBOOL(hAPP(A,C)).
% 48.27/48.34 ** KEPT (pick-wt=7): 346 [copy,345,unit_del,26] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,A)=B.
% 48.27/48.34 ---> New Demodulator: 347 [new_demod,346] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,A)=B.
% 48.27/48.34 ** KEPT (pick-wt=15): 348 [] 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).
% 48.27/48.34 ** KEPT (pick-wt=19): 349 [] 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).
% 48.27/48.34 ** KEPT (pick-wt=22): 350 [] c_List_Olist__update(c_List_Oappend(A,c_List_Olist_OCons(B,C,D),D),c_Nat_Osize__class_Osize(A,tc_List_Olist(D)),E,D)=c_List_Oappend(A,c_List_Olist_OCons(E,C,D),D).
% 48.27/48.34 ** KEPT (pick-wt=11): 352 [copy,351,unit_del,26] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 48.27/48.34 ---> New Demodulator: 353 [new_demod,352] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 48.27/48.34 ** KEPT (pick-wt=19): 355 [copy,354,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).
% 48.27/48.34 ---> New Demodulator: 356 [new_demod,355] 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).
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,356] 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).
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,356] 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).
% 48.27/48.34 ** KEPT (pick-wt=15): 357 [] c_List_Olist_Olist__case(A,B,c_List_Olist_OCons(C,D,E),F,E)=hAPP(hAPP(B,C),D).
% 48.27/48.34 ** KEPT (pick-wt=9): 358 [] c_List_Oremove1(A,c_List_Olist_OCons(A,B,C),C)=B.
% 48.27/48.34 ---> New Demodulator: 359 [new_demod,358] c_List_Oremove1(A,c_List_Olist_OCons(A,B,C),C)=B.
% 48.27/48.34 ** KEPT (pick-wt=15): 360 [] c_List_Olist_OCons(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 48.27/48.34 ---> New Demodulator: 361 [new_demod,360] c_List_Olist_OCons(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,361] c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 48.27/48.34 ** KEPT (pick-wt=17): 362 [] c_List_Orev(c_List_Oappend(c_List_Orev(A,B),c_List_Olist_OCons(C,c_List_Olist_ONil(B),B),B),B)=c_List_Olist_OCons(C,A,B).
% 48.27/48.34 ---> New Demodulator: 363 [new_demod,362] c_List_Orev(c_List_Oappend(c_List_Orev(A,B),c_List_Olist_OCons(C,c_List_Olist_ONil(B),B),B),B)=c_List_Olist_OCons(C,A,B).
% 48.27/48.34 ** KEPT (pick-wt=8): 364 [] c_Lambda_Osubst(c_Lambda_Olift(A,B),C,B)=A.
% 48.27/48.34 ---> New Demodulator: 365 [new_demod,364] c_Lambda_Osubst(c_Lambda_Olift(A,B),C,B)=A.
% 48.27/48.34 ** KEPT (pick-wt=14): 366 [] c_List_Olist__update(c_List_Olist_OCons(A,B,C),c_HOL_Ozero__class_Ozero(tc_nat),D,C)=c_List_Olist_OCons(D,B,C).
% 48.27/48.34 ** KEPT (pick-wt=13): 368 [copy,367,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).
% 48.27/48.34 ---> New Demodulator: 369 [new_demod,368] c_List_Oappend(c_List_Olist_ONil(A),c_List_Olist_OCons(B,C,A),A)=c_List_Olist_OCons(B,C,A).
% 48.27/48.34 ** KEPT (pick-wt=21): 370 [] c_List_Omap(A,c_List_Olist__update(B,C,D,E),E,F)=c_List_Olist__update(c_List_Omap(A,B,E,F),C,hAPP(A,D),F).
% 48.27/48.34 ** KEPT (pick-wt=13): 372 [copy,371,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).
% 48.27/48.34 ---> New Demodulator: 373 [new_demod,372] 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).
% 48.27/48.34 ** KEPT (pick-wt=9): 374 [] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(A,B),B)=c_Transitive__Closure_Ortranclp(A,B).
% 48.27/48.34 ---> New Demodulator: 375 [new_demod,374] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(A,B),B)=c_Transitive__Closure_Ortranclp(A,B).
% 48.27/48.34 ** KEPT (pick-wt=15): 376 [] c_List_Orev(c_List_Oappend(A,B,C),C)=c_List_Oappend(c_List_Orev(B,C),c_List_Orev(A,C),C).
% 48.27/48.34 ---> New Demodulator: 377 [new_demod,376] c_List_Orev(c_List_Oappend(A,B,C),C)=c_List_Oappend(c_List_Orev(B,C),c_List_Orev(A,C),C).
% 48.27/48.34 ** KEPT (pick-wt=18): 378 [] c_List_Ofilter(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(c_List_Ofilter(A,B,D),c_List_Ofilter(A,C,D),D).
% 48.27/48.34 ---> New Demodulator: 379 [new_demod,378] c_List_Ofilter(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(c_List_Ofilter(A,B,D),c_List_Ofilter(A,C,D),D).
% 48.27/48.34 ** KEPT (pick-wt=9): 380 [] c_List_Oappend(c_List_Olist_ONil(A),c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 48.27/48.34 ---> New Demodulator: 381 [new_demod,380] c_List_Oappend(c_List_Olist_ONil(A),c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 48.27/48.34 ** KEPT (pick-wt=7): 383 [copy,382,flip.1] c_List_Orev(c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 48.27/48.34 ---> New Demodulator: 384 [new_demod,383] c_List_Orev(c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 48.27/48.34 ** KEPT (pick-wt=7): 386 [copy,385,flip.1] c_List_Oremdups(c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 48.27/48.34 ---> New Demodulator: 387 [new_demod,386] c_List_Oremdups(c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,387] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 48.27/48.34 ** KEPT (pick-wt=7): 389 [copy,388,flip.1] c_List_Oappend(c_List_Olist_ONil(A),B,A)=B.
% 48.27/48.34 ---> New Demodulator: 390 [new_demod,389] c_List_Oappend(c_List_Olist_ONil(A),B,A)=B.
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,390] B=B.
% 48.27/48.34 ** KEPT (pick-wt=7): 392 [copy,391,flip.1] c_List_Oappend(A,c_List_Olist_ONil(B),B)=A.
% 48.27/48.34 ---> New Demodulator: 393 [new_demod,392] c_List_Oappend(A,c_List_Olist_ONil(B),B)=A.
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,390] A=A.
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,393] A=A.
% 48.27/48.34 ** KEPT (pick-wt=5): 394 [] c_List_Olistsp(A,c_List_Olist_ONil(B),B).
% 48.27/48.34 ** KEPT (pick-wt=9): 395 [] c_List_Omap(A,c_List_Olist_ONil(B),B,C)=c_List_Olist_ONil(C).
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,361] c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C)=c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C).
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,361] c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C)=c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C).
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,373] c_List_Olist_OCons(A,c_List_Olist_ONil(B),B)=c_List_Olist_OCons(A,c_List_Olist_ONil(B),B).
% 48.27/48.34 ** KEPT (pick-wt=17): 396 [] 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).
% 48.27/48.34 ** KEPT (pick-wt=13): 397 [] c_List_Oremdups(c_List_Ofilter(A,B,C),C)=c_List_Ofilter(A,c_List_Oremdups(B,C),C).
% 48.27/48.34 ---> New Demodulator: 398 [new_demod,397] c_List_Oremdups(c_List_Ofilter(A,B,C),C)=c_List_Ofilter(A,c_List_Oremdups(B,C),C).
% 48.27/48.34 ** KEPT (pick-wt=13): 399 [] c_Lambda_Osubstn(A,B,C)=c_Lambda_Osubst(A,c_Lambda_Oliftn(C,B,c_HOL_Ozero__class_Ozero(tc_nat)),C).
% 48.27/48.34 ** KEPT (pick-wt=11): 400 [] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(C,D).
% 48.27/48.34 ** KEPT (pick-wt=15): 401 [] c_List_Orev(c_List_Omap(A,B,C,D),D)=c_List_Omap(A,c_List_Orev(B,C),C,D).
% 48.27/48.34 ---> New Demodulator: 402 [new_demod,401] c_List_Orev(c_List_Omap(A,B,C,D),D)=c_List_Omap(A,c_List_Orev(B,C),C,D).
% 48.27/48.34 ** KEPT (pick-wt=8): 403 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),C)).
% 48.27/48.34 Following clause subsumed by 403 during input processing: 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),C)).
% 48.27/48.34 ** KEPT (pick-wt=17): 404 [] c_List_Orotate(A,c_List_Omap(B,C,D,E),E)=c_List_Omap(B,c_List_Orotate(A,C,D),D,E).
% 48.27/48.34 ---> New Demodulator: 405 [new_demod,404] c_List_Orotate(A,c_List_Omap(B,C,D,E),E)=c_List_Omap(B,c_List_Orotate(A,C,D),D,E).
% 48.27/48.34 ** KEPT (pick-wt=7): 407 [copy,406,flip.1] c_List_Orev(c_List_Orev(A,B),B)=A.
% 48.27/48.34 ---> New Demodulator: 408 [new_demod,407] c_List_Orev(c_List_Orev(A,B),B)=A.
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,408] A=A.
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,408] A=A.
% 48.27/48.34 ** KEPT (pick-wt=18): 409 [] c_List_Oremove1(A,c_List_Olist_OCons(B,C,D),D)=c_List_Olist_OCons(B,c_List_Oremove1(A,C,D),D)|A=B.
% 48.27/48.34 ** KEPT (pick-wt=15): 410 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B)),c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat)))).
% 48.27/48.34 ** KEPT (pick-wt=21): 412 [copy,411,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).
% 48.27/48.34 ---> New Demodulator: 413 [new_demod,412] 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).
% 48.27/48.34 ** KEPT (pick-wt=16): 414 [] c_List_Oremove1(A,c_List_Ofilter(B,C,D),D)=c_List_Ofilter(B,C,D)|hBOOL(hAPP(B,A)).
% 48.27/48.34 ** KEPT (pick-wt=18): 415 [] 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)).
% 48.27/48.34 ** KEPT (pick-wt=7): 416 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 48.27/48.34 ---> New Demodulator: 417 [new_demod,416] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 48.27/48.34 ** KEPT (pick-wt=11): 418 [] c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 48.27/48.34 ---> New Demodulator: 419 [new_demod,418] c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,390] c_List_Olist_OCons(B,C,A)=c_List_Olist_OCons(B,C,A).
% 48.27/48.34 ** KEPT (pick-wt=22): 420 [] c_List_Olist__update(c_List_Olist__update(A,B,C,D),E,F,D)=c_List_Olist__update(c_List_Olist__update(A,E,F,D),B,C,D)|B=E.
% 48.27/48.34 ** KEPT (pick-wt=16): 421 [] c_List_Ofilter(A,c_List_Olist_OCons(B,C,D),D)=c_List_Ofilter(A,C,D)|hBOOL(hAPP(A,B)).
% 48.27/48.34 ** KEPT (pick-wt=13): 422 [] c_List_Orev(c_List_Ofilter(A,B,C),C)=c_List_Ofilter(A,c_List_Orev(B,C),C).
% 48.27/48.34 ---> New Demodulator: 423 [new_demod,422] c_List_Orev(c_List_Ofilter(A,B,C),C)=c_List_Ofilter(A,c_List_Orev(B,C),C).
% 48.27/48.34 ** KEPT (pick-wt=15): 424 [] c_List_Olist__update(c_List_Olist__update(A,B,C,D),B,E,D)=c_List_Olist__update(A,B,E,D).
% 48.27/48.34 ---> New Demodulator: 425 [new_demod,424] c_List_Olist__update(c_List_Olist__update(A,B,C,D),B,E,D)=c_List_Olist__update(A,B,E,D).
% 48.27/48.34 ** KEPT (pick-wt=15): 426 [] c_List_Oappend(c_List_Oappend(A,B,C),D,C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 48.27/48.34 ---> New Demodulator: 427 [new_demod,426] c_List_Oappend(c_List_Oappend(A,B,C),D,C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,427] c_List_Oappend(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(A,c_List_Oappend(B,C,D),D).
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,427] c_List_Oappend(A,c_List_Oappend(B,D,C),C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,427] c_List_Oappend(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(A,c_List_Oappend(B,C,D),D).
% 48.27/48.34 ** KEPT (pick-wt=9): 428 [] c_List_Ofiltermap(A,c_List_Olist_ONil(B),B,C)=c_List_Olist_ONil(C).
% 48.27/48.34 ** KEPT (pick-wt=8): 429 [] c_List_Ofilter(A,c_List_Olist_ONil(B),B)=c_List_Olist_ONil(B).
% 48.27/48.34 ---> New Demodulator: 430 [new_demod,429] c_List_Ofilter(A,c_List_Olist_ONil(B),B)=c_List_Olist_ONil(B).
% 48.27/48.34 ** KEPT (pick-wt=9): 431 [] c_List_Olist__update(c_List_Olist_ONil(A),B,C,A)=c_List_Olist_ONil(A).
% 48.27/48.34 ---> New Demodulator: 432 [new_demod,431] c_List_Olist__update(c_List_Olist_ONil(A),B,C,A)=c_List_Olist_ONil(A).
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,432] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,432] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 48.27/48.34 ** KEPT (pick-wt=8): 433 [] c_List_Oremove1(A,c_List_Olist_ONil(B),B)=c_List_Olist_ONil(B).
% 48.27/48.34 ---> New Demodulator: 434 [new_demod,433] c_List_Oremove1(A,c_List_Olist_ONil(B),B)=c_List_Olist_ONil(B).
% 48.27/48.34 ** KEPT (pick-wt=9): 435 [] c_Map_Omap__upds(A,B,c_List_Olist_ONil(C),D,C)=A.
% 48.27/48.34 ---> New Demodulator: 436 [new_demod,435] c_Map_Omap__upds(A,B,c_List_Olist_ONil(C),D,C)=A.
% 48.27/48.34 ** KEPT (pick-wt=9): 437 [] c_Map_Omap__upds(A,c_List_Olist_ONil(B),C,B,D)=A.
% 48.27/48.34 ---> New Demodulator: 438 [new_demod,437] c_Map_Omap__upds(A,c_List_Olist_ONil(B),C,B,D)=A.
% 48.27/48.34 ** KEPT (pick-wt=9): 439 [] c_List_Olist_Olist__case(A,B,c_List_Olist_ONil(C),D,C)=A.
% 48.27/48.34 ---> New Demodulator: 440 [new_demod,439] c_List_Olist_Olist__case(A,B,c_List_Olist_ONil(C),D,C)=A.
% 48.27/48.34 ** KEPT (pick-wt=8): 441 [] c_List_Orotate(A,c_List_Olist_ONil(B),B)=c_List_Olist_ONil(B).
% 48.27/48.34 ---> New Demodulator: 442 [new_demod,441] c_List_Orotate(A,c_List_Olist_ONil(B),B)=c_List_Olist_ONil(B).
% 48.27/48.34 ** KEPT (pick-wt=9): 443 [] c_List_Olist_ONil(A)=c_List_Omap(B,c_List_Olist_ONil(C),C,A).
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,393] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 48.27/48.34 ** KEPT (pick-wt=7): 444 [] c_List_Olistrelp(A,c_List_Olist_ONil(B),c_List_Olist_ONil(B),B).
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,384] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 48.27/48.34 ** KEPT (pick-wt=20): 446 [copy,445,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(A,B,C)),c_Lambda_Osubst(D,B,C))=c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,A),D),B,C).
% 48.27/48.34 ---> New Demodulator: 447 [new_demod,446] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(A,B,C)),c_Lambda_Osubst(D,B,C))=c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,A),D),B,C).
% 48.27/48.34 ** KEPT (pick-wt=17): 449 [copy,448,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(A,B)),c_Lambda_Olift(C,B))=c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,A),C),B).
% 48.27/48.34 ---> New Demodulator: 450 [new_demod,449] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(A,B)),c_Lambda_Olift(C,B))=c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,A),C),B).
% 48.27/48.34 ** KEPT (pick-wt=16): 451 [] c_Lambda_OdB_OdB__case(A,B,C,hAPP(hAPP(c_Lambda_OdB_OApp,D),E),F)=hAPP(hAPP(B,D),E).
% 48.27/48.34 ** KEPT (pick-wt=30): 453 [copy,452,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).
% 48.27/48.34 ---> New Demodulator: 454 [new_demod,453] 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).
% 48.27/48.34 ** KEPT (pick-wt=20): 456 [copy,455,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).
% 48.27/48.34 ---> New Demodulator: 457 [new_demod,456] 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).
% 48.27/48.34 ** KEPT (pick-wt=20): 459 [copy,458,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).
% 48.27/48.34 ---> New Demodulator: 460 [new_demod,459] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(A,B,C))
% 48.27/48.34 -------- PROOF --------
% 48.27/48.34 ,c_Lambda_Osubstn(D,B,C))=c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,A),D),B,C).
% 48.27/48.34 ** KEPT (pick-wt=10): 462 [copy,461,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.
% 48.27/48.34 ---> New Demodulator: 463 [new_demod,462] 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.
% 48.27/48.34 ** KEPT (pick-wt=20): 464 [] 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).
% 48.27/48.34 ** KEPT (pick-wt=21): 465 [] 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).
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,347] B=B.
% 48.27/48.34 ** KEPT (pick-wt=11): 466 [] c_Lambda_OdB_OdB__rec(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 48.27/48.34 ** KEPT (pick-wt=11): 467 [] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 48.27/48.34 ** KEPT (pick-wt=7): 468 [] c_Type_Otyping(A,c_Lambda_OdB_OVar(B),hAPP(A,B)).
% 48.27/48.34 ** KEPT (pick-wt=35): 469 [] 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).
% 48.27/48.34 ** KEPT (pick-wt=24): 470 [] 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).
% 48.27/48.34 ** KEPT (pick-wt=11): 472 [copy,471,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OAbs(A).
% 48.27/48.34 ---> New Demodulator: 473 [new_demod,472] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OAbs(A).
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,473] c_Lambda_OdB_OAbs(A)=c_Lambda_OdB_OAbs(A).
% 48.27/48.34 ** KEPT (pick-wt=17): 475 [copy,474,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,A),B),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=hAPP(hAPP(c_Lambda_OdB_OApp,A),B).
% 48.27/48.34 ---> New Demodulator: 476 [new_demod,475] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,A),B),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=hAPP(hAPP(c_Lambda_OdB_OApp,A),B).
% 48.27/48.34 ** KEPT (pick-wt=9): 477 [] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 48.27/48.34 ---> New Demodulator: 478 [new_demod,477] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 48.27/48.34 Following clause subsumed by 307 during input processing: 0 [demod,478] c_Lambda_OdB_OVar(A)=c_Lambda_OdB_OVar(A).
% 48.27/48.34 ** KEPT (pick-wt=5): 480 [copy,479,demod,478] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(v_n))).
% 48.27/48.34
% 48.27/48.34 ----> UNIT CONFLICT at 0.03 sec ----> 481 [binary,480.1,289.1] $F.
% 48.27/48.34
% 48.27/48.34 Length of proof is 1. Level of proof is 1.
% 48.27/48.34
% 48.27/48.34 ---------------- PROOF ----------------
% 48.27/48.34 % SZS status Unsatisfiable
% 48.27/48.34 % SZS output start Refutation
% See solution above
% 48.27/48.34 ------------ end of proof -------------
% 48.27/48.34
% 48.27/48.34
% 48.27/48.34 Search stopped by max_proofs option.
% 48.27/48.34
% 48.27/48.34
% 48.27/48.34 Search stopped by max_proofs option.
% 48.27/48.34
% 48.27/48.34 ============ end of search ============
% 48.27/48.34
% 48.27/48.34 -------------- statistics -------------
% 48.27/48.34 clauses given 0
% 48.27/48.34 clauses generated 18
% 48.27/48.34 clauses kept 369
% 48.27/48.34 clauses forward subsumed 64
% 48.27/48.34 clauses back subsumed 0
% 48.27/48.34 Kbytes malloced 8789
% 48.27/48.34
% 48.27/48.34 ----------- times (seconds) -----------
% 48.27/48.34 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 48.27/48.34 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 48.27/48.34 wall-clock time 48 (0 hr, 0 min, 48 sec)
% 48.27/48.34
% 48.27/48.34 That finishes the proof of the theorem.
% 48.27/48.34
% 48.27/48.34 Process 28085 finished Wed Jul 27 09:10:28 2022
% 48.27/48.34 Otter interrupted
% 48.27/48.34 PROOF FOUND
%------------------------------------------------------------------------------