TSTP Solution File: SCT169+6 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SCT169+6 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n013.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 13:12:38 EDT 2022
% Result : Unknown 12.20s 12.19s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT169+6 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 08:59:45 EDT 2022
% 0.12/0.34 % CPUTime :
% 12.20/12.13 ----- Otter 3.3f, August 2004 -----
% 12.20/12.13 The process was started by sandbox2 on n013.cluster.edu,
% 12.20/12.13 Wed Jul 27 08:59:45 2022
% 12.20/12.13 The command was "./otter". The process ID is 31757.
% 12.20/12.13
% 12.20/12.13 set(prolog_style_variables).
% 12.20/12.13 set(auto).
% 12.20/12.13 dependent: set(auto1).
% 12.20/12.13 dependent: set(process_input).
% 12.20/12.13 dependent: clear(print_kept).
% 12.20/12.13 dependent: clear(print_new_demod).
% 12.20/12.13 dependent: clear(print_back_demod).
% 12.20/12.13 dependent: clear(print_back_sub).
% 12.20/12.13 dependent: set(control_memory).
% 12.20/12.13 dependent: assign(max_mem, 12000).
% 12.20/12.13 dependent: assign(pick_given_ratio, 4).
% 12.20/12.13 dependent: assign(stats_level, 1).
% 12.20/12.13 dependent: assign(max_seconds, 10800).
% 12.20/12.13 clear(print_given).
% 12.20/12.13
% 12.20/12.13 formula_list(usable).
% 12.20/12.13 all A (A=A).
% 12.20/12.13 all X_b X_c X_a (ti(fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),combb(X_b,X_c,X_a))=combb(X_b,X_c,X_a)).
% 12.20/12.13 all X_a X_b X_c (ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c))=combc(X_a,X_b,X_c)).
% 12.20/12.13 all X_a X_b (ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b))=combk(X_a,X_b)).
% 12.20/12.13 all X_a X_b X_c (ti(fun(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c))),combs(X_a,X_b,X_c))=combs(X_a,X_b,X_c)).
% 12.20/12.13 all X_a (minus(X_a)->ti(fun(X_a,fun(X_a,X_a)),minus_minus(X_a))=minus_minus(X_a)).
% 12.20/12.13 all X_a (one(X_a)->ti(X_a,one_one(X_a))=one_one(X_a)).
% 12.20/12.13 all X_a (monoid_add(X_a)->ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a)).
% 12.20/12.13 all X_a (ab_semigroup_add(X_a)->ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a)).
% 12.20/12.13 all X_a (cancel_semigroup_add(X_a)->ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a)).
% 12.20/12.13 all X_a (zero(X_a)->ti(X_a,zero_zero(X_a))=zero_zero(X_a)).
% 12.20/12.13 all X_a (cl_HOL_Oe_qual(X_a)->ti(fun(X_a,fun(X_a,bool)),e_qual_e_qual(X_a))=e_qual_e_qual(X_a)).
% 12.20/12.13 all X_a (ti(X_a,undefined(X_a))=undefined(X_a)).
% 12.20/12.13 all X_a (number_ring(X_a)->ti(fun(int,X_a),number_number_of(X_a))=number_number_of(X_a)).
% 12.20/12.13 ti(fun(int,nat),number_number_of(nat))=number_number_of(nat).
% 12.20/12.13 all X_a (ring_1(X_a)->ti(fun(X_a,bool),ring_1_Ints(X_a))=ring_1_Ints(X_a)).
% 12.20/12.13 all X_a (ti(fun(X_a,fun(list(X_a),bool)),listMem(X_a))=listMem(X_a)).
% 12.20/12.13 all X_a (ti(fun(list(X_a),fun(list(X_a),list(X_a))),append(X_a))=append(X_a)).
% 12.20/12.13 all X_a (ti(fun(list(X_a),list(X_a)),butlast(X_a))=butlast(X_a)).
% 12.20/12.13 all X_a (ti(fun(list(X_a),bool),distinct(X_a))=distinct(X_a)).
% 12.20/12.13 all X_a (ti(fun(nat,fun(list(X_a),list(X_a))),drop(X_a))=drop(X_a)).
% 12.20/12.13 all X_a (ti(fun(fun(X_a,bool),fun(list(X_a),list(X_a))),dropWhile(X_a))=dropWhile(X_a)).
% 12.20/12.13 all X_b X_a (ti(fun(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a))),foldr(X_b,X_a))=foldr(X_b,X_a)).
% 12.20/12.13 all X_a (ti(fun(list(X_a),X_a),hd(X_a))=hd(X_a)).
% 12.20/12.13 all X_a (ti(fun(X_a,fun(list(X_a),list(X_a))),insert(X_a))=insert(X_a)).
% 12.20/12.13 all X_a (ti(fun(list(X_a),X_a),last(X_a))=last(X_a)).
% 12.20/12.13 all X_a (linorder(X_a)->ti(fun(list(X_a),bool),linorder_sorted(X_a))=linorder_sorted(X_a)).
% 12.20/12.13 all X_a (linorder(X_a)->ti(fun(fun(X_a,bool),list(X_a)),linord467138063of_set(X_a))=linord467138063of_set(X_a)).
% 12.20/12.13 all X_a (ti(fun(X_a,fun(list(X_a),list(X_a))),cons(X_a))=cons(X_a)).
% 12.20/12.13 all X_a (ti(list(X_a),nil(X_a))=nil(X_a)).
% 12.20/12.13 all X_a X_b (ti(fun(X_a,fun(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a))),list_case(X_a,X_b))=list_case(X_a,X_b)).
% 12.20/12.13 all X_a X_b (ti(fun(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a))),list_rec(X_a,X_b))=list_rec(X_a,X_b)).
% 12.20/12.13 all X_a (ti(fun(fun(X_a,nat),fun(list(X_a),nat)),list_size(X_a))=list_size(X_a)).
% 12.20/12.13 all X_a (ti(fun(fun(X_a,bool),fun(list(X_a),bool)),list_ex(X_a))=list_ex(X_a)).
% 12.20/12.13 all X_a (ti(fun(fun(X_a,bool),fun(list(X_a),bool)),list_ex1(X_a))=list_ex1(X_a)).
% 12.20/12.13 all X_a (ti(fun(list(X_a),fun(nat,fun(X_a,list(X_a)))),list_update(X_a))=list_update(X_a)).
% 12.20/12.13 all X_a (ti(fun(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool))),listrelp(X_a))=listrelp(X_a)).
% 12.20/12.13 all X_b X_a (ti(fun(fun(X_b,option(X_a)),fun(list(X_b),list(X_a))),map_filter(X_b,X_a))=map_filter(X_b,X_a)).
% 12.20/12.13 all X_b X_a (ti(fun(fun(X_b,list(X_a)),fun(list(X_b),list(X_a))),maps(X_b,X_a))=maps(X_b,X_a)).
% 12.20/12.13 all X_a (ti(fun(list(X_a),fun(X_a,bool)),member_1(X_a))=member_1(X_a)).
% 12.20/12.13 all X_a (ti(fun(list(X_a),fun(nat,X_a)),nth(X_a))=nth(X_a)).
% 12.20/12.13 all X_a (ti(fun(list(X_a),bool),null(X_a))=null(X_a)).
% 12.20/12.13 all X_a (ti(fun(nat,fun(X_a,list(X_a))),replicate(X_a))=replicate(X_a)).
% 12.20/12.13 all X_a (ti(fun(list(X_a),list(X_a)),rev(X_a))=rev(X_a)).
% 12.20/12.13 all X_a (ti(fun(list(X_a),list(X_a)),rotate1(X_a))=rotate1(X_a)).
% 12.20/12.13 all X_a (ti(fun(list(X_a),fun(list(X_a),list(X_a))),splice(X_a))=splice(X_a)).
% 12.20/12.13 all X_a (ti(fun(list(X_a),fun(fun(nat,bool),list(X_a))),sublist(X_a))=sublist(X_a)).
% 12.20/12.13 all X_a (ti(fun(nat,fun(list(X_a),list(X_a))),take(X_a))=take(X_a)).
% 12.20/12.13 all X_a (ti(fun(fun(X_a,bool),fun(list(X_a),list(X_a))),takeWhile(X_a))=takeWhile(X_a)).
% 12.20/12.13 all X_a (ti(fun(list(X_a),list(X_a)),tl(X_a))=tl(X_a)).
% 12.20/12.13 ti(fun(nat,nat),suc)=suc.
% 12.20/12.13 all X_a (ti(fun(list(X_a),nat),size_size(list(X_a)))=size_size(list(X_a))).
% 12.20/12.13 all X_b (bot(X_b)->ti(X_b,bot_bot(X_b))=bot_bot(X_b)).
% 12.20/12.13 all X_a (ord(X_a)->ti(fun(X_a,fun(X_a,bool)),ord_less(X_a))=ord_less(X_a)).
% 12.20/12.13 all X_a (ordere236663937imp_le(X_a)->ti(fun(X_a,fun(X_a,X_a)),ord_max(X_a))=ord_max(X_a)).
% 12.20/12.13 all X_a (linorder(X_a)->ti(fun(X_a,fun(X_a,X_a)),ord_max(X_a))=ord_max(X_a)).
% 12.20/12.13 all X_a (ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a))=collect(X_a)).
% 12.20/12.13 ti(bool,fFalse)=fFalse.
% 12.20/12.13 ti(fun(bool,bool),fNot)=fNot.
% 12.20/12.13 ti(bool,fTrue)=fTrue.
% 12.20/12.13 ti(fun(bool,fun(bool,bool)),fconj)=fconj.
% 12.20/12.13 all X_a (ti(fun(X_a,fun(X_a,bool)),fe_qual(X_a))=fe_qual(X_a)).
% 12.20/12.13 all X_a X_c B_1_1 B_2_1 (hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1)=hAPP(X_a,X_c,B_1_1,B_2_1)).
% 12.20/12.13 all X_a X_c B_1_1 B_2_1 (hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1))=hAPP(X_a,X_c,B_1_1,B_2_1)).
% 12.20/12.13 all X_c X_a B_1_1 B_2_1 (ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1))=hAPP(X_a,X_c,B_1_1,B_2_1)).
% 12.20/12.13 all B_1_1 (hBOOL(ti(bool,B_1_1))<->hBOOL(B_1_1)).
% 12.20/12.13 all X_a (ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a))=member(X_a)).
% 12.20/12.13 ti(arrow_490897120le_alt,a)=a.
% 12.20/12.13 ti(arrow_490897120le_alt,b)=b.
% 12.20/12.13 exists A_4 B_2 C hBOOL(hAPP(list(arrow_490897120le_alt),bool,distinct(arrow_490897120le_alt),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),A_4),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),B_2),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),C),nil(arrow_490897120le_alt)))))).
% 12.20/12.13 all X_a hBOOL(hAPP(list(X_a),bool,distinct(X_a),nil(X_a))).
% 12.20/12.13 all X_a A_5 List_4 (nil(X_a)!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_5),List_4)).
% 12.20/12.13 all X_a A_5 List_4 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_5),List_4)!=nil(X_a)).
% 12.20/12.13 all X_a Xs_1 (Xs_1!=nil(X_a)<-> (exists Y_1 Ys_2 (Xs_1=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_2)))).
% 12.20/12.13 all X_a Y (Y!=nil(X_a)-> -(all A_4 List_3 (Y!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_4),List_3)))).
% 12.20/12.13 all X_a Xs X (Xs!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)).
% 12.20/12.13 all X_a X Xs (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)!=Xs).
% 12.20/12.13 all X_a Aa List A_3 List_2 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Aa),List)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_3),List_2)<->ti(X_a,Aa)=ti(X_a,A_3)&List=List_2).
% 12.20/12.13 all X_a V Va (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),V),Va)),nil(X_a))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),V),Va)).
% 12.20/12.13 all X_a X (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X),nil(X_a))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a))).
% 12.20/12.13 all X_a P_1 Xs_1 (Xs_1!=nil(X_a)-> ((all X_2 hBOOL(hAPP(list(X_a),bool,P_1,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),nil(X_a)))))-> ((all X_2 Xs_2 (Xs_2!=nil(X_a)-> (hBOOL(hAPP(list(X_a),bool,P_1,Xs_2))->hBOOL(hAPP(list(X_a),bool,P_1,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2))))))->hBOOL(hAPP(list(X_a),bool,P_1,Xs_1))))).
% 12.20/12.14 all X_a Xs (Xs!=nil(X_a)-> (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs))->hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs))))).
% 12.20/12.14 all X_a (hAPP(list(X_a),list(X_a),butlast(X_a),nil(X_a))=nil(X_a)).
% 12.20/12.14 all X_a X Xs (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs))->hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X),Xs)))).
% 12.20/12.14 all X_a X Xs Y Ys (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Ys))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),Xs),Ys)))).
% 12.20/12.14 all X_a Xs (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),Xs),nil(X_a))=Xs).
% 12.20/12.14 all X_a Ys (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),nil(X_a)),Ys)=Ys).
% 12.20/12.14 all X_a X Xs ((Xs=nil(X_a)->hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=nil(X_a))& (Xs!=nil(X_a)->hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)))).
% 12.20/12.14 all X_b X_a F1 F2 (hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a)),list_case(X_a,X_b),F1),F2),nil(X_b))=ti(X_a,F1)).
% 12.20/12.14 all X_b X_a F1 F2 Aa List (hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a)),list_case(X_a,X_b),F1),F2),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Aa),List))=hAPP(list(X_b),X_a,hAPP(X_b,fun(list(X_b),X_a),F2,Aa),List)).
% 12.20/12.14 all X_b X_a F1 F2 (hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a)),list_rec(X_a,X_b),F1),F2),nil(X_b))=ti(X_a,F1)).
% 12.20/12.14 all X_b X_a F1 F2 Aa List (hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a)),list_rec(X_a,X_b),F1),F2),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Aa),List))=hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(X_b,fun(list(X_b),fun(X_a,X_a)),F2,Aa),List),hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a)),list_rec(X_a,X_b),F1),F2),List))).
% 12.20/12.14 all X_a Xs_1 (Xs_1=nil(X_a)<->hBOOL(hAPP(list(X_a),bool,null(X_a),Xs_1))).
% 12.20/12.14 all X_a Xs_1 (hBOOL(hAPP(list(X_a),bool,null(X_a),Xs_1))<->Xs_1=nil(X_a)).
% 12.20/12.14 all X_b hBOOL(hAPP(list(X_b),bool,null(X_b),nil(X_b))).
% 12.20/12.14 all X_a X Xs (-hBOOL(hAPP(list(X_a),bool,null(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)))).
% 12.20/12.14 all X_a Xs X (hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a))))=Xs).
% 12.20/12.14 all X_b X_a F (hAPP(list(X_b),list(X_a),hAPP(fun(X_b,list(X_a)),fun(list(X_b),list(X_a)),maps(X_b,X_a),F),nil(X_b))=nil(X_a)).
% 12.20/12.14 all X_a (linorder(X_a)-> (all X hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a)))))).
% 12.20/12.14 all X_a (linorder(X_a)->hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),nil(X_a)))).
% 12.20/12.14 all X_a Xs Ys Zs_2 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys)),Zs_2)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),Zs_2))).
% 12.20/12.14 all X_a Xs_1 Ys_1 Zs Ts (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),Ts)<-> (exists Us_1 (Xs_1=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),Us_1)&hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us_1),Ys_1)=Ts|hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Us_1)=Zs&Ys_1=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us_1),Ts)))).
% 12.20/12.14 all X_a Xs_1 Ys_1 Zs (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Zs)<->Ys_1=Zs).
% 12.20/12.14 all X_a Ys_1 Xs_1 Zs (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),Xs_1)<->Ys_1=Zs).
% 12.20/12.14 all X_a Ys Us Xs Xs1 Zs_2 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Xs1)=Zs_2-> (Ys=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs1),Us)->hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs_2),Us))).
% 12.20/12.14 all X_b X_a F X_1 Xs_1 (hAPP(list(X_b),list(X_a),hAPP(fun(X_b,list(X_a)),fun(list(X_b),list(X_a)),maps(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X_1),Xs_1))=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_b,list(X_a),F,X_1)),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,list(X_a)),fun(list(X_b),list(X_a)),maps(X_b,X_a),F),Xs_1))).
% 12.20/12.14 all X_a X Xs Ys (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),Ys)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))).
% 12.20/12.14 all X_a Xs Zs_2 X Xs1 Ys (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs1)=Ys-> (Xs=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs1),Zs_2)->hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),Zs_2))).
% 12.20/12.14 all X_a Ys (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),nil(X_a)),Ys)=Ys).
% 12.20/12.14 all X_a Xs_1 Ys_1 (nil(X_a)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)<->Xs_1=nil(X_a)&Ys_1=nil(X_a)).
% 12.20/12.14 all X_a Xs (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),nil(X_a))=Xs).
% 12.20/12.14 all X_a Xs_1 Ys_1 (Xs_1=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)<->Ys_1=nil(X_a)).
% 12.20/12.14 all X_a Ys_1 Xs_1 (Ys_1=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)<->Xs_1=nil(X_a)).
% 12.20/12.14 all X_a Xs_1 Ys_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)=nil(X_a)<->Xs_1=nil(X_a)&Ys_1=nil(X_a)).
% 12.20/12.14 all X_a Xs_1 Ys_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)=Xs_1<->Ys_1=nil(X_a)).
% 12.20/12.14 all X_a Xs_1 Ys_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)=Ys_1<->Xs_1=nil(X_a)).
% 12.20/12.14 all X_a Xs Ys (Xs=Ys->Xs=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),nil(X_a)),Ys)).
% 12.20/12.14 all X_a Ys_1 Zs X_1 Xs_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)<->Ys_1=nil(X_a)&Zs=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)| (exists Ys_3 (Ys_1=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Ys_3)&hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),Zs)=Xs_1))).
% 12.20/12.14 all X_a X_1 Xs_1 Ys_1 Zs (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs)<->Ys_1=nil(X_a)&hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)=Zs| (exists Ys_3 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Ys_3)=Ys_1&Xs_1=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),Zs)))).
% 12.20/12.14 all X_a Xs_1 X_1 Ys_1 Y_2 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)))=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),nil(X_a)))<->Xs_1=Ys_1&ti(X_a,X_1)=ti(X_a,Y_2)).
% 12.20/12.14 all X_a Xs Ys ((Ys=nil(X_a)->hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),list(X_a),butlast(X_a),Xs))& (Ys!=nil(X_a)->hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),butlast(X_a),Ys)))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all Xs (Xs!=nil(X_a)-> (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs))->hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs))))))).
% 12.20/12.14 all X_a Xs_1 P_1 (hBOOL(hAPP(list(X_a),bool,P_1,nil(X_a)))-> ((all X_2 Xs_2 (hBOOL(hAPP(list(X_a),bool,P_1,Xs_2))->hBOOL(hAPP(list(X_a),bool,P_1,hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),nil(X_a)))))))->hBOOL(hAPP(list(X_a),bool,P_1,Xs_1)))).
% 12.20/12.14 all X_a Xs (Xs!=nil(X_a)-> -(all Ys_2 Y_1 (Xs!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),nil(X_a)))))).
% 12.20/12.14 all X_a Xs_1 (hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),e_qual_e_qual(list(X_a)),Xs_1),nil(X_a)))<->hBOOL(hAPP(list(X_a),bool,null(X_a),Xs_1))).
% 12.20/12.14 all X_a Xs_1 X_1 Ys_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)))=Ys_1<->Ys_1!=nil(X_a)&hAPP(list(X_a),list(X_a),butlast(X_a),Ys_1)=Xs_1&hAPP(list(X_a),X_a,last(X_a),Ys_1)=ti(X_a,X_1)).
% 12.20/12.14 all X_a Xs (Xs!=nil(X_a)->hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,last(X_a),Xs)),nil(X_a)))=Xs).
% 12.20/12.14 all X_b X_a X Xs (hAPP(list(X_a),list(X_a),rotate1(X_a),nil(X_a))=nil(X_a)&hAPP(list(X_b),list(X_b),rotate1(X_b),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X),Xs))=hAPP(list(X_b),list(X_b),hAPP(list(X_b),fun(list(X_b),list(X_b)),append(X_b),Xs),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X),nil(X_b)))).
% 12.20/12.14 all X_a Xs X (hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a))))=ti(X_a,X)).
% 12.20/12.14 all X_a Ws (-hBOOL(hAPP(list(X_a),bool,distinct(X_a),Ws))-> (exists Xs_2 Ys_2 Zs_1 Y_1 (Ws=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_2),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),nil(X_a))),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),nil(X_a))),Zs_1))))))).
% 12.20/12.14 all X_a I_1 X (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),I_1),X)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a)))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),I_1),X))).
% 12.20/12.14 all X_a X Xs (hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a)))).
% 12.20/12.14 all X_a Xs_1 Ys_1 (hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)=hAPP(list(X_a),list(X_a),rev(X_a),Ys_1)<->Xs_1=Ys_1).
% 12.20/12.14 all X_a Xs_1 Ys_1 (hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)=Ys_1<->Xs_1=hAPP(list(X_a),list(X_a),rev(X_a),Ys_1)).
% 12.20/12.14 all X_a N X (hAPP(list(X_a),list(X_a),rev(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X))=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)).
% 12.20/12.14 all X_a Xs (hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs))=Xs).
% 12.20/12.14 all X_a X_1 Y_2 (hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),e_qual_e_qual(list(X_a)),X_1),Y_2))<->X_1=Y_2).
% 12.20/12.14 all X_a Xs_1 (hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)=nil(X_a)<->Xs_1=nil(X_a)).
% 12.20/12.14 all X_a Xs_1 (nil(X_a)=hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)<->Xs_1=nil(X_a)).
% 12.20/12.14 all X_a (hAPP(list(X_a),list(X_a),rev(X_a),nil(X_a))=nil(X_a)).
% 12.20/12.14 all X_a Xs Ys (hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Ys)),hAPP(list(X_a),list(X_a),rev(X_a),Xs))).
% 12.20/12.14 all X_a Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)))<->hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1))).
% 12.20/12.14 all X_a N X K (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),K),X))=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),K),X)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X))).
% 12.20/12.14 all X_a Xs_1 (hAPP(list(X_a),list(X_a),rotate1(X_a),Xs_1)=nil(X_a)<->Xs_1=nil(X_a)).
% 12.20/12.14 all X_a X_b F G ((all X_2 (hAPP(X_a,X_b,F,X_2)=hAPP(X_a,X_b,G,X_2)))->ti(fun(X_a,X_b),F)=ti(fun(X_a,X_b),G)).
% 12.20/12.14 all X_a X_1 A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))<->hBOOL(hAPP(X_a,bool,A_1,X_1))).
% 12.20/12.14 all X_a P_1 (hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)=ti(fun(X_a,bool),P_1)).
% 12.20/12.14 all X_a Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),rotate1(X_a),Xs_1)))<->hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1))).
% 12.20/12.14 all X_a X_1 Xs_1 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))=hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)<->Xs_1=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))).
% 12.20/12.14 all X_a Xs_1 X_1 (hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))<->Xs_1=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))).
% 12.20/12.14 all X_a N X Xs (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)),Xs))).
% 12.20/12.14 all X_a X Xs (Xs=nil(X_a)->hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=ti(X_a,X)).
% 12.20/12.14 all X_a X Xs (Xs!=nil(X_a)->hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),X_a,last(X_a),Xs)).
% 12.20/12.14 all X_a X Xs ((Xs=nil(X_a)->hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=ti(X_a,X))& (Xs!=nil(X_a)->hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),X_a,last(X_a),Xs))).
% 12.20/12.14 all X_a Xs Ys ((Ys=nil(X_a)->hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),X_a,last(X_a),Xs))& (Ys!=nil(X_a)->hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),X_a,last(X_a),Ys))).
% 12.20/12.14 all X_a Xs Ys (Ys!=nil(X_a)->hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),X_a,last(X_a),Ys)).
% 12.20/12.14 all X_a Xs Ys (Ys=nil(X_a)->hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),X_a,last(X_a),Xs)).
% 12.20/12.14 all X_a Xs_1 Y_2 Ys_1 (hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_1)<->Xs_1=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Ys_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),nil(X_a)))).
% 12.20/12.14 all X_a Xs (Xs!=nil(X_a)->hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs))=hAPP(list(X_a),X_a,hd(X_a),Xs)).
% 12.20/12.14 all X_a Xs (Xs!=nil(X_a)->hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs))=hAPP(list(X_a),X_a,last(X_a),Xs)).
% 12.20/12.14 all X_a (cl_HOL_Oe_qual(X_a)->e_qual_e_qual(X_a)=fe_qual(X_a)).
% 12.20/12.14 all X_a (cl_HOL_Oe_qual(X_a)-> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),e_qual_e_qual(X_a),X),X)))).
% 12.20/12.14 all X_a (cl_HOL_Oe_qual(X_a)-> (all X_1 Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),e_qual_e_qual(X_a),X_1),Y_2))<->ti(X_a,X_1)=ti(X_a,Y_2)))).
% 12.20/12.14 all X_a (cl_HOL_Oe_qual(X_a)->fe_qual(X_a)=e_qual_e_qual(X_a)).
% 12.20/12.14 all X_a Ys Xs ((Xs=nil(X_a)->hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),X_a,hd(X_a),Ys))& (Xs!=nil(X_a)->hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),X_a,hd(X_a),Xs))).
% 12.20/12.14 all X_a Ys Xs (Xs!=nil(X_a)->hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),X_a,hd(X_a),Xs)).
% 12.20/12.14 all X_a Xs (Xs!=nil(X_a)->hAPP(list(X_a),list(X_a),rotate1(X_a),Xs)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),tl(X_a),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,hd(X_a),Xs)),nil(X_a)))).
% 12.20/12.14 all X_a X Xs (hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=Xs).
% 12.20/12.14 all X_a (hAPP(list(X_a),list(X_a),tl(X_a),nil(X_a))=nil(X_a)).
% 12.20/12.14 all X_a X Xs (hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=ti(X_a,X)).
% 12.20/12.14 all X_a Xs (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs))->hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),tl(X_a),Xs)))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all Xs (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs))->hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),tl(X_a),Xs)))))).
% 12.20/12.14 all X_a Ys Xs (Xs!=nil(X_a)->hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),tl(X_a),Xs)),Ys)).
% 12.20/12.14 all X_a P_1 Xs_1 (hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)!=nil(X_a)-> -hBOOL(hAPP(X_a,bool,P_1,hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1))))).
% 12.20/12.14 all X_a Y (-hBOOL(hAPP(X_a,bool,hAPP(list(X_a),fun(X_a,bool),member_1(X_a),nil(X_a)),Y))).
% 12.20/12.14 all X_a P_1 (-hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex1(X_a),P_1),nil(X_a)))).
% 12.20/12.14 all X_a X Xs hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),X),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))).
% 12.20/12.14 all X_a X_1 Xs_1 Y_2 (hBOOL(hAPP(X_a,bool,hAPP(list(X_a),fun(X_a,bool),member_1(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),Y_2))<->ti(X_a,X_1)=ti(X_a,Y_2)|hBOOL(hAPP(X_a,bool,hAPP(list(X_a),fun(X_a,bool),member_1(X_a),Xs_1),Y_2))).
% 12.20/12.14 all X_a Y X Xs (hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),X),Xs))->hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),X),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Xs)))).
% 12.20/12.14 all X_a X N (N!=zero_zero(nat)->hAPP(list(X_a),X_a,hd(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X))=ti(X_a,X)).
% 12.20/12.14 all X_a X N (N!=zero_zero(nat)->hAPP(list(X_a),X_a,last(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X))=ti(X_a,X)).
% 12.20/12.14 all X_a M_1 X_1 N_2 Y_2 (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),M_1),X_1)=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),Y_2)<->M_1=N_2& (M_1!=zero_zero(nat)->ti(X_a,X_1)=ti(X_a,Y_2))).
% 12.20/12.14 all X_a Xs_1 P_1 X_1 ((hBOOL(hAPP(X_a,bool,P_1,X_1))->hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))=hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1))& (-hBOOL(hAPP(X_a,bool,P_1,X_1))->hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))).
% 12.20/12.14 all X_a P_1 (hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),nil(X_a))=nil(X_a)).
% 12.20/12.14 all X_a P_1 Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1))->hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all P_1 Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1))->hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)))))).
% 12.20/12.14 all X_a X (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),zero_zero(nat)),X)=nil(X_a)).
% 12.20/12.14 all X_a N_2 X_1 (nil(X_a)=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),X_1)<->N_2=zero_zero(nat)).
% 12.20/12.14 all X_a N_2 X_1 (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),X_1)=nil(X_a)<->N_2=zero_zero(nat)).
% 12.20/12.14 all X_a X_1 A_1 ((hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),A_1))->hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))),A_1)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)))& (-hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),A_1))->hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))),A_1)=nil(X_a))).
% 12.20/12.14 all X_a P_1 Xs_1 Y_2 Ys_1 (hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_1)<->Xs_1=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_1))& -hBOOL(hAPP(X_a,bool,P_1,Y_2))).
% 12.20/12.14 all X_a Fa (hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),Fa),nil(X_a))=zero_zero(nat)).
% 12.20/12.14 all X_a A1 A2 (hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),A1),A2))<-> (exists X_2 Xs_2 (ti(X_a,A1)=ti(X_a,X_2)&A2=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2)))| (exists X_2 Xs_2 Y_1 (ti(X_a,A1)=ti(X_a,X_2)&A2=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Xs_2)&hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),X_2),Xs_2))))).
% 12.20/12.14 all X_a (zero(X_a)-> (all X_1 (zero_zero(X_a)=ti(X_a,X_1)<->ti(X_a,X_1)=zero_zero(X_a)))).
% 12.20/12.14 all X_a Xs (Xs!=nil(X_a)->hAPP(list(X_a),X_a,hd(X_a),Xs)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),zero_zero(nat))).
% 12.20/12.14 all X_a P_1 (hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),nil(X_a))=nil(X_a)).
% 12.20/12.14 all X_a P_1 Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1))->hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all P_1 Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1))->hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)))))).
% 12.20/12.14 all X_a A_1 (hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),nil(X_a)),A_1)=nil(X_a)).
% 12.20/12.14 all X_a I_4 Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1))->hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),Xs_1),I_4)))).
% 12.20/12.14 all X_a X Xs (hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),zero_zero(nat))=ti(X_a,X)).
% 12.20/12.14 all X_a Xs_1 P_1 X_1 ((hBOOL(hAPP(X_a,bool,P_1,X_1))->hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)))& (-hBOOL(hAPP(X_a,bool,P_1,X_1))->hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))=nil(X_a))).
% 12.20/12.14 all X_a Xs_1 L_1 P_1 X_1 (-hBOOL(hAPP(X_a,bool,P_1,X_1))->hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),L_1)))=hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)).
% 12.20/12.14 all X_a P_1 Xs_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1))=Xs_1).
% 12.20/12.14 all X_a Xs X Ys (hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Ys))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))=ti(X_a,X)).
% 12.20/12.14 all X_a (linorder(X_a)-> (all Y_2 Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)))-> (Xs_1=nil(X_a)->hAPP(X_a,X_a,hAPP(list(X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(list(X_a),fun(X_a,X_a)),foldr(X_a,X_a),ord_max(X_a)),Xs_1),Y_2)=ti(X_a,Y_2))& (Xs_1!=nil(X_a)->hAPP(X_a,X_a,hAPP(list(X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(list(X_a),fun(X_a,X_a)),foldr(X_a,X_a),ord_max(X_a)),Xs_1),Y_2)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),zero_zero(nat))),Y_2))))).
% 12.20/12.14 all X_b X_a Xs_1 Ys_1 P_1 (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,nil(X_a)),nil(X_b)))-> ((all X_2 Xs_2 hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2)),nil(X_b))))-> ((all Y_1 Ys_2 hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,nil(X_a)),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Y_1),Ys_2))))-> ((all X_2 Xs_2 Y_1 Ys_2 (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,Xs_2),Ys_2))->hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2)),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Y_1),Ys_2)))))->hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,Xs_1),Ys_1)))))).
% 12.20/12.14 all X_b X_a F (hAPP(list(X_b),list(X_a),hAPP(fun(X_b,option(X_a)),fun(list(X_b),list(X_a)),map_filter(X_b,X_a),F),nil(X_b))=nil(X_a)).
% 12.20/12.14 all X_a R_1 hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),nil(X_a)),nil(X_a))).
% 12.20/12.14 all X_a Xs_1 Ys_1 R_1 X_1 Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,X_1),Y_2))-> (hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),Xs_1),Ys_1))->hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_1))))).
% 12.20/12.14 all X_a Xs_1 (hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),Xs_1),bot_bot(fun(nat,bool)))=nil(X_a)).
% 12.20/12.14 all X_a Xs Ys (hAPP(list(X_a),nat,size_size(list(X_a)),Xs)!=hAPP(list(X_a),nat,size_size(list(X_a)),Ys)->Xs!=Ys).
% 12.20/12.14 all X_a Xs (hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),rev(X_a),Xs))=hAPP(list(X_a),nat,size_size(list(X_a)),Xs)).
% 12.20/12.14 all X_a N X (hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X))=N).
% 12.20/12.14 all X_a Xs (hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),rotate1(X_a),Xs))=hAPP(list(X_a),nat,size_size(list(X_a)),Xs)).
% 12.20/12.14 all X_a X_b F X_1 Xs_1 Aa (hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X_1),Xs_1)),Aa)=hAPP(X_a,X_a,hAPP(X_b,fun(X_a,X_a),F,X_1),hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),Xs_1),Aa))).
% 12.20/12.14 all X_a X_b F Aa (hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),nil(X_b)),Aa)=ti(X_a,Aa)).
% 12.20/12.14 all X_a X_b F Xs_1 Ys_1 Aa (hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(list(X_b),fun(list(X_b),list(X_b)),append(X_b),Xs_1),Ys_1)),Aa)=hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),Xs_1),hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),Ys_1),Aa))).
% 12.20/12.14 all X_a Xs_1 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)=zero_zero(nat)<->Xs_1=nil(X_a)).
% 12.20/12.14 all X_a (hAPP(list(X_a),nat,size_size(list(X_a)),nil(X_a))=zero_zero(nat)).
% 12.20/12.14 all X_a X_b P_1 Xs_1 Ys_1 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)=hAPP(list(X_b),nat,size_size(list(X_b)),Ys_1)-> (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,nil(X_a)),nil(X_b)))-> ((all X_2 Xs_2 Y_1 Ys_2 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_2)=hAPP(list(X_b),nat,size_size(list(X_b)),Ys_2)-> (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,Xs_2),Ys_2))->hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2)),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Y_1),Ys_2))))))->hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,Xs_1),Ys_1))))).
% 12.20/12.14 all X_a Aa (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),bot_bot(fun(X_a,bool))))).
% 12.20/12.14 all X_a X_b (bot(X_b)-> (all X_2 (hAPP(X_a,X_b,bot_bot(fun(X_a,X_b)),X_2)=bot_bot(X_b)))).
% 12.20/12.14 all X_b X_a (bot(X_a)-> (all X_1 (hAPP(X_b,X_a,bot_bot(fun(X_b,X_a)),X_1)=bot_bot(X_a)))).
% 12.20/12.14 all X_a N exists Xs_2 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_2)=N).
% 12.20/12.14 all X_a R_1 A1 A2 (hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),A1),A2))<->A1=nil(X_a)&A2=nil(X_a)| (exists X_2 Y_1 Xs_2 Ys_2 (A1=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2)&A2=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_2)&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,X_2),Y_1))&hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),Xs_2),Ys_2))))).
% 12.20/12.14 all X_a Aa A_1 (ti(fun(X_a,bool),A_1)=bot_bot(fun(X_a,bool))-> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),A_1))).
% 12.20/12.14 all X_a P_1 (hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)=bot_bot(fun(X_a,bool))<-> (all X_2 (-hBOOL(hAPP(X_a,bool,P_1,X_2))))).
% 12.20/12.14 all X_a C_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),bot_bot(fun(X_a,bool))))).
% 12.20/12.14 all X_a P_1 (bot_bot(fun(X_a,bool))=hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)<-> (all X_2 (-hBOOL(hAPP(X_a,bool,P_1,X_2))))).
% 12.20/12.14 all X_a A_1 ((exists X_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)))<->ti(fun(X_a,bool),A_1)!=bot_bot(fun(X_a,bool))).
% 12.20/12.14 all X_a A_1 ((all X_2 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))))<->ti(fun(X_a,bool),A_1)=bot_bot(fun(X_a,bool))).
% 12.20/12.14 all X_a (bot_bot(fun(X_a,bool))=hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(bool,fun(X_a,bool),combk(bool,X_a),fFalse))).
% 12.20/12.14 all X_a A_1 ((all Y_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1))))->ti(fun(X_a,bool),A_1)=bot_bot(fun(X_a,bool))).
% 12.20/12.14 all X_a (linorder(X_a)->hAPP(fun(X_a,bool),list(X_a),linord467138063of_set(X_a),bot_bot(fun(X_a,bool)))=nil(X_a)).
% 12.20/12.14 all X_a (linorder(X_a)-> (all X Y Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z))))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all A_2 B_1 C_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_1)),C_2)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_1),C_2))))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all X Y Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z))))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all B_1 A_2 C_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),C_2))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_1),C_2))))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all A_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),A_2)=ti(X_a,A_2)))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all A_2 B_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_1)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_1),A_2)))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all X Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),X)))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all A_2 B_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_1)))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all X Y (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all X (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),X)=ti(X_a,X)))).
% 12.20/12.14 all X_a P_1 Xs_1 (hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))),Xs_1)).
% 12.20/12.14 all X_a P_1 Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))-> -hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)))))).
% 12.20/12.14 all X_a J_1 P_1 Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))))->hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)),J_1)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),J_1)).
% 12.20/12.14 all X_a Xs X Ys Y (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Ys))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),Y)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Ys))).
% 12.20/12.14 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),zero_zero(nat)),N)=N).
% 12.20/12.14 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))).
% 12.20/12.14 all X_a Xs I_1 X Y (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),I_1),Y)=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),Y)).
% 12.20/12.14 all X_a Xs X X_3 I_1 I_3 (I_1!=I_3->hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),I_3),X_3)=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_3),X_3)),I_1),X)).
% 12.20/12.14 all P_1 M_1 N_2 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),M_1)))-> ((M_1=N_2->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),M_1)))-> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),M_1)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),M_1))))).
% 12.20/12.14 all S T_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3))->S!=T_3).
% 12.20/12.14 all N M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M))->M!=N).
% 12.20/12.14 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))).
% 12.20/12.14 all X Y (X!=Y-> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X)))).
% 12.20/12.14 all M_1 N_2 (M_1!=N_2<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))).
% 12.20/12.14 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))).
% 12.20/12.14 all N (N!=zero_zero(nat)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))).
% 12.20/12.14 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))->N!=zero_zero(nat)).
% 12.20/12.14 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))).
% 12.20/12.14 all N_2 (N_2!=zero_zero(nat)<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2))).
% 12.20/12.14 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))).
% 12.20/12.14 all X_a (preorder(X_a)-> (all X (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X))))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all X_1 Y_2 (ti(X_a,X_1)!=ti(X_a,Y_2)<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1))))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all X_1 Y_2 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1))|ti(X_a,X_1)=ti(X_a,Y_2)))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|ti(X_a,X)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all Y_2 X_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1))-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))<->ti(X_a,X_1)=ti(X_a,Y_2))))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all X Y (ti(X_a,X)!=ti(X_a,Y)-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))).
% 12.20/12.14 all X_a (order(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))->X!=Y))).
% 12.20/12.14 all X_a (preorder(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))).
% 12.20/12.14 all X_a (preorder(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))).
% 12.20/12.14 all X_a (order(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))->X!=Y))).
% 12.20/12.14 all X_a (order(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))->Y!=X))).
% 12.20/12.14 all X_a (preorder(X_a)-> (all P_1 X_1 Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1))->hBOOL(P_1))))).
% 12.20/12.14 all X_a (preorder(X_a)-> (all A_2 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))))).
% 12.20/12.14 all X_a (order(X_a)-> (all B_1 A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))))).
% 12.20/12.14 all X_a (ord(X_a)-> (all C_2 A_2 B_1 (A_2=B_1-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C_2)))))).
% 12.20/12.14 all X_a (order(X_a)-> (all C_2 A_2 B_1 (A_2=B_1-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_2),B_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_2),A_2)))))).
% 12.20/12.14 all X_a (ord(X_a)-> (all C_2 A_2 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))-> (B_1=C_2->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C_2)))))).
% 12.20/12.14 all X_a (order(X_a)-> (all C_2 B_1 A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))-> (B_1=C_2->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_2),A_2)))))).
% 12.20/12.14 all X_a (preorder(X_a)-> (all Z X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z)))))).
% 12.20/12.14 all X_a (order(X_a)-> (all Z Y X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X)))))).
% 12.20/12.14 all X_a (preorder(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all X Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))-> (ti(X_a,X)!=ti(X_a,Y)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))).
% 12.20/12.14 all X_a Ys X I_1 Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))->hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys)),I_1),X)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),Ys)).
% 12.20/12.14 all X_a X J I_1 Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))-> (I_1=J->hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),J)=ti(X_a,X))& (I_1!=J->hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),J)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),J))).
% 12.20/12.14 all X_a X_1 I Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))-> (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs_1),I),X_1)=Xs_1<->hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I)=ti(X_a,X_1))).
% 12.20/12.14 all X_a X I_1 Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))->hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),I_1)=ti(X_a,X)).
% 12.20/12.14 all X_a N Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))->hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))=hAPP(list(X_a),X_a,last(X_a),Xs)).
% 12.20/12.14 all X_a (bot(X_a)-> (all A_2 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),bot_bot(X_a)))))).
% 12.20/12.14 all X_a (bot(X_a)-> (all Aa (ti(X_a,Aa)!=bot_bot(X_a)<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),bot_bot(X_a)),Aa))))).
% 12.20/12.14 all X_a Xs (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),zero_zero(nat)),Xs)=Xs).
% 12.20/12.14 all X_a N (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),nil(X_a))=nil(X_a)).
% 12.20/12.14 all X_a (linorder(X_a)-> (all Z_1 X_1 Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y_2))))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all X_1 Y_2 Z_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_2)),Z_1))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z_1))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),Z_1))))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all B_1 X A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_1)))))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all A_2 X B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),B_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_1)))))).
% 12.20/12.14 all X_a I_1 Xs (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs))->hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_1),Xs)))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all N Xs (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs))->hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)))))).
% 12.20/12.14 all X_a Xs_1 K_1 X_1 (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs_1),K_1),X_1)=nil(X_a)<->Xs_1=nil(X_a)).
% 12.20/12.14 all X_a I_1 V (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),nil(X_a)),I_1),V)=nil(X_a)).
% 12.20/12.14 all X_a I_1 Y (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),nil(X_a)),I_1),Y)=nil(X_a)).
% 12.20/12.14 all X_a Xs I_1 X (hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X))=hAPP(list(X_a),nat,size_size(list(X_a)),Xs)).
% 12.20/12.14 all X_a Xs I_1 (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_1))=Xs).
% 12.20/12.14 all X_a Xs X I_1 J (I_1!=J->hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),J)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),J)).
% 12.20/12.14 all X_a N Xs (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),butlast(X_a),Xs))=hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))).
% 12.20/12.14 all X_a N Xs (hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),butlast(X_a),Xs))).
% 12.20/12.14 all X_a N Xs (hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),tl(X_a),Xs))).
% 12.20/12.14 all X_a N Xs (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),tl(X_a),Xs))=hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))).
% 12.20/12.14 all X_a N Xs (Xs!=nil(X_a)-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))->hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N))).
% 12.20/12.14 all X_a N Xs Y Ys (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Ys)->hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N)=ti(X_a,Y)).
% 12.20/12.14 all X_a Xs_1 Ys_1 (Xs_1=Ys_1<->hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)=hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1)& (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))->hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I_2)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys_1),I_2)))).
% 12.20/12.14 all X_a X Xs Y (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),zero_zero(nat)),Y)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Xs)).
% 12.20/12.14 all X_a X I_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),N))->hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)),I_1)=ti(X_a,X)).
% 12.20/12.14 all X_a Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))<->Xs_1!=nil(X_a)).
% 12.20/12.14 all X_a Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1))<-> (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))-> (all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))-> (I_2!=J_2->hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I_2)!=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),J_2))))))).
% 12.20/12.14 all X_a J_1 I Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))-> (hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),J_1)<->I=J_1)))).
% 12.20/12.14 bot_bot(nat)=zero_zero(nat).
% 12.20/12.14 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N),zero_zero(nat))=N).
% 12.20/12.14 all X_a Xs Ys (hAPP(list(X_a),nat,size_size(list(X_a)),Xs)=hAPP(list(X_a),nat,size_size(list(X_a)),Ys)-> ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))->hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_2)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys),I_2)))->Xs=Ys)).
% 12.20/12.14 all X_a P_1 K_1 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1))-> (exists X1 hBOOL(hAPP(X_a,bool,hAPP(nat,fun(X_a,bool),P_1,I_2),X1)))))<-> (exists Xs_2 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_2)=K_1& (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1))->hBOOL(hAPP(X_a,bool,hAPP(nat,fun(X_a,bool),P_1,I_2),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_2),I_2)))))))).
% 12.20/12.14 all X_a J_1 P_1 Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1))))->hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)),J_1)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))))).
% 12.20/12.14 all X_a I_1 Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))->hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_1)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,I_1)),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_1),Xs)).
% 12.20/12.14 all X_a P_1 Xs_1 (hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),Xs_1))<-> (exists N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))&hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),N_1)))))).
% 12.20/12.14 all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,N))).
% 12.20/12.14 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N)))).
% 12.20/12.14 all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N))).
% 12.20/12.14 all X Y (hAPP(nat,nat,suc,X)=hAPP(nat,nat,suc,Y)->X=Y).
% 12.20/12.14 all M_1 K_1 N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K_1)<->M_1=N_2).
% 12.20/12.14 all K_1 M_1 N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2)<->M_1=N_2).
% 12.20/12.14 all M N K (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K))).
% 12.20/12.14 all Nat_4 Nat_3 (hAPP(nat,nat,suc,Nat_4)=hAPP(nat,nat,suc,Nat_3)<->Nat_4=Nat_3).
% 12.20/12.14 all M N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N))).
% 12.20/12.14 all M N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))).
% 12.20/12.14 all X Y Z (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Z))).
% 12.20/12.14 all M N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N))=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))).
% 12.20/12.14 all M N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)).
% 12.20/12.14 all M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))<-> (exists K_2 (N_2=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2))))).
% 12.20/12.14 all I_1 M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),I_1)))).
% 12.20/12.14 all I_1 M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),M)))).
% 12.20/12.14 all N (hAPP(nat,nat,suc,N)!=N).
% 12.20/12.14 all N (N!=hAPP(nat,nat,suc,N)).
% 12.20/12.14 all M_1 N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)=hAPP(nat,nat,suc,zero_zero(nat))<->M_1=hAPP(nat,nat,suc,zero_zero(nat))&N_2=zero_zero(nat)|M_1=zero_zero(nat)&N_2=hAPP(nat,nat,suc,zero_zero(nat))).
% 12.20/12.14 all M_1 N_2 (hAPP(nat,nat,suc,zero_zero(nat))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)<->M_1=hAPP(nat,nat,suc,zero_zero(nat))&N_2=zero_zero(nat)|M_1=zero_zero(nat)&N_2=hAPP(nat,nat,suc,zero_zero(nat))).
% 12.20/12.14 all X_a (cancel_semigroup_add(X_a)-> (all B_1 A_2 C_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),A_2)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),A_2)->ti(X_a,B_1)=ti(X_a,C_2)))).
% 12.20/12.14 all X_a (cancel146912293up_add(X_a)-> (all A_2 B_1 C_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)->ti(X_a,B_1)=ti(X_a,C_2)))).
% 12.20/12.14 all X_a (cancel_semigroup_add(X_a)-> (all A_2 B_1 C_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)->ti(X_a,B_1)=ti(X_a,C_2)))).
% 12.20/12.14 all X_a (cancel_semigroup_add(X_a)-> (all Ba Aa C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa)<->ti(X_a,Ba)=ti(X_a,C_1)))).
% 12.20/12.14 all X_a (cancel_semigroup_add(X_a)-> (all Aa Ba C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1)<->ti(X_a,Ba)=ti(X_a,C_1)))).
% 12.20/12.14 all X_a (ab_semigroup_add(X_a)-> (all A_2 B_1 C_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),C_2)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_2))))).
% 12.20/12.14 all X_a (comm_monoid_add(X_a)-> (all A_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),zero_zero(X_a))=ti(X_a,A_2)))).
% 12.20/12.14 all X_a (monoid_add(X_a)-> (all A_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),zero_zero(X_a))=ti(X_a,A_2)))).
% 12.20/12.14 all X_a (linord219039673up_add(X_a)-> (all Aa (zero_zero(X_a)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)<->ti(X_a,Aa)=zero_zero(X_a)))).
% 12.20/12.14 all X_a (comm_monoid_add(X_a)-> (all A_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_2)=ti(X_a,A_2)))).
% 12.20/12.14 all X_a (monoid_add(X_a)-> (all A_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_2)=ti(X_a,A_2)))).
% 12.20/12.14 all X_a (ordere236663937imp_le(X_a)-> (all C_2 A_2 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),B_1)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))))).
% 12.20/12.14 all X_a (ordere236663937imp_le(X_a)-> (all A_2 C_2 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_2)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))))).
% 12.20/12.14 all X_a (ordere223160158up_add(X_a)-> (all C_2 D_2 A_2 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_2),D_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D_2))))))).
% 12.20/12.14 all X_a (ordere223160158up_add(X_a)-> (all C_2 A_2 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),B_1)))))).
% 12.20/12.14 all X_a (ordere223160158up_add(X_a)-> (all C_2 A_2 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_2)))))).
% 12.20/12.14 all X_a (ordere236663937imp_le(X_a)-> (all C_1 Aa Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Ba)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))))).
% 12.20/12.14 all X_a (ordere236663937imp_le(X_a)-> (all Aa C_1 Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),C_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))))).
% 12.20/12.14 all M (zero_zero(nat)!=hAPP(nat,nat,suc,M)).
% 12.20/12.14 all Nat_2 (zero_zero(nat)!=hAPP(nat,nat,suc,Nat_2)).
% 12.20/12.14 all M (hAPP(nat,nat,suc,M)!=zero_zero(nat)).
% 12.20/12.14 all Nat_1 (hAPP(nat,nat,suc,Nat_1)!=zero_zero(nat)).
% 12.20/12.14 all M (zero_zero(nat)!=hAPP(nat,nat,suc,M)).
% 12.20/12.14 all M (hAPP(nat,nat,suc,M)!=zero_zero(nat)).
% 12.20/12.14 all M_1 N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1)))).
% 12.20/12.14 all M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|M_1=N_2).
% 12.20/12.14 all M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))).
% 12.20/12.14 all N_2 M_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1)))<->N_2=M_1)).
% 12.20/12.14 all N M (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M)))->M=N)).
% 12.20/12.14 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N)))).
% 12.20/12.14 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))-> (hAPP(nat,nat,suc,M)!=N->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N)))).
% 12.20/12.14 all K I_1 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_1)),K)))).
% 12.20/12.14 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N)))-> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))->M=N)).
% 12.20/12.14 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))).
% 12.20/12.14 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))).
% 12.20/12.14 all X_a A_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),bot_bot(fun(X_a,bool))))).
% 12.20/12.14 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N)=N).
% 12.20/12.14 all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),zero_zero(nat))=M).
% 12.20/12.14 all M_1 N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)=zero_zero(nat)<->M_1=zero_zero(nat)&N_2=zero_zero(nat)).
% 12.20/12.14 all M N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)=M->N=zero_zero(nat)).
% 12.20/12.14 all I_1 J (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J)),I_1))).
% 12.20/12.14 all J I_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_1)),I_1))).
% 12.20/12.14 all K_1 M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))).
% 12.20/12.14 all M I_1 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M)))).
% 12.20/12.14 all M I_1 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J)))).
% 12.20/12.14 all K I_1 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K)))).
% 12.20/12.14 all K L I_1 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L))))).
% 12.20/12.14 all M N K L (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L))-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))).
% 12.20/12.14 all I_1 J K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J)),K))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K))).
% 12.20/12.14 all X_a (ordere236663937imp_le(X_a)-> (all X Y Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z))))).
% 12.20/12.14 all X_a N M Xs (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),M),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),Xs)).
% 12.20/12.14 all M N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),M),N))).
% 12.20/12.14 all X_a A_2 List_1 (hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_2),List_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),List_1)),hAPP(nat,nat,suc,zero_zero(nat)))).
% 12.20/12.14 all X_a Fa Aa List (hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),Fa),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Aa),List))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(X_a,nat,Fa,Aa)),hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),Fa),List))),hAPP(nat,nat,suc,zero_zero(nat)))).
% 12.20/12.14 all X_a P_1 X_1 Xs_1 (hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)))<->hBOOL(hAPP(X_a,bool,P_1,X_1))|hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),Xs_1))).
% 12.20/12.14 all X_a P_1 (-hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),nil(X_a)))).
% 12.20/12.14 all X_a P_1 Xs_1 Ys_1 (hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)))<->hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),Xs_1))|hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),Ys_1))).
% 12.20/12.14 all X_a (linord219039673up_add(X_a)-> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa))))).
% 12.20/12.14 all X_a (linord219039673up_add(X_a)-> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a)))))).
% 12.20/12.14 all X_a (ordere216010020id_add(X_a)-> (all B_1 A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1))))))).
% 12.20/12.14 all X_a (ordere216010020id_add(X_a)-> (all B_1 A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),zero_zero(X_a))))))).
% 12.20/12.14 all X_a P_1 Xs_1 (hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)))<->hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),Xs_1))).
% 12.20/12.14 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2))<-> (exists M_2 (N_2=hAPP(nat,nat,suc,M_2)))).
% 12.20/12.14 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,zero_zero(nat))))<->N_2=zero_zero(nat)).
% 12.20/12.14 all M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))<->M_1=zero_zero(nat)| (exists J_2 (M_1=hAPP(nat,nat,suc,J_2)&hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),N_2))))).
% 12.20/12.14 all M_1 N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2))).
% 12.20/12.14 all X_a X Xs N (hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),hAPP(nat,nat,suc,N))=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N)).
% 12.20/12.14 all X_a Xs Ys (hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),hAPP(list(X_a),nat,size_size(list(X_a)),Ys))).
% 12.20/12.14 all X_a N X Xs (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,N)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)).
% 12.20/12.14 all X_a X Xs I_1 Y (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),hAPP(nat,nat,suc,I_1)),Y)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),Y))).
% 12.20/12.14 all X_a N X (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,suc,N)),X)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X))).
% 12.20/12.14 all X_a N M X (hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),X)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),M),X))).
% 12.20/12.14 all X_a N Xs (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,N)),Xs)=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),tl(X_a),Xs))).
% 12.20/12.14 all X_a Xs Ys (hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),Xs),Ys))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),hAPP(list(X_a),nat,size_size(list(X_a)),Ys))).
% 12.20/12.14 all X_a Xs Ys N (hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),N))=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys),N)).
% 12.20/12.14 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))-> (exists K_2 (N=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_2))))).
% 12.20/12.14 all X_a Xs_1 N_2 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)=hAPP(nat,nat,suc,N_2)<-> (exists Y_1 Ys_2 (Xs_1=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_2)&hAPP(list(X_a),nat,size_size(list(X_a)),Ys_2)=N_2))).
% 12.20/12.14 all X_a N_2 Xs_1 (hAPP(nat,nat,suc,N_2)=hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)<-> (exists Y_1 Ys_2 (Xs_1=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_2)&hAPP(list(X_a),nat,size_size(list(X_a)),Ys_2)=N_2))).
% 12.20/12.14 all I_1 J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J))-> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2))&hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_2)=J))).
% 12.20/12.14 all X_a C_1 A_1 B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))-> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1))->hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)))).
% 12.20/12.14 all X_a C_3 A_1 B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))-> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B),C_3))->hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),C_3)))).
% 12.20/12.14 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))-> (exists M_2 (N=hAPP(nat,nat,suc,M_2)))).
% 12.20/12.14 all X_a (order(X_a)-> (all N_2 N_3 F ((all N_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_1)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_1)))))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),N_3))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,N_3))))))).
% 12.20/12.14 all X_a (order(X_a)-> (all N_2 M_1 F ((all N_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_1)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_1)))))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,M_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1)))))).
% 12.20/12.14 all X_a (linordered_idom(X_a)-> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a)))))).
% 12.20/12.14 all X_a (linordered_semidom(X_a)-> (all B_1 C_2 A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C_2))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2))))))).
% 12.20/12.14 all X_a (linordered_idom(X_a)-> (all X Y (ti(X_a,X)!=ti(X_a,Y)-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))).
% 12.20/12.14 all X_a (linord219039673up_add(X_a)-> (all Aa (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)=zero_zero(X_a)<->ti(X_a,Aa)=zero_zero(X_a)))).
% 12.20/12.14 all I_1 K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K))-> (K!=hAPP(nat,nat,suc,I_1)-> -(all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2))->K!=hAPP(nat,nat,suc,J_2))))).
% 12.20/12.14 all I_1 K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_1)),K))-> -(all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2))->K!=hAPP(nat,nat,suc,J_2)))).
% 12.20/12.14 all Y (Y!=zero_zero(nat)-> -(all Nat (Y!=hAPP(nat,nat,suc,Nat)))).
% 12.20/12.14 all N (N!=zero_zero(nat)-> (exists M_2 (N=hAPP(nat,nat,suc,M_2)))).
% 12.20/12.14 all N_2 P_1 (hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))-> ((all N_1 (hBOOL(hAPP(nat,bool,P_1,N_1))->hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_1)))))->hBOOL(hAPP(nat,bool,P_1,N_2)))).
% 12.20/12.14 all P_1 K_1 (hBOOL(hAPP(nat,bool,P_1,K_1))-> ((all N_1 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_1)))->hBOOL(hAPP(nat,bool,P_1,N_1))))->hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))))).
% 12.20/12.14 all X_a N Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))->hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))),nil(X_a)))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N)),Xs)).
% 12.20/12.14 all X_a N Xs (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),tl(X_a),Xs))=hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N)),Xs))).
% 12.20/12.14 all X_a N (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),nil(X_a))=nil(X_a)).
% 12.20/12.14 all X_a I_1 Xs (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs))->hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),Xs)))).
% 12.20/12.14 all X_a (linorder(X_a)-> (all N Xs (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs))->hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs)))))).
% 12.20/12.14 all X_a P_1 Xs_1 (hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))),Xs_1)).
% 12.20/12.14 all X_a N Xs (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))=Xs).
% 12.20/12.14 all X_a N M Xs (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),M),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),M),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),Xs))).
% 12.20/12.14 all X_a Xs I_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),N))->hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs)),I_1)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_1)).
% 12.20/12.14 all X_a N X Xs (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs))).
% 12.20/12.14 all X_a N_2 Xs_1 (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_2),Xs_1)=nil(X_a)<->N_2=zero_zero(nat)|Xs_1=nil(X_a)).
% 12.20/12.14 all X_a Xs (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),zero_zero(nat)),Xs)=nil(X_a)).
% 12.20/12.14 all X_a Xs_1 Ys_1 Zs (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)=Zs<->Xs_1=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)),Zs)&Ys_1=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)),Zs)).
% 12.20/12.14 all X_a I_1 J Xs (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J)),Xs)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),J),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_1),Xs)))).
% 12.20/12.14 all X_a N Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))->hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),butlast(X_a),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs)).
% 12.20/12.14 all X_a N Xs (Xs!=nil(X_a)->hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N)),Xs)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,hd(X_a),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),tl(X_a),Xs)))).
% 12.20/12.14 all X_a I_1 Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))->hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,I_1)),Xs)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_1)),nil(X_a)))).
% 12.20/12.14 all X_a I_1 Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))->Xs=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_1)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,I_1)),Xs)))).
% 12.20/12.14 all X_a A_2 I_1 Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))->hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),A_2)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_2),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,I_1)),Xs)))).
% 12.20/12.14 all X_a P_1 Xs_1 N_2 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))->hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I_2))))))-> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))-> -hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),N_2))))->hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_2),Xs_1))).
% 12.20/12.14 all Z X Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)))).
% 12.20/12.14 all Y X Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)))).
% 12.20/12.14 all X_a (comm_semiring_1(X_a)-> (all A_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_2)=ti(X_a,A_2)))).
% 12.20/12.14 all X_a (comm_semiring_1(X_a)-> (all A_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),zero_zero(X_a))=ti(X_a,A_2)))).
% 12.20/12.14 all X_a (comm_semiring_1(X_a)-> (all A_2 B_1 C_2 D_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),D_2))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D_2))))).
% 12.20/12.14 all X_a (comm_semiring_1(X_a)-> (all A_2 B_1 C_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),C_2)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)),B_1)))).
% 12.20/12.14 all X_a (comm_semiring_1(X_a)-> (all A_2 B_1 C_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),C_2)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_2))))).
% 12.20/12.14 all X_a (comm_semiring_1(X_a)-> (all A_2 C_2 D_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),D_2))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)),D_2)))).
% 12.20/12.14 all X_a (comm_semiring_1(X_a)-> (all A_2 C_2 D_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),D_2))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),D_2))))).
% 12.20/12.14 all X_a (comm_semiring_1(X_a)-> (all A_2 C_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),A_2)))).
% 12.20/12.14 all X_a (semiri456707255roduct(X_a)-> (all Ba Aa (ti(X_a,Ba)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa)<->ti(X_a,Aa)=zero_zero(X_a)))).
% 12.20/12.14 all X_a N Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))->hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs)),N)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),hAPP(nat,nat,suc,N)))).
% 12.20/12.14 all X_a Xs Ys ((all I_2 (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_2),Xs)=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_2),Ys)))->Xs=Ys).
% 12.20/12.14 all X_a N M Xs (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),M),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))).
% 12.20/12.14 all X_a I_1 K X (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_1),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),K),X))=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K),I_1)),X)).
% 12.20/12.14 all M K N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)).
% 12.20/12.14 all K M N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)).
% 12.20/12.14 all I_1 J K (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))).
% 12.20/12.14 all N M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),N)=M).
% 12.20/12.14 all M N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),N)=M).
% 12.20/12.14 all X_a (ordered_ab_group_add(X_a)-> (all Aa Ba C_1 D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_1)-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_1)))))).
% 12.20/12.14 all X_a (group_add(X_a)-> (all A_2 B_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),B_1)=ti(X_a,A_2)))).
% 12.20/12.14 all X_a (group_add(X_a)-> (all A_2 B_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),B_1)=ti(X_a,A_2)))).
% 12.20/12.14 all N J K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),N)),K))).
% 12.20/12.14 all L M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M))))).
% 12.20/12.14 all X_a (ordered_ab_group_add(X_a)-> (all Aa Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),zero_zero(X_a)))))).
% 12.20/12.14 all M N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),M)))).
% 12.20/12.14 all N_2 M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),M_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))).
% 12.20/12.14 all M N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),hAPP(nat,nat,suc,M))).
% 12.20/12.14 all N M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M))=zero_zero(nat)).
% 12.20/12.14 all I J_1 K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_1)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_1)),J_1))).
% 12.20/12.14 all M N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))=M).
% 12.20/12.14 all X_a N Xs (hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),N)).
% 12.20/12.14 all I_1 J K (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),K)),J)).
% 12.20/12.15 all X_a (ordered_ab_group_add(X_a)-> (all X Y Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z))))).
% 12.20/12.15 all X_a (ab_group_add(X_a)-> (all Aa Ba C_1 D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_1)-> (ti(X_a,Aa)=ti(X_a,Ba)<->ti(X_a,C_1)=ti(X_a,D_1))))).
% 12.20/12.15 all X_a (group_add(X_a)-> (all A_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),zero_zero(X_a))=ti(X_a,A_2)))).
% 12.20/12.15 all X_a (group_add(X_a)-> (all A_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),A_2)=zero_zero(X_a)))).
% 12.20/12.15 all X_a (ab_group_add(X_a)-> (all Aa Ba (ti(X_a,Aa)=ti(X_a,Ba)<->hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)=zero_zero(X_a)))).
% 12.20/12.15 all X_a (group_add(X_a)-> (all Aa Ba (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)=zero_zero(X_a)<->ti(X_a,Aa)=ti(X_a,Ba)))).
% 12.20/12.15 all X_b X_a (minus(X_a)-> (all A_1 B X_1 (hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),minus_minus(fun(X_b,X_a)),A_1),B),X_1)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_b,X_a,A_1,X_1)),hAPP(X_b,X_a,B,X_1))))).
% 12.20/12.15 all X_a X_b (minus(X_b)-> (all A_1 B X_2 (hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),minus_minus(fun(X_a,X_b)),A_1),B),X_2)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,A_1,X_2)),hAPP(X_a,X_b,B,X_2))))).
% 12.20/12.15 all M N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)=zero_zero(nat)-> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M)=zero_zero(nat)->M=N)).
% 12.20/12.15 all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M)=zero_zero(nat)).
% 12.20/12.15 all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat))=M).
% 12.20/12.15 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N)=zero_zero(nat)).
% 12.20/12.15 all M N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)).
% 12.20/12.15 all M N K (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N)),hAPP(nat,nat,suc,K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),K)).
% 12.20/12.15 all N M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M)),M)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N),M)).
% 12.20/12.15 all I_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,I_1))),N))).
% 12.20/12.15 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))->hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat))))=N).
% 12.20/12.15 all P_1 Aa Ba (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))<-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba))->hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))))& (all D (Aa=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),D)->hBOOL(hAPP(nat,bool,P_1,D))))).
% 12.20/12.15 all P_1 Aa Ba (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))<-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba))& -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| (exists D (Aa=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),D)& -hBOOL(hAPP(nat,bool,P_1,D)))))).
% 12.20/12.15 all X_a N Xs Ys (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))),Ys))).
% 12.20/12.15 all X_a N Xs Ys (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))),Ys))).
% 12.20/12.15 all X_a Ys N Xs ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))->hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys)),N)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N))& (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))->hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys)),N)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))))).
% 12.20/12.15 all X_a Ys X N Xs ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))->hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys)),N),X)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),N),X)),Ys))& (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))->hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys)),N),X)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Ys),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))),X)))).
% 12.20/12.15 all X_a I_1 Xs (hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_1),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),I_1)),hAPP(list(X_a),list(X_a),rev(X_a),Xs))).
% 12.20/12.15 all X_a I_1 Xs (hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),I_1)),hAPP(list(X_a),list(X_a),rev(X_a),Xs))).
% 12.20/12.15 all I P_1 K_1 (hBOOL(hAPP(nat,bool,P_1,K_1))-> ((all N_1 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_1)))->hBOOL(hAPP(nat,bool,P_1,N_1))))->hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K_1),I))))).
% 12.20/12.15 all X_a X K Xs (Xs!=nil(X_a)-> (K=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat))->hAPP(list(X_a),X_a,last(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),K),X))=ti(X_a,X))& (K!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat))->hAPP(list(X_a),X_a,last(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),K),X))=hAPP(list(X_a),X_a,last(X_a),Xs))).
% 12.20/12.15 all X_a A_1 (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),bot_bot(fun(X_a,bool))),A_1)=bot_bot(fun(X_a,bool))).
% 12.20/12.15 all X_a A_1 (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),bot_bot(fun(X_a,bool)))=ti(fun(X_a,bool),A_1)).
% 12.20/12.15 all X_a A_1 (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),A_1)=bot_bot(fun(X_a,bool))).
% 12.20/12.15 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N)),one_one(nat))=N).
% 12.20/12.15 all M N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N)).
% 12.20/12.15 all N (hAPP(nat,nat,suc,N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N)).
% 12.20/12.15 all N (hAPP(nat,nat,suc,N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))).
% 12.20/12.15 all X_a X Xs (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),one_one(nat)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=Xs).
% 12.20/12.15 all X_a (one(X_a)-> (all X_1 (one_one(X_a)=ti(X_a,X_1)<->ti(X_a,X_1)=one_one(X_a)))).
% 12.20/12.15 one_one(nat)=hAPP(nat,nat,suc,zero_zero(nat)).
% 12.20/12.15 all X_a (linordered_semidom(X_a)-> (all A_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),one_one(X_a)))))).
% 12.20/12.15 all X_a (linordered_semidom(X_a)-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a)))).
% 12.20/12.15 all X_a (linordered_semidom(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a)))).
% 12.20/12.15 all X_a (zero_ne_q_one(X_a)->one_one(X_a)!=zero_zero(X_a)).
% 12.20/12.15 all X_a (zero_ne_q_one(X_a)->zero_zero(X_a)!=one_one(X_a)).
% 12.20/12.15 all X_a (linordered_semidom(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))))).
% 12.20/12.15 all X_a X Xs (hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),one_one(nat)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a))).
% 12.20/12.15 all X_a Xs (hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),butlast(X_a),Xs))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat))).
% 12.20/12.15 all X_a Xs (hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),tl(X_a),Xs))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat))).
% 12.20/12.15 all X_a N Xs (hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),hAPP(list(X_a),list(X_a),tl(X_a),Xs))).
% 12.20/12.15 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))->N=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))).
% 12.20/12.15 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))->hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))=N).
% 12.20/12.15 all N M ((M=zero_zero(nat)->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)=N)& (M!=zero_zero(nat)->hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N)))).
% 12.20/12.15 all X_a X Xs N ((N=zero_zero(nat)->hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),N)=ti(X_a,X))& (N!=zero_zero(nat)->hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),N)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))))).
% 12.20/12.15 all X_a X Xs N ((N=zero_zero(nat)->hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))& (N!=zero_zero(nat)->hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),Xs))).
% 12.20/12.15 all X_a Xs (hAPP(list(X_a),list(X_a),butlast(X_a),Xs)=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat))),Xs)).
% 12.20/12.15 all X_a X K Xs ((K=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat))->hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),K),X))=hAPP(list(X_a),list(X_a),butlast(X_a),Xs))& (K!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat))->hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),K),X))=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)),K),X))).
% 12.20/12.15 all X_a X N (N!=zero_zero(nat)->hAPP(list(X_a),list(X_a),tl(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X))=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),X)).
% 12.20/12.15 all X_a X Xs N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))->hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),N)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))).
% 12.20/12.15 all X_a X Xs N ((N=zero_zero(nat)->hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=nil(X_a))& (N!=zero_zero(nat)->hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),Xs)))).
% 12.20/12.15 all X_a Y K Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))->hAPP(list(X_a),list(X_a),rev(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),K),Y))=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),K)),one_one(nat))),Y)).
% 12.20/12.15 all X_a Xs (Xs!=nil(X_a)->hAPP(list(X_a),X_a,last(X_a),Xs)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat)))).
% 12.20/12.15 all X_a X Xs V ((hAPP(int,nat,number_number_of(nat),V)=zero_zero(nat)->hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(int,nat,number_number_of(nat),V)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=nil(X_a))& (hAPP(int,nat,number_number_of(nat),V)!=zero_zero(nat)->hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(int,nat,number_number_of(nat),V)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))),Xs)))).
% 12.20/12.15 all X_a (linordered_idom(X_a)-> (all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),Aa)),Aa)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))))))).
% 12.20/12.15 all X_a C_1 A_1 B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)))-> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1))->hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)))).
% 12.20/12.15 all X_a B C_1 A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1))-> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B))->hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B))))).
% 12.20/12.15 all X_a (ring_1(X_a)-> (all Ba Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))-> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a)))->hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),ring_1_Ints(X_a))))))).
% 12.20/12.15 all X_a (number_ring(X_a)-> (all V W (hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),V),W))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))))).
% 12.20/12.15 all X_a (number_ring(X_a)-> (all V W C_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),W)),C_2))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),C_2)))).
% 12.20/12.15 all X_a C_1 A_1 B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)))-> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B))).
% 12.20/12.15 all X_a C_1 A_1 B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)))->hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1))).
% 12.20/12.15 all X_a A_1 B (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)),B)=hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)).
% 12.20/12.15 all X_a C_1 A_1 B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)))<->hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1))& -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B))).
% 12.20/12.15 all X_a A_1 B (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)=hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B))))).
% 12.20/12.15 enum(bool).
% 12.20/12.15 all T_2 T_1 (enum(T_1)&enum(T_2)->enum(fun(T_2,T_1))).
% 12.20/12.15 all T_2 T_1 (preorder(T_1)->preorder(fun(T_2,T_1))).
% 12.20/12.15 all T_2 T_1 (order(T_1)->order(fun(T_2,T_1))).
% 12.20/12.15 all T_2 T_1 (ord(T_1)->ord(fun(T_2,T_1))).
% 12.20/12.15 all T_2 T_1 (bot(T_1)->bot(fun(T_2,T_1))).
% 12.20/12.15 all T_2 T_1 (minus(T_1)->minus(fun(T_2,T_1))).
% 12.20/12.15 all T_2 T_1 (cl_HOL_Oe_qual(T_1)&enum(T_2)->cl_HOL_Oe_qual(fun(T_2,T_1))).
% 12.20/12.15 semiri456707255roduct(int).
% 12.20/12.15 ordere223160158up_add(int).
% 12.20/12.15 ordere236663937imp_le(int).
% 12.20/12.15 ordere216010020id_add(int).
% 12.20/12.15 linord219039673up_add(int).
% 12.20/12.15 cancel146912293up_add(int).
% 12.20/12.15 ordered_ab_group_add(int).
% 12.20/12.15 cancel_semigroup_add(int).
% 12.20/12.15 linordered_semidom(int).
% 12.20/12.15 ab_semigroup_add(int).
% 12.20/12.15 comm_monoid_add(int).
% 12.20/12.15 linordered_idom(int).
% 12.20/12.15 comm_semiring_1(int).
% 12.20/12.15 ab_group_add(int).
% 12.20/12.15 zero_ne_q_one(int).
% 12.20/12.15 preorder(int).
% 12.20/12.15 linorder(int).
% 12.20/12.15 monoid_add(int).
% 12.20/12.15 group_add(int).
% 12.20/12.15 order(int).
% 12.20/12.15 number_ring(int).
% 12.20/12.15 ord(int).
% 12.20/12.15 ring_1(int).
% 12.20/12.15 minus(int).
% 12.20/12.15 zero(int).
% 12.20/12.15 one(int).
% 12.20/12.15 cl_HOL_Oe_qual(int).
% 12.20/12.15 semiri456707255roduct(nat).
% 12.20/12.15 ordere223160158up_add(nat).
% 12.20/12.15 ordere236663937imp_le(nat).
% 12.20/12.15 ordere216010020id_add(nat).
% 12.20/12.15 cancel146912293up_add(nat).
% 12.20/12.15 cancel_semigroup_add(nat).
% 12.20/12.15 linordered_semidom(nat).
% 12.20/12.15 ab_semigroup_add(nat).
% 12.20/12.15 comm_monoid_add(nat).
% 12.20/12.15 comm_semiring_1(nat).
% 12.20/12.15 zero_ne_q_one(nat).
% 12.20/12.15 preorder(nat).
% 12.20/12.15 linorder(nat).
% 12.20/12.15 monoid_add(nat).
% 12.20/12.16 order(nat).
% 12.20/12.16 ord(nat).
% 12.20/12.16 bot(nat).
% 12.20/12.16 minus(nat).
% 12.20/12.16 zero(nat).
% 12.20/12.16 one(nat).
% 12.20/12.16 cl_HOL_Oe_qual(nat).
% 12.20/12.16 preorder(bool).
% 12.20/12.16 order(bool).
% 12.20/12.16 ord(bool).
% 12.20/12.16 bot(bool).
% 12.20/12.16 minus(bool).
% 12.20/12.16 cl_HOL_Oe_qual(bool).
% 12.20/12.16 all T_1 cl_HOL_Oe_qual(list(T_1)).
% 12.20/12.16 all T A (ti(T,ti(T,A))=ti(T,A)).
% 12.20/12.16 all P (-hBOOL(hAPP(bool,bool,fNot,P))| -hBOOL(P)).
% 12.20/12.16 all P (hBOOL(P)|hBOOL(hAPP(bool,bool,fNot,P))).
% 12.20/12.16 all X_a X_c X_b P Q R (hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R)=hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R))).
% 12.20/12.16 all X_a X_c X_b P Q R (hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R)=hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q)).
% 12.20/12.16 all X_b X_a P Q (hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q)=ti(X_a,P)).
% 12.20/12.16 all X_a X_c X_b P Q R (hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R)=hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R))).
% 12.20/12.16 all Q P (-hBOOL(P)| -hBOOL(Q)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))).
% 12.20/12.16 all P Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(P)).
% 12.20/12.16 all P Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(Q)).
% 12.20/12.16 -hBOOL(fFalse).
% 12.20/12.16 all P (ti(bool,P)=fTrue|ti(bool,P)=fFalse).
% 12.20/12.16 all X_a X Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fe_qual(X_a),X),Y))|ti(X_a,X)=ti(X_a,Y)).
% 12.20/12.16 all X_a X Y (ti(X_a,X)!=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fe_qual(X_a),X),Y))).
% 12.20/12.16 a!=b.
% 12.20/12.16 -(exists C hBOOL(hAPP(list(arrow_490897120le_alt),bool,distinct(arrow_490897120le_alt),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),a),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),b),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),C),nil(arrow_490897120le_alt))))))).
% 12.20/12.16 end_of_list.
% 12.20/12.16
% 12.20/12.16 -------> usable clausifies to:
% 12.20/12.16
% 12.20/12.16 list(usable).
% 12.20/12.16 0 [] A=A.
% 12.20/12.16 0 [] ti(fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),combb(X_b,X_c,X_a))=combb(X_b,X_c,X_a).
% 12.20/12.16 0 [] ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c))=combc(X_a,X_b,X_c).
% 12.20/12.16 0 [] ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b))=combk(X_a,X_b).
% 12.20/12.16 0 [] ti(fun(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c))),combs(X_a,X_b,X_c))=combs(X_a,X_b,X_c).
% 12.20/12.16 0 [] -minus(X_a)|ti(fun(X_a,fun(X_a,X_a)),minus_minus(X_a))=minus_minus(X_a).
% 12.20/12.16 0 [] -one(X_a)|ti(X_a,one_one(X_a))=one_one(X_a).
% 12.20/12.16 0 [] -monoid_add(X_a)|ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a).
% 12.20/12.16 0 [] -ab_semigroup_add(X_a)|ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a).
% 12.20/12.16 0 [] -cancel_semigroup_add(X_a)|ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a))=plus_plus(X_a).
% 12.20/12.16 0 [] -zero(X_a)|ti(X_a,zero_zero(X_a))=zero_zero(X_a).
% 12.20/12.16 0 [] -cl_HOL_Oe_qual(X_a)|ti(fun(X_a,fun(X_a,bool)),e_qual_e_qual(X_a))=e_qual_e_qual(X_a).
% 12.20/12.16 0 [] ti(X_a,undefined(X_a))=undefined(X_a).
% 12.20/12.16 0 [] -number_ring(X_a)|ti(fun(int,X_a),number_number_of(X_a))=number_number_of(X_a).
% 12.20/12.16 0 [] ti(fun(int,nat),number_number_of(nat))=number_number_of(nat).
% 12.20/12.16 0 [] -ring_1(X_a)|ti(fun(X_a,bool),ring_1_Ints(X_a))=ring_1_Ints(X_a).
% 12.20/12.16 0 [] ti(fun(X_a,fun(list(X_a),bool)),listMem(X_a))=listMem(X_a).
% 12.20/12.16 0 [] ti(fun(list(X_a),fun(list(X_a),list(X_a))),append(X_a))=append(X_a).
% 12.20/12.16 0 [] ti(fun(list(X_a),list(X_a)),butlast(X_a))=butlast(X_a).
% 12.20/12.16 0 [] ti(fun(list(X_a),bool),distinct(X_a))=distinct(X_a).
% 12.20/12.16 0 [] ti(fun(nat,fun(list(X_a),list(X_a))),drop(X_a))=drop(X_a).
% 12.20/12.16 0 [] ti(fun(fun(X_a,bool),fun(list(X_a),list(X_a))),dropWhile(X_a))=dropWhile(X_a).
% 12.20/12.16 0 [] ti(fun(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a))),foldr(X_b,X_a))=foldr(X_b,X_a).
% 12.20/12.16 0 [] ti(fun(list(X_a),X_a),hd(X_a))=hd(X_a).
% 12.20/12.16 0 [] ti(fun(X_a,fun(list(X_a),list(X_a))),insert(X_a))=insert(X_a).
% 12.20/12.16 0 [] ti(fun(list(X_a),X_a),last(X_a))=last(X_a).
% 12.20/12.16 0 [] -linorder(X_a)|ti(fun(list(X_a),bool),linorder_sorted(X_a))=linorder_sorted(X_a).
% 12.20/12.16 0 [] -linorder(X_a)|ti(fun(fun(X_a,bool),list(X_a)),linord467138063of_set(X_a))=linord467138063of_set(X_a).
% 12.20/12.16 0 [] ti(fun(X_a,fun(list(X_a),list(X_a))),cons(X_a))=cons(X_a).
% 12.20/12.16 0 [] ti(list(X_a),nil(X_a))=nil(X_a).
% 12.20/12.16 0 [] ti(fun(X_a,fun(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a))),list_case(X_a,X_b))=list_case(X_a,X_b).
% 12.20/12.16 0 [] ti(fun(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a))),list_rec(X_a,X_b))=list_rec(X_a,X_b).
% 12.20/12.16 0 [] ti(fun(fun(X_a,nat),fun(list(X_a),nat)),list_size(X_a))=list_size(X_a).
% 12.20/12.16 0 [] ti(fun(fun(X_a,bool),fun(list(X_a),bool)),list_ex(X_a))=list_ex(X_a).
% 12.20/12.16 0 [] ti(fun(fun(X_a,bool),fun(list(X_a),bool)),list_ex1(X_a))=list_ex1(X_a).
% 12.20/12.16 0 [] ti(fun(list(X_a),fun(nat,fun(X_a,list(X_a)))),list_update(X_a))=list_update(X_a).
% 12.20/12.16 0 [] ti(fun(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool))),listrelp(X_a))=listrelp(X_a).
% 12.20/12.16 0 [] ti(fun(fun(X_b,option(X_a)),fun(list(X_b),list(X_a))),map_filter(X_b,X_a))=map_filter(X_b,X_a).
% 12.20/12.16 0 [] ti(fun(fun(X_b,list(X_a)),fun(list(X_b),list(X_a))),maps(X_b,X_a))=maps(X_b,X_a).
% 12.20/12.16 0 [] ti(fun(list(X_a),fun(X_a,bool)),member_1(X_a))=member_1(X_a).
% 12.20/12.16 0 [] ti(fun(list(X_a),fun(nat,X_a)),nth(X_a))=nth(X_a).
% 12.20/12.16 0 [] ti(fun(list(X_a),bool),null(X_a))=null(X_a).
% 12.20/12.16 0 [] ti(fun(nat,fun(X_a,list(X_a))),replicate(X_a))=replicate(X_a).
% 12.20/12.16 0 [] ti(fun(list(X_a),list(X_a)),rev(X_a))=rev(X_a).
% 12.20/12.16 0 [] ti(fun(list(X_a),list(X_a)),rotate1(X_a))=rotate1(X_a).
% 12.20/12.16 0 [] ti(fun(list(X_a),fun(list(X_a),list(X_a))),splice(X_a))=splice(X_a).
% 12.20/12.16 0 [] ti(fun(list(X_a),fun(fun(nat,bool),list(X_a))),sublist(X_a))=sublist(X_a).
% 12.20/12.16 0 [] ti(fun(nat,fun(list(X_a),list(X_a))),take(X_a))=take(X_a).
% 12.20/12.16 0 [] ti(fun(fun(X_a,bool),fun(list(X_a),list(X_a))),takeWhile(X_a))=takeWhile(X_a).
% 12.20/12.16 0 [] ti(fun(list(X_a),list(X_a)),tl(X_a))=tl(X_a).
% 12.20/12.16 0 [] ti(fun(nat,nat),suc)=suc.
% 12.20/12.16 0 [] ti(fun(list(X_a),nat),size_size(list(X_a)))=size_size(list(X_a)).
% 12.20/12.16 0 [] -bot(X_b)|ti(X_b,bot_bot(X_b))=bot_bot(X_b).
% 12.20/12.16 0 [] -ord(X_a)|ti(fun(X_a,fun(X_a,bool)),ord_less(X_a))=ord_less(X_a).
% 12.20/12.16 0 [] -ordere236663937imp_le(X_a)|ti(fun(X_a,fun(X_a,X_a)),ord_max(X_a))=ord_max(X_a).
% 12.20/12.16 0 [] -linorder(X_a)|ti(fun(X_a,fun(X_a,X_a)),ord_max(X_a))=ord_max(X_a).
% 12.20/12.16 0 [] ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a))=collect(X_a).
% 12.20/12.16 0 [] ti(bool,fFalse)=fFalse.
% 12.20/12.16 0 [] ti(fun(bool,bool),fNot)=fNot.
% 12.20/12.16 0 [] ti(bool,fTrue)=fTrue.
% 12.20/12.16 0 [] ti(fun(bool,fun(bool,bool)),fconj)=fconj.
% 12.20/12.16 0 [] ti(fun(X_a,fun(X_a,bool)),fe_qual(X_a))=fe_qual(X_a).
% 12.20/12.16 0 [] hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1)=hAPP(X_a,X_c,B_1_1,B_2_1).
% 12.20/12.16 0 [] hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1))=hAPP(X_a,X_c,B_1_1,B_2_1).
% 12.20/12.16 0 [] ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1))=hAPP(X_a,X_c,B_1_1,B_2_1).
% 12.20/12.16 0 [] -hBOOL(ti(bool,B_1_1))|hBOOL(B_1_1).
% 12.20/12.16 0 [] hBOOL(ti(bool,B_1_1))| -hBOOL(B_1_1).
% 12.20/12.16 0 [] ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a))=member(X_a).
% 12.20/12.16 0 [] ti(arrow_490897120le_alt,a)=a.
% 12.20/12.16 0 [] ti(arrow_490897120le_alt,b)=b.
% 12.20/12.16 0 [] hBOOL(hAPP(list(arrow_490897120le_alt),bool,distinct(arrow_490897120le_alt),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),$c3),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),$c2),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),$c1),nil(arrow_490897120le_alt)))))).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,distinct(X_a),nil(X_a))).
% 12.20/12.16 0 [] nil(X_a)!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_5),List_4).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_5),List_4)!=nil(X_a).
% 12.20/12.16 0 [] Xs_1=nil(X_a)|Xs_1=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f2(X_a,Xs_1)),$f1(X_a,Xs_1)).
% 12.20/12.16 0 [] Xs_1!=nil(X_a)|Xs_1!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_2).
% 12.20/12.16 0 [] Y=nil(X_a)|Y=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f4(X_a,Y)),$f3(X_a,Y)).
% 12.20/12.16 0 [] Xs!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)!=Xs.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Aa),List)!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_3),List_2)|ti(X_a,Aa)=ti(X_a,A_3).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Aa),List)!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_3),List_2)|List=List_2.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Aa),List)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_3),List_2)|ti(X_a,Aa)!=ti(X_a,A_3)|List!=List_2.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),V),Va)),nil(X_a))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),V),Va).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X),nil(X_a))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a)).
% 12.20/12.16 0 [] Xs_1=nil(X_a)| -hBOOL(hAPP(list(X_a),bool,P_1,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f5(X_a,P_1,Xs_1)),nil(X_a))))|$f6(X_a,P_1,Xs_1)!=nil(X_a)|hBOOL(hAPP(list(X_a),bool,P_1,Xs_1)).
% 12.20/12.16 0 [] Xs_1=nil(X_a)| -hBOOL(hAPP(list(X_a),bool,P_1,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f5(X_a,P_1,Xs_1)),nil(X_a))))|hBOOL(hAPP(list(X_a),bool,P_1,$f6(X_a,P_1,Xs_1)))|hBOOL(hAPP(list(X_a),bool,P_1,Xs_1)).
% 12.20/12.16 0 [] Xs_1=nil(X_a)| -hBOOL(hAPP(list(X_a),bool,P_1,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f5(X_a,P_1,Xs_1)),nil(X_a))))| -hBOOL(hAPP(list(X_a),bool,P_1,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f7(X_a,P_1,Xs_1)),$f6(X_a,P_1,Xs_1))))|hBOOL(hAPP(list(X_a),bool,P_1,Xs_1)).
% 12.20/12.16 0 [] Xs=nil(X_a)| -hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs))|hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs))).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),butlast(X_a),nil(X_a))=nil(X_a).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs))|hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X),Xs))).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Ys))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),Xs),Ys))).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),Xs),nil(X_a))=Xs.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),nil(X_a)),Ys)=Ys.
% 12.20/12.16 0 [] Xs!=nil(X_a)|hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=nil(X_a).
% 12.20/12.16 0 [] Xs=nil(X_a)|hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)).
% 12.20/12.16 0 [] hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a)),list_case(X_a,X_b),F1),F2),nil(X_b))=ti(X_a,F1).
% 12.20/12.16 0 [] hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a)),list_case(X_a,X_b),F1),F2),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Aa),List))=hAPP(list(X_b),X_a,hAPP(X_b,fun(list(X_b),X_a),F2,Aa),List).
% 12.20/12.16 0 [] hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a)),list_rec(X_a,X_b),F1),F2),nil(X_b))=ti(X_a,F1).
% 12.20/12.16 0 [] hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a)),list_rec(X_a,X_b),F1),F2),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Aa),List))=hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(X_b,fun(list(X_b),fun(X_a,X_a)),F2,Aa),List),hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a)),list_rec(X_a,X_b),F1),F2),List)).
% 12.20/12.16 0 [] Xs_1!=nil(X_a)|hBOOL(hAPP(list(X_a),bool,null(X_a),Xs_1)).
% 12.20/12.16 0 [] Xs_1=nil(X_a)| -hBOOL(hAPP(list(X_a),bool,null(X_a),Xs_1)).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,null(X_a),Xs_1))|Xs_1=nil(X_a).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,null(X_a),Xs_1))|Xs_1!=nil(X_a).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_b),bool,null(X_b),nil(X_b))).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,null(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a))))=Xs.
% 12.20/12.16 0 [] hAPP(list(X_b),list(X_a),hAPP(fun(X_b,list(X_a)),fun(list(X_b),list(X_a)),maps(X_b,X_a),F),nil(X_b))=nil(X_a).
% 12.20/12.16 0 [] -linorder(X_a)|hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a)))).
% 12.20/12.16 0 [] -linorder(X_a)|hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),nil(X_a))).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys)),Zs_2)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),Zs_2)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),Ts)|Xs_1=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),$f8(X_a,Xs_1,Ys_1,Zs,Ts))|hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),$f8(X_a,Xs_1,Ys_1,Zs,Ts))=Zs.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),Ts)|Xs_1=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),$f8(X_a,Xs_1,Ys_1,Zs,Ts))|Ys_1=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),$f8(X_a,Xs_1,Ys_1,Zs,Ts)),Ts).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),Ts)|hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),$f8(X_a,Xs_1,Ys_1,Zs,Ts)),Ys_1)=Ts|hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),$f8(X_a,Xs_1,Ys_1,Zs,Ts))=Zs.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),Ts)|hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),$f8(X_a,Xs_1,Ys_1,Zs,Ts)),Ys_1)=Ts|Ys_1=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),$f8(X_a,Xs_1,Ys_1,Zs,Ts)),Ts).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),Ts)|Xs_1!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),Us_1)|hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us_1),Ys_1)!=Ts.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),Ts)|hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Us_1)!=Zs|Ys_1!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us_1),Ts).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Zs)|Ys_1=Zs.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Zs)|Ys_1!=Zs.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Xs_1)!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),Xs_1)|Ys_1=Zs.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),Xs_1)|Ys_1!=Zs.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Xs1)!=Zs_2|Ys!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs1),Us)|hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs_2),Us).
% 12.20/12.16 0 [] hAPP(list(X_b),list(X_a),hAPP(fun(X_b,list(X_a)),fun(list(X_b),list(X_a)),maps(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X_1),Xs_1))=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_b,list(X_a),F,X_1)),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,list(X_a)),fun(list(X_b),list(X_a)),maps(X_b,X_a),F),Xs_1)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),Ys)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs1)!=Ys|Xs!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs1),Zs_2)|hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),Zs_2).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),nil(X_a)),Ys)=Ys.
% 12.20/12.16 0 [] nil(X_a)!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)|Xs_1=nil(X_a).
% 12.20/12.16 0 [] nil(X_a)!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)|Ys_1=nil(X_a).
% 12.20/12.16 0 [] nil(X_a)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)|Xs_1!=nil(X_a)|Ys_1!=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),nil(X_a))=Xs.
% 12.20/12.16 0 [] Xs_1!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)|Ys_1=nil(X_a).
% 12.20/12.16 0 [] Xs_1=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)|Ys_1!=nil(X_a).
% 12.20/12.16 0 [] Ys_1!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)|Xs_1=nil(X_a).
% 12.20/12.16 0 [] Ys_1=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)|Xs_1!=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)!=nil(X_a)|Xs_1=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)!=nil(X_a)|Ys_1=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)=nil(X_a)|Xs_1!=nil(X_a)|Ys_1!=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)!=Xs_1|Ys_1=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)=Xs_1|Ys_1!=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)!=Ys_1|Xs_1=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)=Ys_1|Xs_1!=nil(X_a).
% 12.20/12.16 0 [] Xs!=Ys|Xs=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),nil(X_a)),Ys).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs)!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)|Ys_1=nil(X_a)|Ys_1=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),$f9(X_a,Ys_1,Zs,X_1,Xs_1)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs)!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)|Ys_1=nil(X_a)|hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),$f9(X_a,Ys_1,Zs,X_1,Xs_1)),Zs)=Xs_1.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs)!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)|Zs=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)|Ys_1=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),$f9(X_a,Ys_1,Zs,X_1,Xs_1)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs)!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)|Zs=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)|hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),$f9(X_a,Ys_1,Zs,X_1,Xs_1)),Zs)=Xs_1.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)|Ys_1!=nil(X_a)|Zs!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)|Ys_1!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Ys_3)|hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),Zs)!=Xs_1.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs)|Ys_1=nil(X_a)|hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),$f10(X_a,X_1,Xs_1,Ys_1,Zs))=Ys_1.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs)|Ys_1=nil(X_a)|Xs_1=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),$f10(X_a,X_1,Xs_1,Ys_1,Zs)),Zs).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs)|hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)=Zs|hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),$f10(X_a,X_1,Xs_1,Ys_1,Zs))=Ys_1.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs)|hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)=Zs|Xs_1=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),$f10(X_a,X_1,Xs_1,Ys_1,Zs)),Zs).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs)|Ys_1!=nil(X_a)|hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)!=Zs.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs)|hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Ys_3)!=Ys_1|Xs_1!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),Zs).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)))!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),nil(X_a)))|Xs_1=Ys_1.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)))!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),nil(X_a)))|ti(X_a,X_1)=ti(X_a,Y_2).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)))=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),nil(X_a)))|Xs_1!=Ys_1|ti(X_a,X_1)!=ti(X_a,Y_2).
% 12.20/12.16 0 [] Ys!=nil(X_a)|hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),list(X_a),butlast(X_a),Xs).
% 12.20/12.16 0 [] Ys=nil(X_a)|hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),butlast(X_a),Ys)).
% 12.20/12.16 0 [] -linorder(X_a)|Xs=nil(X_a)| -hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs))|hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs))).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,P_1,nil(X_a)))|hBOOL(hAPP(list(X_a),bool,P_1,$f11(X_a,Xs_1,P_1)))|hBOOL(hAPP(list(X_a),bool,P_1,Xs_1)).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,P_1,nil(X_a)))| -hBOOL(hAPP(list(X_a),bool,P_1,hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),$f11(X_a,Xs_1,P_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f12(X_a,Xs_1,P_1)),nil(X_a)))))|hBOOL(hAPP(list(X_a),bool,P_1,Xs_1)).
% 12.20/12.16 0 [] Xs=nil(X_a)|Xs=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),$f14(X_a,Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f13(X_a,Xs)),nil(X_a))).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),e_qual_e_qual(list(X_a)),Xs_1),nil(X_a)))|hBOOL(hAPP(list(X_a),bool,null(X_a),Xs_1)).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),e_qual_e_qual(list(X_a)),Xs_1),nil(X_a)))| -hBOOL(hAPP(list(X_a),bool,null(X_a),Xs_1)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)))!=Ys_1|Ys_1!=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)))!=Ys_1|hAPP(list(X_a),list(X_a),butlast(X_a),Ys_1)=Xs_1.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)))!=Ys_1|hAPP(list(X_a),X_a,last(X_a),Ys_1)=ti(X_a,X_1).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)))=Ys_1|Ys_1=nil(X_a)|hAPP(list(X_a),list(X_a),butlast(X_a),Ys_1)!=Xs_1|hAPP(list(X_a),X_a,last(X_a),Ys_1)!=ti(X_a,X_1).
% 12.20/12.16 0 [] Xs=nil(X_a)|hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,last(X_a),Xs)),nil(X_a)))=Xs.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),rotate1(X_a),nil(X_a))=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_b),list(X_b),rotate1(X_b),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X),Xs))=hAPP(list(X_b),list(X_b),hAPP(list(X_b),fun(list(X_b),list(X_b)),append(X_b),Xs),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X),nil(X_b))).
% 12.20/12.16 0 [] hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a))))=ti(X_a,X).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,distinct(X_a),Ws))|Ws=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),$f18(X_a,Ws)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f15(X_a,Ws)),nil(X_a))),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),$f17(X_a,Ws)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f15(X_a,Ws)),nil(X_a))),$f16(X_a,Ws))))).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),I_1),X)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a)))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),I_1),X)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a))).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)!=hAPP(list(X_a),list(X_a),rev(X_a),Ys_1)|Xs_1=Ys_1.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)=hAPP(list(X_a),list(X_a),rev(X_a),Ys_1)|Xs_1!=Ys_1.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)!=Ys_1|Xs_1=hAPP(list(X_a),list(X_a),rev(X_a),Ys_1).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)=Ys_1|Xs_1!=hAPP(list(X_a),list(X_a),rev(X_a),Ys_1).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),rev(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X))=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs))=Xs.
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),e_qual_e_qual(list(X_a)),X_1),Y_2))|X_1=Y_2.
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),e_qual_e_qual(list(X_a)),X_1),Y_2))|X_1!=Y_2.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)!=nil(X_a)|Xs_1=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)=nil(X_a)|Xs_1!=nil(X_a).
% 12.20/12.16 0 [] nil(X_a)!=hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)|Xs_1=nil(X_a).
% 12.20/12.16 0 [] nil(X_a)=hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)|Xs_1!=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),rev(X_a),nil(X_a))=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Ys)),hAPP(list(X_a),list(X_a),rev(X_a),Xs)).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)))|hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)))| -hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),K),X))=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),K),X)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),rotate1(X_a),Xs_1)!=nil(X_a)|Xs_1=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),rotate1(X_a),Xs_1)=nil(X_a)|Xs_1!=nil(X_a).
% 12.20/12.16 0 [] hAPP(X_a,X_b,F,$f19(X_a,X_b,F,G))!=hAPP(X_a,X_b,G,$f19(X_a,X_b,F,G))|ti(fun(X_a,X_b),F)=ti(fun(X_a,X_b),G).
% 12.20/12.16 0 [] -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))|hBOOL(hAPP(X_a,bool,A_1,X_1)).
% 12.20/12.16 0 [] hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))| -hBOOL(hAPP(X_a,bool,A_1,X_1)).
% 12.20/12.16 0 [] hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)=ti(fun(X_a,bool),P_1).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),rotate1(X_a),Xs_1)))|hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),rotate1(X_a),Xs_1)))| -hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))!=hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)|Xs_1=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))=hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)|Xs_1!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))|Xs_1=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))|Xs_1!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)),Xs)).
% 12.20/12.16 0 [] Xs!=nil(X_a)|hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=ti(X_a,X).
% 12.20/12.16 0 [] Xs=nil(X_a)|hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),X_a,last(X_a),Xs).
% 12.20/12.16 0 [] Xs!=nil(X_a)|hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=ti(X_a,X).
% 12.20/12.16 0 [] Xs=nil(X_a)|hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),X_a,last(X_a),Xs).
% 12.20/12.16 0 [] Ys!=nil(X_a)|hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),X_a,last(X_a),Xs).
% 12.20/12.16 0 [] Ys=nil(X_a)|hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),X_a,last(X_a),Ys).
% 12.20/12.16 0 [] Ys=nil(X_a)|hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),X_a,last(X_a),Ys).
% 12.20/12.16 0 [] Ys!=nil(X_a)|hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),X_a,last(X_a),Xs).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_1)|Xs_1=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Ys_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),nil(X_a))).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_1)|Xs_1!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Ys_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),nil(X_a))).
% 12.20/12.16 0 [] Xs=nil(X_a)|hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs))=hAPP(list(X_a),X_a,hd(X_a),Xs).
% 12.20/12.16 0 [] Xs=nil(X_a)|hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs))=hAPP(list(X_a),X_a,last(X_a),Xs).
% 12.20/12.16 0 [] -cl_HOL_Oe_qual(X_a)|e_qual_e_qual(X_a)=fe_qual(X_a).
% 12.20/12.16 0 [] -cl_HOL_Oe_qual(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),e_qual_e_qual(X_a),X),X)).
% 12.20/12.16 0 [] -cl_HOL_Oe_qual(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),e_qual_e_qual(X_a),X_1),Y_2))|ti(X_a,X_1)=ti(X_a,Y_2).
% 12.20/12.16 0 [] -cl_HOL_Oe_qual(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),e_qual_e_qual(X_a),X_1),Y_2))|ti(X_a,X_1)!=ti(X_a,Y_2).
% 12.20/12.16 0 [] -cl_HOL_Oe_qual(X_a)|fe_qual(X_a)=e_qual_e_qual(X_a).
% 12.20/12.16 0 [] Xs!=nil(X_a)|hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),X_a,hd(X_a),Ys).
% 12.20/12.16 0 [] Xs=nil(X_a)|hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),X_a,hd(X_a),Xs).
% 12.20/12.16 0 [] Xs=nil(X_a)|hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),X_a,hd(X_a),Xs).
% 12.20/12.16 0 [] Xs=nil(X_a)|hAPP(list(X_a),list(X_a),rotate1(X_a),Xs)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),tl(X_a),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,hd(X_a),Xs)),nil(X_a))).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=Xs.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),tl(X_a),nil(X_a))=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=ti(X_a,X).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs))|hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),tl(X_a),Xs))).
% 12.20/12.16 0 [] -linorder(X_a)| -hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs))|hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),tl(X_a),Xs))).
% 12.20/12.16 0 [] Xs=nil(X_a)|hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),tl(X_a),Xs)),Ys).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)=nil(X_a)| -hBOOL(hAPP(X_a,bool,P_1,hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)))).
% 12.20/12.16 0 [] -hBOOL(hAPP(X_a,bool,hAPP(list(X_a),fun(X_a,bool),member_1(X_a),nil(X_a)),Y)).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex1(X_a),P_1),nil(X_a))).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),X),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))).
% 12.20/12.16 0 [] -hBOOL(hAPP(X_a,bool,hAPP(list(X_a),fun(X_a,bool),member_1(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),Y_2))|ti(X_a,X_1)=ti(X_a,Y_2)|hBOOL(hAPP(X_a,bool,hAPP(list(X_a),fun(X_a,bool),member_1(X_a),Xs_1),Y_2)).
% 12.20/12.16 0 [] hBOOL(hAPP(X_a,bool,hAPP(list(X_a),fun(X_a,bool),member_1(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),Y_2))|ti(X_a,X_1)!=ti(X_a,Y_2).
% 12.20/12.16 0 [] hBOOL(hAPP(X_a,bool,hAPP(list(X_a),fun(X_a,bool),member_1(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),Y_2))| -hBOOL(hAPP(X_a,bool,hAPP(list(X_a),fun(X_a,bool),member_1(X_a),Xs_1),Y_2)).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),X),Xs))|hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),X),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Xs))).
% 12.20/12.16 0 [] N=zero_zero(nat)|hAPP(list(X_a),X_a,hd(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X))=ti(X_a,X).
% 12.20/12.16 0 [] N=zero_zero(nat)|hAPP(list(X_a),X_a,last(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X))=ti(X_a,X).
% 12.20/12.16 0 [] hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),M_1),X_1)!=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),Y_2)|M_1=N_2.
% 12.20/12.16 0 [] hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),M_1),X_1)!=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),Y_2)|M_1=zero_zero(nat)|ti(X_a,X_1)=ti(X_a,Y_2).
% 12.20/12.16 0 [] hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),M_1),X_1)=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),Y_2)|M_1!=N_2|M_1!=zero_zero(nat).
% 12.20/12.16 0 [] hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),M_1),X_1)=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),Y_2)|M_1!=N_2|ti(X_a,X_1)!=ti(X_a,Y_2).
% 12.20/12.16 0 [] -hBOOL(hAPP(X_a,bool,P_1,X_1))|hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))=hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1).
% 12.20/12.16 0 [] hBOOL(hAPP(X_a,bool,P_1,X_1))|hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),nil(X_a))=nil(X_a).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1))|hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1))).
% 12.20/12.16 0 [] -linorder(X_a)| -hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1))|hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1))).
% 12.20/12.16 0 [] hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),zero_zero(nat)),X)=nil(X_a).
% 12.20/12.16 0 [] nil(X_a)!=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),X_1)|N_2=zero_zero(nat).
% 12.20/12.16 0 [] nil(X_a)=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),X_1)|N_2!=zero_zero(nat).
% 12.20/12.16 0 [] hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),X_1)!=nil(X_a)|N_2=zero_zero(nat).
% 12.20/12.16 0 [] hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_2),X_1)=nil(X_a)|N_2!=zero_zero(nat).
% 12.20/12.16 0 [] -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),A_1))|hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))),A_1)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)).
% 12.20/12.16 0 [] hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),A_1))|hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))),A_1)=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_1)|Xs_1=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_1)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_1)| -hBOOL(hAPP(X_a,bool,P_1,Y_2)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_1)|Xs_1!=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_1))|hBOOL(hAPP(X_a,bool,P_1,Y_2)).
% 12.20/12.16 0 [] hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),Fa),nil(X_a))=zero_zero(nat).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),A1),A2))|ti(X_a,A1)=ti(X_a,$f21(X_a,A1,A2))|ti(X_a,A1)=ti(X_a,$f24(X_a,A1,A2)).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),A1),A2))|ti(X_a,A1)=ti(X_a,$f21(X_a,A1,A2))|A2=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f22(X_a,A1,A2)),$f23(X_a,A1,A2)).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),A1),A2))|ti(X_a,A1)=ti(X_a,$f21(X_a,A1,A2))|hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),$f24(X_a,A1,A2)),$f23(X_a,A1,A2))).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),A1),A2))|A2=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f21(X_a,A1,A2)),$f20(X_a,A1,A2))|ti(X_a,A1)=ti(X_a,$f24(X_a,A1,A2)).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),A1),A2))|A2=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f21(X_a,A1,A2)),$f20(X_a,A1,A2))|A2=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f22(X_a,A1,A2)),$f23(X_a,A1,A2)).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),A1),A2))|A2=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f21(X_a,A1,A2)),$f20(X_a,A1,A2))|hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),$f24(X_a,A1,A2)),$f23(X_a,A1,A2))).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),A1),A2))|ti(X_a,A1)!=ti(X_a,X_2)|A2!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),A1),A2))|ti(X_a,A1)!=ti(X_a,X2)|A2!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),X3)| -hBOOL(hAPP(list(X_a),bool,hAPP(X_a,fun(list(X_a),bool),listMem(X_a),X2),X3)).
% 12.20/12.16 0 [] -zero(X_a)|zero_zero(X_a)!=ti(X_a,X_1)|ti(X_a,X_1)=zero_zero(X_a).
% 12.20/12.16 0 [] -zero(X_a)|zero_zero(X_a)=ti(X_a,X_1)|ti(X_a,X_1)!=zero_zero(X_a).
% 12.20/12.16 0 [] Xs=nil(X_a)|hAPP(list(X_a),X_a,hd(X_a),Xs)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),zero_zero(nat)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),nil(X_a))=nil(X_a).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1))|hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))).
% 12.20/12.16 0 [] -linorder(X_a)| -hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1))|hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))).
% 12.20/12.16 0 [] hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),nil(X_a)),A_1)=nil(X_a).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1))|hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),Xs_1),I_4))).
% 12.20/12.16 0 [] hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),zero_zero(nat))=ti(X_a,X).
% 12.20/12.16 0 [] -hBOOL(hAPP(X_a,bool,P_1,X_1))|hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)).
% 12.20/12.16 0 [] hBOOL(hAPP(X_a,bool,P_1,X_1))|hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))=nil(X_a).
% 12.20/12.16 0 [] hBOOL(hAPP(X_a,bool,P_1,X_1))|hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),L_1)))=hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1))=Xs_1.
% 12.20/12.16 0 [] hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Ys))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))=ti(X_a,X).
% 12.20/12.16 0 [] -linorder(X_a)| -hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)))|Xs_1!=nil(X_a)|hAPP(X_a,X_a,hAPP(list(X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(list(X_a),fun(X_a,X_a)),foldr(X_a,X_a),ord_max(X_a)),Xs_1),Y_2)=ti(X_a,Y_2).
% 12.20/12.16 0 [] -linorder(X_a)| -hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)))|Xs_1=nil(X_a)|hAPP(X_a,X_a,hAPP(list(X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(list(X_a),fun(X_a,X_a)),foldr(X_a,X_a),ord_max(X_a)),Xs_1),Y_2)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),zero_zero(nat))),Y_2).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,nil(X_a)),nil(X_b)))| -hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f26(X_b,X_a,Xs_1,Ys_1,P_1)),$f25(X_b,X_a,Xs_1,Ys_1,P_1))),nil(X_b)))| -hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,nil(X_a)),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),$f28(X_b,X_a,Xs_1,Ys_1,P_1)),$f27(X_b,X_a,Xs_1,Ys_1,P_1))))|hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,$f31(X_b,X_a,Xs_1,Ys_1,P_1)),$f29(X_b,X_a,Xs_1,Ys_1,P_1)))|hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,Xs_1),Ys_1)).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,nil(X_a)),nil(X_b)))| -hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f26(X_b,X_a,Xs_1,Ys_1,P_1)),$f25(X_b,X_a,Xs_1,Ys_1,P_1))),nil(X_b)))| -hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,nil(X_a)),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),$f28(X_b,X_a,Xs_1,Ys_1,P_1)),$f27(X_b,X_a,Xs_1,Ys_1,P_1))))| -hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f32(X_b,X_a,Xs_1,Ys_1,P_1)),$f31(X_b,X_a,Xs_1,Ys_1,P_1))),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),$f30(X_b,X_a,Xs_1,Ys_1,P_1)),$f29(X_b,X_a,Xs_1,Ys_1,P_1))))|hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,Xs_1),Ys_1)).
% 12.20/12.16 0 [] hAPP(list(X_b),list(X_a),hAPP(fun(X_b,option(X_a)),fun(list(X_b),list(X_a)),map_filter(X_b,X_a),F),nil(X_b))=nil(X_a).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),nil(X_a)),nil(X_a))).
% 12.20/12.16 0 [] -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,X_1),Y_2))| -hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),Xs_1),Ys_1))|hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_1))).
% 12.20/12.16 0 [] hAPP(fun(nat,bool),list(X_a),hAPP(list(X_a),fun(fun(nat,bool),list(X_a)),sublist(X_a),Xs_1),bot_bot(fun(nat,bool)))=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),Xs)=hAPP(list(X_a),nat,size_size(list(X_a)),Ys)|Xs!=Ys.
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),rev(X_a),Xs))=hAPP(list(X_a),nat,size_size(list(X_a)),Xs).
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X))=N.
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),rotate1(X_a),Xs))=hAPP(list(X_a),nat,size_size(list(X_a)),Xs).
% 12.20/12.16 0 [] hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X_1),Xs_1)),Aa)=hAPP(X_a,X_a,hAPP(X_b,fun(X_a,X_a),F,X_1),hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),Xs_1),Aa)).
% 12.20/12.16 0 [] hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),nil(X_b)),Aa)=ti(X_a,Aa).
% 12.20/12.16 0 [] hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(list(X_b),fun(list(X_b),list(X_b)),append(X_b),Xs_1),Ys_1)),Aa)=hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),Xs_1),hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(list(X_b),fun(X_a,X_a)),foldr(X_b,X_a),F),Ys_1),Aa)).
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)!=zero_zero(nat)|Xs_1=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)=zero_zero(nat)|Xs_1!=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),nil(X_a))=zero_zero(nat).
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)!=hAPP(list(X_b),nat,size_size(list(X_b)),Ys_1)| -hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,nil(X_a)),nil(X_b)))|hAPP(list(X_a),nat,size_size(list(X_a)),$f35(X_a,X_b,P_1,Xs_1,Ys_1))=hAPP(list(X_b),nat,size_size(list(X_b)),$f33(X_a,X_b,P_1,Xs_1,Ys_1))|hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,Xs_1),Ys_1)).
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)!=hAPP(list(X_b),nat,size_size(list(X_b)),Ys_1)| -hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,nil(X_a)),nil(X_b)))|hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,$f35(X_a,X_b,P_1,Xs_1,Ys_1)),$f33(X_a,X_b,P_1,Xs_1,Ys_1)))|hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,Xs_1),Ys_1)).
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)!=hAPP(list(X_b),nat,size_size(list(X_b)),Ys_1)| -hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,nil(X_a)),nil(X_b)))| -hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f36(X_a,X_b,P_1,Xs_1,Ys_1)),$f35(X_a,X_b,P_1,Xs_1,Ys_1))),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),$f34(X_a,X_b,P_1,Xs_1,Ys_1)),$f33(X_a,X_b,P_1,Xs_1,Ys_1))))|hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),P_1,Xs_1),Ys_1)).
% 12.20/12.16 0 [] -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),bot_bot(fun(X_a,bool)))).
% 12.20/12.16 0 [] -bot(X_b)|hAPP(X_a,X_b,bot_bot(fun(X_a,X_b)),X_2)=bot_bot(X_b).
% 12.20/12.16 0 [] -bot(X_a)|hAPP(X_b,X_a,bot_bot(fun(X_b,X_a)),X_1)=bot_bot(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),$f37(X_a,N))=N.
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),A1),A2))|A1=nil(X_a)|A1=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f41(X_a,R_1,A1,A2)),$f39(X_a,R_1,A1,A2)).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),A1),A2))|A1=nil(X_a)|A2=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f40(X_a,R_1,A1,A2)),$f38(X_a,R_1,A1,A2)).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),A1),A2))|A1=nil(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,$f41(X_a,R_1,A1,A2)),$f40(X_a,R_1,A1,A2))).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),A1),A2))|A1=nil(X_a)|hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),$f39(X_a,R_1,A1,A2)),$f38(X_a,R_1,A1,A2))).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),A1),A2))|A2=nil(X_a)|A1=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f41(X_a,R_1,A1,A2)),$f39(X_a,R_1,A1,A2)).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),A1),A2))|A2=nil(X_a)|A2=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f40(X_a,R_1,A1,A2)),$f38(X_a,R_1,A1,A2)).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),A1),A2))|A2=nil(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,$f41(X_a,R_1,A1,A2)),$f40(X_a,R_1,A1,A2))).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),A1),A2))|A2=nil(X_a)|hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),$f39(X_a,R_1,A1,A2)),$f38(X_a,R_1,A1,A2))).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),A1),A2))|A1!=nil(X_a)|A2!=nil(X_a).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),A1),A2))|A1!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2)|A2!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_2)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,X_2),Y_1))| -hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_1),Xs_2),Ys_2)).
% 12.20/12.16 0 [] ti(fun(X_a,bool),A_1)!=bot_bot(fun(X_a,bool))| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),A_1)).
% 12.20/12.16 0 [] hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)!=bot_bot(fun(X_a,bool))| -hBOOL(hAPP(X_a,bool,P_1,X_2)).
% 12.20/12.16 0 [] hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)=bot_bot(fun(X_a,bool))|hBOOL(hAPP(X_a,bool,P_1,$f42(X_a,P_1))).
% 12.20/12.16 0 [] -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),bot_bot(fun(X_a,bool)))).
% 12.20/12.16 0 [] bot_bot(fun(X_a,bool))!=hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)| -hBOOL(hAPP(X_a,bool,P_1,X_2)).
% 12.20/12.16 0 [] bot_bot(fun(X_a,bool))=hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)|hBOOL(hAPP(X_a,bool,P_1,$f43(X_a,P_1))).
% 12.20/12.16 0 [] -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))|ti(fun(X_a,bool),A_1)!=bot_bot(fun(X_a,bool)).
% 12.20/12.16 0 [] hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),$f44(X_a,A_1)),A_1))|ti(fun(X_a,bool),A_1)=bot_bot(fun(X_a,bool)).
% 12.20/12.16 0 [] hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),$f45(X_a,A_1)),A_1))|ti(fun(X_a,bool),A_1)=bot_bot(fun(X_a,bool)).
% 12.20/12.16 0 [] -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))|ti(fun(X_a,bool),A_1)!=bot_bot(fun(X_a,bool)).
% 12.20/12.16 0 [] bot_bot(fun(X_a,bool))=hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(bool,fun(X_a,bool),combk(bool,X_a),fFalse)).
% 12.20/12.16 0 [] hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),$f46(X_a,A_1)),A_1))|ti(fun(X_a,bool),A_1)=bot_bot(fun(X_a,bool)).
% 12.20/12.16 0 [] -linorder(X_a)|hAPP(fun(X_a,bool),list(X_a),linord467138063of_set(X_a),bot_bot(fun(X_a,bool)))=nil(X_a).
% 12.20/12.16 0 [] -linorder(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)).
% 12.20/12.16 0 [] -linorder(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_1)),C_2)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_1),C_2)).
% 12.20/12.16 0 [] -linorder(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z)).
% 12.20/12.16 0 [] -linorder(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),C_2))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_1),C_2)).
% 12.20/12.16 0 [] -linorder(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),A_2)=ti(X_a,A_2).
% 12.20/12.16 0 [] -linorder(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_1)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B_1),A_2).
% 12.20/12.16 0 [] -linorder(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),X).
% 12.20/12.16 0 [] -linorder(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_1))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_1).
% 12.20/12.16 0 [] -linorder(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y).
% 12.20/12.16 0 [] -linorder(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),X)=ti(X_a,X).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))),Xs_1).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))| -hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))))|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)),J_1)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),J_1).
% 12.20/12.16 0 [] hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Ys))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),Y)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Ys)).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),zero_zero(nat)),N)=N.
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))).
% 12.20/12.16 0 [] hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),I_1),Y)=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),Y).
% 12.20/12.16 0 [] I_1=I_3|hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),I_3),X_3)=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_3),X_3)),I_1),X).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|M_1=N_2|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),M_1)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3))|S!=T_3.
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M))|M!=N.
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)).
% 12.20/12.16 0 [] X=Y|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X)).
% 12.20/12.16 0 [] M_1=N_2|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1)).
% 12.20/12.16 0 [] M_1!=N_2| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 12.20/12.16 0 [] M_1!=N_2| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)).
% 12.20/12.16 0 [] N=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))|N!=zero_zero(nat).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))).
% 12.20/12.16 0 [] N_2=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)).
% 12.20/12.16 0 [] N_2!=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))).
% 12.20/12.16 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X)).
% 12.20/12.16 0 [] -linorder(X_a)|ti(X_a,X_1)=ti(X_a,Y_2)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1)).
% 12.20/12.16 0 [] -linorder(X_a)|ti(X_a,X_1)!=ti(X_a,Y_2)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2)).
% 12.20/12.16 0 [] -linorder(X_a)|ti(X_a,X_1)!=ti(X_a,Y_2)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1)).
% 12.20/12.16 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1))|ti(X_a,X_1)=ti(X_a,Y_2).
% 12.20/12.16 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1)).
% 12.20/12.16 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))|ti(X_a,X_1)!=ti(X_a,Y_2).
% 12.20/12.16 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|ti(X_a,X)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)).
% 12.20/12.16 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))|ti(X_a,X_1)=ti(X_a,Y_2).
% 12.20/12.16 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))|ti(X_a,X_1)!=ti(X_a,Y_2).
% 12.20/12.16 0 [] -linorder(X_a)|ti(X_a,X)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)).
% 12.20/12.16 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|X!=Y.
% 12.20/12.16 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)).
% 12.20/12.16 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)).
% 12.20/12.16 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|X!=Y.
% 12.20/12.16 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|Y!=X.
% 12.20/12.16 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_1))|hBOOL(P_1).
% 12.20/12.16 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)).
% 12.20/12.16 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)).
% 12.20/12.16 0 [] -ord(X_a)|A_2!=B_1| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C_2)).
% 12.20/12.16 0 [] -order(X_a)|A_2!=B_1| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_2),B_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_2),A_2)).
% 12.20/12.16 0 [] -ord(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))|B_1!=C_2|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C_2)).
% 12.20/12.16 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))|B_1!=C_2|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_2),A_2)).
% 12.20/12.16 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z)).
% 12.20/12.16 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X)).
% 12.20/12.16 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)).
% 12.20/12.16 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|ti(X_a,X)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))|hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys)),I_1),X)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),Ys).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))|I_1!=J|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),J)=ti(X_a,X).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))|I_1=J|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),J)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),J).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))|hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs_1),I),X_1)!=Xs_1|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I)=ti(X_a,X_1).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))|hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs_1),I),X_1)=Xs_1|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I)!=ti(X_a,X_1).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),I_1)=ti(X_a,X).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))|hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))=hAPP(list(X_a),X_a,last(X_a),Xs).
% 12.20/12.16 0 [] -bot(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),bot_bot(X_a))).
% 12.20/12.16 0 [] -bot(X_a)|ti(X_a,Aa)=bot_bot(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),bot_bot(X_a)),Aa)).
% 12.20/12.16 0 [] -bot(X_a)|ti(X_a,Aa)!=bot_bot(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),bot_bot(X_a)),Aa)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),zero_zero(nat)),Xs)=Xs.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),nil(X_a))=nil(X_a).
% 12.20/12.16 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y_2)).
% 12.20/12.16 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X_1)).
% 12.20/12.16 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y_2)).
% 12.20/12.16 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_2)),Z_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z_1)).
% 12.20/12.16 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_2)),Z_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),Z_1)).
% 12.20/12.16 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_2)),Z_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),Z_1)).
% 12.20/12.16 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_1))).
% 12.20/12.16 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),B_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_2),B_1))).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs))|hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_1),Xs))).
% 12.20/12.16 0 [] -linorder(X_a)| -hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs))|hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))).
% 12.20/12.16 0 [] hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs_1),K_1),X_1)!=nil(X_a)|Xs_1=nil(X_a).
% 12.20/12.16 0 [] hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs_1),K_1),X_1)=nil(X_a)|Xs_1!=nil(X_a).
% 12.20/12.16 0 [] hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),nil(X_a)),I_1),V)=nil(X_a).
% 12.20/12.16 0 [] hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),nil(X_a)),I_1),Y)=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X))=hAPP(list(X_a),nat,size_size(list(X_a)),Xs).
% 12.20/12.16 0 [] hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_1))=Xs.
% 12.20/12.16 0 [] I_1=J|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),X)),J)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),J).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),butlast(X_a),Xs))=hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),tl(X_a),Xs)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),tl(X_a),Xs))=hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)).
% 12.20/12.16 0 [] Xs=nil(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))|hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Ys)|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N)=ti(X_a,Y).
% 12.20/12.16 0 [] Xs_1!=Ys_1|hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)=hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1).
% 12.20/12.16 0 [] Xs_1!=Ys_1| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I_2)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys_1),I_2).
% 12.20/12.16 0 [] Xs_1=Ys_1|hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)!=hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f47(X_a,Xs_1,Ys_1)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))).
% 12.20/12.16 0 [] Xs_1=Ys_1|hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)!=hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1)|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),$f47(X_a,Xs_1,Ys_1))!=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys_1),$f47(X_a,Xs_1,Ys_1)).
% 12.20/12.16 0 [] hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),zero_zero(nat)),Y)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Xs).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),N))|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)),I_1)=ti(X_a,X).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))|Xs_1!=nil(X_a).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))|Xs_1=nil(X_a).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))|I_2=J_2|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I_2)!=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),J_2).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f49(X_a,Xs_1)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f48(X_a,Xs_1)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1))|$f49(X_a,Xs_1)!=$f48(X_a,Xs_1).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1))|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),$f49(X_a,Xs_1))=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),$f48(X_a,Xs_1)).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I)!=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),J_1)|I=J_1.
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),I)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),J_1)|I!=J_1.
% 12.20/12.16 0 [] bot_bot(nat)=zero_zero(nat).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N),zero_zero(nat))=N.
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),Xs)!=hAPP(list(X_a),nat,size_size(list(X_a)),Ys)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f50(X_a,Xs,Ys)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))|Xs=Ys.
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),Xs)!=hAPP(list(X_a),nat,size_size(list(X_a)),Ys)|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),$f50(X_a,Xs,Ys))!=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys),$f50(X_a,Xs,Ys))|Xs=Ys.
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f51(X_a,P_1,K_1)),K_1))|hAPP(list(X_a),nat,size_size(list(X_a)),$f52(X_a,P_1,K_1))=K_1.
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f51(X_a,P_1,K_1)),K_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1))|hBOOL(hAPP(X_a,bool,hAPP(nat,fun(X_a,bool),P_1,I_2),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),$f52(X_a,P_1,K_1)),I_2))).
% 12.20/12.16 0 [] -hBOOL(hAPP(X_a,bool,hAPP(nat,fun(X_a,bool),P_1,$f51(X_a,P_1,K_1)),X1))|hAPP(list(X_a),nat,size_size(list(X_a)),$f52(X_a,P_1,K_1))=K_1.
% 12.20/12.16 0 [] -hBOOL(hAPP(X_a,bool,hAPP(nat,fun(X_a,bool),P_1,$f51(X_a,P_1,K_1)),X1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_1))|hBOOL(hAPP(X_a,bool,hAPP(nat,fun(X_a,bool),P_1,I_2),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),$f52(X_a,P_1,K_1)),I_2))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),K_1))|hBOOL(hAPP(X_a,bool,hAPP(nat,fun(X_a,bool),P_1,X4),$f53(X_a,P_1,K_1,X4)))|hAPP(list(X_a),nat,size_size(list(X_a)),Xs_2)!=K_1|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f54(X_a,P_1,K_1,Xs_2)),K_1)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),K_1))|hBOOL(hAPP(X_a,bool,hAPP(nat,fun(X_a,bool),P_1,X4),$f53(X_a,P_1,K_1,X4)))|hAPP(list(X_a),nat,size_size(list(X_a)),Xs_2)!=K_1| -hBOOL(hAPP(X_a,bool,hAPP(nat,fun(X_a,bool),P_1,$f54(X_a,P_1,K_1,Xs_2)),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_2),$f54(X_a,P_1,K_1,Xs_2)))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1))))|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P_1),Xs_1)),J_1)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))|hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_1)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,I_1)),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_1),Xs).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),Xs_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f55(X_a,P_1,Xs_1)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),Xs_1))|hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),$f55(X_a,P_1,Xs_1)))).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),Xs_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))| -hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),N_1))).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,N))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N))).
% 12.20/12.16 0 [] hAPP(nat,nat,suc,X)!=hAPP(nat,nat,suc,Y)|X=Y.
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K_1)|M_1=N_2.
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K_1)|M_1!=N_2.
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2)|M_1=N_2.
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2)|M_1!=N_2.
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K)).
% 12.20/12.16 0 [] hAPP(nat,nat,suc,Nat_4)!=hAPP(nat,nat,suc,Nat_3)|Nat_4=Nat_3.
% 12.20/12.16 0 [] hAPP(nat,nat,suc,Nat_4)=hAPP(nat,nat,suc,Nat_3)|Nat_4!=Nat_3.
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N)).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Z)).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N))=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|N_2=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),$f56(M_1,N_2))).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|N_2!=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2)).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),I_1)))).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),M)))).
% 12.20/12.16 0 [] hAPP(nat,nat,suc,N)!=N.
% 12.20/12.16 0 [] N!=hAPP(nat,nat,suc,N).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)!=hAPP(nat,nat,suc,zero_zero(nat))|M_1=hAPP(nat,nat,suc,zero_zero(nat))|M_1=zero_zero(nat).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)!=hAPP(nat,nat,suc,zero_zero(nat))|M_1=hAPP(nat,nat,suc,zero_zero(nat))|N_2=hAPP(nat,nat,suc,zero_zero(nat)).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)!=hAPP(nat,nat,suc,zero_zero(nat))|N_2=zero_zero(nat)|M_1=zero_zero(nat).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)!=hAPP(nat,nat,suc,zero_zero(nat))|N_2=zero_zero(nat)|N_2=hAPP(nat,nat,suc,zero_zero(nat)).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)=hAPP(nat,nat,suc,zero_zero(nat))|M_1!=hAPP(nat,nat,suc,zero_zero(nat))|N_2!=zero_zero(nat).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)=hAPP(nat,nat,suc,zero_zero(nat))|M_1!=zero_zero(nat)|N_2!=hAPP(nat,nat,suc,zero_zero(nat)).
% 12.20/12.16 0 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)|M_1=hAPP(nat,nat,suc,zero_zero(nat))|M_1=zero_zero(nat).
% 12.20/12.16 0 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)|M_1=hAPP(nat,nat,suc,zero_zero(nat))|N_2=hAPP(nat,nat,suc,zero_zero(nat)).
% 12.20/12.16 0 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)|N_2=zero_zero(nat)|M_1=zero_zero(nat).
% 12.20/12.16 0 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)|N_2=zero_zero(nat)|N_2=hAPP(nat,nat,suc,zero_zero(nat)).
% 12.20/12.16 0 [] hAPP(nat,nat,suc,zero_zero(nat))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)|M_1!=hAPP(nat,nat,suc,zero_zero(nat))|N_2!=zero_zero(nat).
% 12.20/12.16 0 [] hAPP(nat,nat,suc,zero_zero(nat))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)|M_1!=zero_zero(nat)|N_2!=hAPP(nat,nat,suc,zero_zero(nat)).
% 12.20/12.16 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),A_2)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),A_2)|ti(X_a,B_1)=ti(X_a,C_2).
% 12.20/12.16 0 [] -cancel146912293up_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)|ti(X_a,B_1)=ti(X_a,C_2).
% 12.20/12.16 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)|ti(X_a,B_1)=ti(X_a,C_2).
% 12.20/12.16 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa)|ti(X_a,Ba)=ti(X_a,C_1).
% 12.20/12.16 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa)|ti(X_a,Ba)!=ti(X_a,C_1).
% 12.20/12.16 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1)|ti(X_a,Ba)=ti(X_a,C_1).
% 12.20/12.16 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1)|ti(X_a,Ba)!=ti(X_a,C_1).
% 12.20/12.16 0 [] -ab_semigroup_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),C_2)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_2)).
% 12.20/12.16 0 [] -comm_monoid_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),zero_zero(X_a))=ti(X_a,A_2).
% 12.20/12.16 0 [] -monoid_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),zero_zero(X_a))=ti(X_a,A_2).
% 12.20/12.16 0 [] -linord219039673up_add(X_a)|zero_zero(X_a)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)|ti(X_a,Aa)=zero_zero(X_a).
% 12.20/12.16 0 [] -linord219039673up_add(X_a)|zero_zero(X_a)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)|ti(X_a,Aa)!=zero_zero(X_a).
% 12.20/12.16 0 [] -comm_monoid_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_2)=ti(X_a,A_2).
% 12.20/12.16 0 [] -monoid_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_2)=ti(X_a,A_2).
% 12.20/12.16 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),B_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)).
% 12.20/12.16 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)).
% 12.20/12.16 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_2),D_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D_2))).
% 12.20/12.16 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),B_1))).
% 12.20/12.16 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_2))).
% 12.20/12.16 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Ba)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)).
% 12.20/12.16 0 [] -ordere236663937imp_le(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Ba)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)).
% 12.20/12.16 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)).
% 12.20/12.16 0 [] -ordere236663937imp_le(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),C_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)).
% 12.20/12.16 0 [] zero_zero(nat)!=hAPP(nat,nat,suc,M).
% 12.20/12.16 0 [] zero_zero(nat)!=hAPP(nat,nat,suc,Nat_2).
% 12.20/12.16 0 [] hAPP(nat,nat,suc,M)!=zero_zero(nat).
% 12.20/12.16 0 [] hAPP(nat,nat,suc,Nat_1)!=zero_zero(nat).
% 12.20/12.16 0 [] zero_zero(nat)!=hAPP(nat,nat,suc,M).
% 12.20/12.16 0 [] hAPP(nat,nat,suc,M)!=zero_zero(nat).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))|M_1=N_2.
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))|M_1!=N_2.
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1)))|N_2=M_1.
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1)))|N_2!=M_1.
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M)))|M=N.
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))|hAPP(nat,nat,suc,M)=N|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_1)),K)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))|M=N.
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)).
% 12.20/12.16 0 [] -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),bot_bot(fun(X_a,bool)))).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N)=N.
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),zero_zero(nat))=M.
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)!=zero_zero(nat)|M_1=zero_zero(nat).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)!=zero_zero(nat)|N_2=zero_zero(nat).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)=zero_zero(nat)|M_1!=zero_zero(nat)|N_2!=zero_zero(nat).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)!=M|N=zero_zero(nat).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J)),I_1)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I_1)),I_1)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K)).
% 12.20/12.16 0 [] -ordere236663937imp_le(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),M),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),Xs).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),M),N)).
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_2),List_1))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),List_1)),hAPP(nat,nat,suc,zero_zero(nat))).
% 12.20/12.16 0 [] hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),Fa),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Aa),List))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(X_a,nat,Fa,Aa)),hAPP(list(X_a),nat,hAPP(fun(X_a,nat),fun(list(X_a),nat),list_size(X_a),Fa),List))),hAPP(nat,nat,suc,zero_zero(nat))).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)))|hBOOL(hAPP(X_a,bool,P_1,X_1))|hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),Xs_1)).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)))| -hBOOL(hAPP(X_a,bool,P_1,X_1)).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)))| -hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),Xs_1)).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),nil(X_a))).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)))|hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),Xs_1))|hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),Ys_1)).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)))| -hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),Xs_1)).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)))| -hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),Ys_1)).
% 12.20/12.16 0 [] -linord219039673up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa)).
% 12.20/12.16 0 [] -linord219039673up_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa)).
% 12.20/12.16 0 [] -linord219039673up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))).
% 12.20/12.16 0 [] -linord219039673up_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))).
% 12.20/12.16 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1))).
% 12.20/12.16 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),zero_zero(X_a))).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)))|hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),Xs_1)).
% 12.20/12.16 0 [] hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)))| -hBOOL(hAPP(list(X_a),bool,hAPP(fun(X_a,bool),fun(list(X_a),bool),list_ex(X_a),P_1),Xs_1)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2))|N_2=hAPP(nat,nat,suc,$f57(N_2)).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2))|N_2!=hAPP(nat,nat,suc,M_2).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,zero_zero(nat))))|N_2=zero_zero(nat).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,zero_zero(nat))))|N_2!=zero_zero(nat).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))|M_1=zero_zero(nat)|M_1=hAPP(nat,nat,suc,$f58(M_1,N_2)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))|M_1=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f58(M_1,N_2)),N_2)).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))|M_1!=zero_zero(nat).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2)))|M_1!=hAPP(nat,nat,suc,J_2)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),N_2)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)).
% 12.20/12.16 0 [] hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),hAPP(nat,nat,suc,N))=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N).
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),hAPP(list(X_a),nat,size_size(list(X_a)),Ys)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,N)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs).
% 12.20/12.16 0 [] hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),hAPP(nat,nat,suc,I_1)),Y)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),Y)).
% 12.20/12.16 0 [] hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,suc,N)),X)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)).
% 12.20/12.16 0 [] hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),X)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),M),X)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,N)),Xs)=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),tl(X_a),Xs)).
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),Xs),Ys))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),hAPP(list(X_a),nat,size_size(list(X_a)),Ys)).
% 12.20/12.16 0 [] hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),N))=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys),N).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))|N=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),$f59(M,N))).
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)!=hAPP(nat,nat,suc,N_2)|Xs_1=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f61(X_a,Xs_1,N_2)),$f60(X_a,Xs_1,N_2)).
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)!=hAPP(nat,nat,suc,N_2)|hAPP(list(X_a),nat,size_size(list(X_a)),$f60(X_a,Xs_1,N_2))=N_2.
% 12.20/12.16 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)=hAPP(nat,nat,suc,N_2)|Xs_1!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_2)|hAPP(list(X_a),nat,size_size(list(X_a)),Ys_2)!=N_2.
% 12.20/12.16 0 [] hAPP(nat,nat,suc,N_2)!=hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)|Xs_1=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),$f63(X_a,N_2,Xs_1)),$f62(X_a,N_2,Xs_1)).
% 12.20/12.16 0 [] hAPP(nat,nat,suc,N_2)!=hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)|hAPP(list(X_a),nat,size_size(list(X_a)),$f62(X_a,N_2,Xs_1))=N_2.
% 12.20/12.16 0 [] hAPP(nat,nat,suc,N_2)=hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)|Xs_1!=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_2)|hAPP(list(X_a),nat,size_size(list(X_a)),Ys_2)!=N_2.
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),$f64(I_1,J))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),$f64(I_1,J))=J.
% 12.20/12.16 0 [] -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1))|hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)).
% 12.20/12.16 0 [] -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B))| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B),C_3))|hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),C_3)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|N=hAPP(nat,nat,suc,$f65(N)).
% 12.20/12.16 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,$f66(X_a,N_2,N_3,F))),hAPP(nat,X_a,F,hAPP(nat,nat,suc,$f66(X_a,N_2,N_3,F)))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),N_3))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,N_3))).
% 12.20/12.16 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,$f67(X_a,N_2,M_1,F))),hAPP(nat,X_a,F,hAPP(nat,nat,suc,$f67(X_a,N_2,M_1,F)))))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,M_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1)).
% 12.20/12.16 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,$f67(X_a,N_2,M_1,F))),hAPP(nat,X_a,F,hAPP(nat,nat,suc,$f67(X_a,N_2,M_1,F)))))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,M_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1)).
% 12.20/12.16 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))).
% 12.20/12.16 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))).
% 12.20/12.16 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C_2))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2))).
% 12.20/12.16 0 [] -linordered_idom(X_a)|ti(X_a,X)=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)).
% 12.20/12.16 0 [] -linord219039673up_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)!=zero_zero(X_a)|ti(X_a,Aa)=zero_zero(X_a).
% 12.20/12.16 0 [] -linord219039673up_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)=zero_zero(X_a)|ti(X_a,Aa)!=zero_zero(X_a).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K))|K=hAPP(nat,nat,suc,I_1)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),$f68(I_1,K))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K))|K=hAPP(nat,nat,suc,I_1)|K=hAPP(nat,nat,suc,$f68(I_1,K)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_1)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),$f69(I_1,K))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_1)),K))|K=hAPP(nat,nat,suc,$f69(I_1,K)).
% 12.20/12.16 0 [] Y=zero_zero(nat)|Y=hAPP(nat,nat,suc,$f70(Y)).
% 12.20/12.16 0 [] N=zero_zero(nat)|N=hAPP(nat,nat,suc,$f71(N)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))|hBOOL(hAPP(nat,bool,P_1,$f72(N_2,P_1)))|hBOOL(hAPP(nat,bool,P_1,N_2)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,$f72(N_2,P_1))))|hBOOL(hAPP(nat,bool,P_1,N_2)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,P_1,K_1))|hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,$f73(P_1,K_1))))|hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,P_1,K_1))| -hBOOL(hAPP(nat,bool,P_1,$f73(P_1,K_1)))|hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))|hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))),nil(X_a)))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N)),Xs).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),tl(X_a),Xs))=hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N)),Xs)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),nil(X_a))=nil(X_a).
% 12.20/12.16 0 [] -hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs))|hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),Xs))).
% 12.20/12.16 0 [] -linorder(X_a)| -hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs))|hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs))).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1))),Xs_1).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))=Xs.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),M),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),M),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),Xs)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),N))|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs)),I_1)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_1).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_2),Xs_1)!=nil(X_a)|N_2=zero_zero(nat)|Xs_1=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_2),Xs_1)=nil(X_a)|N_2!=zero_zero(nat).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_2),Xs_1)=nil(X_a)|Xs_1!=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),zero_zero(nat)),Xs)=nil(X_a).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)!=Zs|Xs_1=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)),Zs).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)!=Zs|Ys_1=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)),Zs).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)=Zs|Xs_1!=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)),Zs)|Ys_1!=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)),Zs).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J)),Xs)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),J),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_1),Xs))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))|hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),butlast(X_a),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs).
% 12.20/12.16 0 [] Xs=nil(X_a)|hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N)),Xs)=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,hd(X_a),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),tl(X_a),Xs))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))|hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,I_1)),Xs)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_1)),nil(X_a))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))|Xs=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),I_1)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,I_1)),Xs))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))|hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),I_1),A_2)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_2),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,I_1)),Xs))).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f74(X_a,P_1,Xs_1,N_2)),N_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))|hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_2),Xs_1).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f74(X_a,P_1,Xs_1,N_2)),N_2))|hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),N_2)))|hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_2),Xs_1).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f74(X_a,P_1,Xs_1,N_2)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))|hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_2),Xs_1).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f74(X_a,P_1,Xs_1,N_2)),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))|hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),N_2)))|hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_2),Xs_1).
% 12.20/12.16 0 [] -hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),$f74(X_a,P_1,Xs_1,N_2))))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))|hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_2),Xs_1).
% 12.20/12.16 0 [] -hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),$f74(X_a,P_1,Xs_1,N_2))))|hBOOL(hAPP(X_a,bool,P_1,hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs_1),N_2)))|hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),P_1),Xs_1)=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_2),Xs_1).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))).
% 12.20/12.16 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_2)=ti(X_a,A_2).
% 12.20/12.16 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),zero_zero(X_a))=ti(X_a,A_2).
% 12.20/12.16 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),D_2))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D_2)).
% 12.20/12.16 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),C_2)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)),B_1).
% 12.20/12.16 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),C_2)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_2)).
% 12.20/12.16 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),D_2))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)),D_2).
% 12.20/12.16 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),D_2))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),D_2)).
% 12.20/12.16 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_2)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_2),A_2).
% 12.20/12.16 0 [] -semiri456707255roduct(X_a)|ti(X_a,Ba)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa)|ti(X_a,Aa)=zero_zero(X_a).
% 12.20/12.16 0 [] -semiri456707255roduct(X_a)|ti(X_a,Ba)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa)|ti(X_a,Aa)!=zero_zero(X_a).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs)),N)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),hAPP(nat,nat,suc,N))).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),$f75(X_a,Xs,Ys)),Xs)!=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),$f75(X_a,Xs,Ys)),Ys)|Xs=Ys.
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),M),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)).
% 12.20/12.16 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_1),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),K),X))=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K),I_1)),X).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K)).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),N)=M.
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),N)=M.
% 12.20/12.16 0 [] -ordered_ab_group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_1)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_1)).
% 12.20/12.16 0 [] -ordered_ab_group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_1)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_1)).
% 12.20/12.16 0 [] -group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),B_1)=ti(X_a,A_2).
% 12.20/12.16 0 [] -group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),B_1)=ti(X_a,A_2).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),N)),K)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M))).
% 12.20/12.16 0 [] -ordered_ab_group_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),zero_zero(X_a))).
% 12.20/12.16 0 [] -ordered_ab_group_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),zero_zero(X_a))).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),M)).
% 12.20/12.16 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),M_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),M_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)).
% 12.20/12.16 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),hAPP(nat,nat,suc,M))).
% 12.20/12.16 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M))=zero_zero(nat).
% 12.20/12.17 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_1)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_1)),J_1)).
% 12.20/12.17 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_1)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_1)),J_1)).
% 12.20/12.17 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))=M.
% 12.20/12.17 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),N).
% 12.20/12.17 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J)),K)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),K)),J).
% 12.20/12.17 0 [] -ordered_ab_group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z)).
% 12.20/12.17 0 [] -ab_group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_1)|ti(X_a,Aa)!=ti(X_a,Ba)|ti(X_a,C_1)=ti(X_a,D_1).
% 12.20/12.17 0 [] -ab_group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)!=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_1)|ti(X_a,Aa)=ti(X_a,Ba)|ti(X_a,C_1)!=ti(X_a,D_1).
% 12.20/12.17 0 [] -group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),zero_zero(X_a))=ti(X_a,A_2).
% 12.20/12.17 0 [] -group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),A_2)=zero_zero(X_a).
% 12.20/12.17 0 [] -ab_group_add(X_a)|ti(X_a,Aa)!=ti(X_a,Ba)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)=zero_zero(X_a).
% 12.20/12.17 0 [] -ab_group_add(X_a)|ti(X_a,Aa)=ti(X_a,Ba)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)!=zero_zero(X_a).
% 12.20/12.17 0 [] -group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)!=zero_zero(X_a)|ti(X_a,Aa)=ti(X_a,Ba).
% 12.20/12.17 0 [] -group_add(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)=zero_zero(X_a)|ti(X_a,Aa)!=ti(X_a,Ba).
% 12.20/12.17 0 [] -minus(X_a)|hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),minus_minus(fun(X_b,X_a)),A_1),B),X_1)=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_b,X_a,A_1,X_1)),hAPP(X_b,X_a,B,X_1)).
% 12.20/12.17 0 [] -minus(X_b)|hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),minus_minus(fun(X_a,X_b)),A_1),B),X_2)=hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,A_1,X_2)),hAPP(X_a,X_b,B,X_2)).
% 12.20/12.17 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)!=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M)!=zero_zero(nat)|M=N.
% 12.20/12.17 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M)=zero_zero(nat).
% 12.20/12.17 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat))=M.
% 12.20/12.17 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N)=zero_zero(nat).
% 12.20/12.17 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N).
% 12.20/12.17 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N)),hAPP(nat,nat,suc,K))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),K).
% 12.20/12.17 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M)),M)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N),M).
% 12.20/12.17 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,I_1))),N)).
% 12.20/12.17 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat))))=N.
% 12.20/12.17 0 [] -hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba))|hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))).
% 12.20/12.17 0 [] -hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))|Aa!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),D)|hBOOL(hAPP(nat,bool,P_1,D)).
% 12.20/12.17 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba))|Aa=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),$f76(P_1,Aa,Ba)).
% 12.20/12.17 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba))| -hBOOL(hAPP(nat,bool,P_1,$f76(P_1,Aa,Ba))).
% 12.20/12.17 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))| -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))|Aa=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),$f76(P_1,Aa,Ba)).
% 12.20/12.17 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))| -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,$f76(P_1,Aa,Ba))).
% 12.20/12.17 0 [] -hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba))|hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))).
% 12.20/12.17 0 [] -hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))|Aa!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),D)|hBOOL(hAPP(nat,bool,P_1,D)).
% 12.20/12.17 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba))|Aa=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),$f77(P_1,Aa,Ba)).
% 12.20/12.17 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba))| -hBOOL(hAPP(nat,bool,P_1,$f77(P_1,Aa,Ba))).
% 12.20/12.17 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))| -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))|Aa=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),$f77(P_1,Aa,Ba)).
% 12.20/12.17 0 [] hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba)))| -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,$f77(P_1,Aa,Ba))).
% 12.20/12.17 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))),Ys)).
% 12.20/12.17 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys))=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))),Ys)).
% 12.20/12.17 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys)),N)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),N).
% 12.20/12.17 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys)),N)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Ys),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))).
% 12.20/12.17 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))|hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys)),N),X)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),N),X)),Ys).
% 12.20/12.17 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))|hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys)),N),X)=hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Ys),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))),X)).
% 12.20/12.17 0 [] hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_1),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),I_1)),hAPP(list(X_a),list(X_a),rev(X_a),Xs)).
% 12.20/12.17 0 [] hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),I_1)),hAPP(list(X_a),list(X_a),rev(X_a),Xs)).
% 12.20/12.17 0 [] -hBOOL(hAPP(nat,bool,P_1,K_1))|hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,$f78(I,P_1,K_1))))|hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K_1),I))).
% 12.20/12.17 0 [] -hBOOL(hAPP(nat,bool,P_1,K_1))| -hBOOL(hAPP(nat,bool,P_1,$f78(I,P_1,K_1)))|hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K_1),I))).
% 12.20/12.17 0 [] Xs=nil(X_a)|K!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat))|hAPP(list(X_a),X_a,last(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),K),X))=ti(X_a,X).
% 12.20/12.17 0 [] Xs=nil(X_a)|K=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat))|hAPP(list(X_a),X_a,last(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),K),X))=hAPP(list(X_a),X_a,last(X_a),Xs).
% 12.20/12.17 0 [] hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),bot_bot(fun(X_a,bool))),A_1)=bot_bot(fun(X_a,bool)).
% 12.20/12.17 0 [] hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),bot_bot(fun(X_a,bool)))=ti(fun(X_a,bool),A_1).
% 12.20/12.17 0 [] hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),A_1)=bot_bot(fun(X_a,bool)).
% 12.20/12.17 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N)),one_one(nat))=N.
% 12.20/12.17 0 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,N))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N).
% 12.20/12.17 0 [] hAPP(nat,nat,suc,N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N).
% 12.20/12.17 0 [] hAPP(nat,nat,suc,N)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat)).
% 12.20/12.17 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),one_one(nat)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=Xs.
% 12.20/12.17 0 [] -one(X_a)|one_one(X_a)!=ti(X_a,X_1)|ti(X_a,X_1)=one_one(X_a).
% 12.20/12.17 0 [] -one(X_a)|one_one(X_a)=ti(X_a,X_1)|ti(X_a,X_1)!=one_one(X_a).
% 12.20/12.17 0 [] one_one(nat)=hAPP(nat,nat,suc,zero_zero(nat)).
% 12.20/12.17 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),one_one(X_a)))).
% 12.20/12.17 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a))).
% 12.20/12.17 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a))).
% 12.20/12.17 0 [] -zero_ne_q_one(X_a)|one_one(X_a)!=zero_zero(X_a).
% 12.20/12.17 0 [] -zero_ne_q_one(X_a)|zero_zero(X_a)!=one_one(X_a).
% 12.20/12.17 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))).
% 12.20/12.17 0 [] hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),one_one(nat)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a)).
% 12.20/12.17 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),butlast(X_a),Xs))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat)).
% 12.20/12.17 0 [] hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),tl(X_a),Xs))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat)).
% 12.20/12.17 0 [] hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),hAPP(list(X_a),list(X_a),tl(X_a),Xs)).
% 12.20/12.17 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|N=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))).
% 12.20/12.17 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))=N.
% 12.20/12.17 0 [] M!=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)=N.
% 12.20/12.17 0 [] M=zero_zero(nat)|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N)).
% 12.20/12.17 0 [] N!=zero_zero(nat)|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),N)=ti(X_a,X).
% 12.20/12.17 0 [] N=zero_zero(nat)|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),N)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))).
% 12.20/12.17 0 [] N!=zero_zero(nat)|hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs).
% 12.20/12.17 0 [] N=zero_zero(nat)|hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),Xs).
% 12.20/12.17 0 [] hAPP(list(X_a),list(X_a),butlast(X_a),Xs)=hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat))),Xs).
% 12.20/12.17 0 [] K!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat))|hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),K),X))=hAPP(list(X_a),list(X_a),butlast(X_a),Xs).
% 12.20/12.17 0 [] K=hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat))|hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),K),X))=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)),K),X).
% 12.20/12.17 0 [] N=zero_zero(nat)|hAPP(list(X_a),list(X_a),tl(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X))=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),X).
% 12.20/12.17 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),N)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))).
% 12.20/12.17 0 [] N!=zero_zero(nat)|hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=nil(X_a).
% 12.20/12.17 0 [] N=zero_zero(nat)|hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),Xs)).
% 12.20/12.17 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)))|hAPP(list(X_a),list(X_a),rev(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),Xs),K),Y))=hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),hAPP(list(X_a),fun(nat,fun(X_a,list(X_a))),list_update(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),K)),one_one(nat))),Y).
% 12.20/12.17 0 [] Xs=nil(X_a)|hAPP(list(X_a),X_a,last(X_a),Xs)=hAPP(nat,X_a,hAPP(list(X_a),fun(nat,X_a),nth(X_a),Xs),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),one_one(nat))).
% 12.20/12.17 0 [] hAPP(int,nat,number_number_of(nat),V)!=zero_zero(nat)|hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(int,nat,number_number_of(nat),V)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=nil(X_a).
% 12.20/12.17 0 [] hAPP(int,nat,number_number_of(nat),V)=zero_zero(nat)|hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(int,nat,number_number_of(nat),V)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))=hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))),Xs)).
% 12.20/12.17 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),Aa)),Aa)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))).
% 12.20/12.17 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),Aa)),Aa)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))).
% 12.20/12.17 0 [] -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)))|hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)).
% 12.20/12.17 0 [] -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)))| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)).
% 12.20/12.17 0 [] -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1))|hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B))|hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B))).
% 12.20/12.17 0 [] -ring_1(X_a)| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a)))| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a)))|hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),ring_1_Ints(X_a))).
% 12.20/12.17 0 [] -number_ring(X_a)|hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),V),W))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W)).
% 12.20/12.17 0 [] -number_ring(X_a)|hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),W)),C_2))=hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),C_2).
% 12.20/12.17 0 [] -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)))| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)).
% 12.20/12.17 0 [] -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)))|hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)).
% 12.20/12.17 0 [] hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)),B)=hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B).
% 12.20/12.17 0 [] -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)))|hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1)).
% 12.20/12.17 0 [] -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)))| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)).
% 12.20/12.17 0 [] hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)))| -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1))|hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)).
% 12.20/12.17 0 [] hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_1),B)=hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B)))).
% 12.20/12.17 0 [] enum(bool).
% 12.20/12.17 0 [] -enum(T_1)| -enum(T_2)|enum(fun(T_2,T_1)).
% 12.20/12.17 0 [] -preorder(T_1)|preorder(fun(T_2,T_1)).
% 12.20/12.17 0 [] -order(T_1)|order(fun(T_2,T_1)).
% 12.20/12.17 0 [] -ord(T_1)|ord(fun(T_2,T_1)).
% 12.20/12.17 0 [] -bot(T_1)|bot(fun(T_2,T_1)).
% 12.20/12.17 0 [] -minus(T_1)|minus(fun(T_2,T_1)).
% 12.20/12.17 0 [] -cl_HOL_Oe_qual(T_1)| -enum(T_2)|cl_HOL_Oe_qual(fun(T_2,T_1)).
% 12.20/12.17 0 [] semiri456707255roduct(int).
% 12.20/12.17 0 [] ordere223160158up_add(int).
% 12.20/12.17 0 [] ordere236663937imp_le(int).
% 12.20/12.17 0 [] ordere216010020id_add(int).
% 12.20/12.17 0 [] linord219039673up_add(int).
% 12.20/12.17 0 [] cancel146912293up_add(int).
% 12.20/12.17 0 [] ordered_ab_group_add(int).
% 12.20/12.17 0 [] cancel_semigroup_add(int).
% 12.20/12.17 0 [] linordered_semidom(int).
% 12.20/12.17 0 [] ab_semigroup_add(int).
% 12.20/12.17 0 [] comm_monoid_add(int).
% 12.20/12.17 0 [] linordered_idom(int).
% 12.20/12.17 0 [] comm_semiring_1(int).
% 12.20/12.17 0 [] ab_group_add(int).
% 12.20/12.17 0 [] zero_ne_q_one(int).
% 12.20/12.17 0 [] preorder(int).
% 12.20/12.17 0 [] linorder(int).
% 12.20/12.17 0 [] monoid_add(int).
% 12.20/12.17 0 [] group_add(int).
% 12.20/12.17 0 [] order(int).
% 12.20/12.17 0 [] number_ring(int).
% 12.20/12.17 0 [] ord(int).
% 12.20/12.17 0 [] ring_1(int).
% 12.20/12.17 0 [] minus(int).
% 12.20/12.17 0 [] zero(int).
% 12.20/12.17 0 [] one(int).
% 12.20/12.17 0 [] cl_HOL_Oe_qual(int).
% 12.20/12.17 0 [] semiri456707255roduct(nat).
% 12.20/12.17 0 [] ordere223160158up_add(nat).
% 12.20/12.17 0 [] ordere236663937imp_le(nat).
% 12.20/12.17 0 [] ordere216010020id_add(nat).
% 12.20/12.17 0 [] cancel146912293up_add(nat).
% 12.20/12.17 0 [] cancel_semigroup_add(nat).
% 12.20/12.17 0 [] linordered_semidom(nat).
% 12.20/12.17 0 [] ab_semigroup_add(nat).
% 12.20/12.17 0 [] comm_monoid_add(nat).
% 12.20/12.17 0 [] comm_semiring_1(nat).
% 12.20/12.17 0 [] zero_ne_q_one(nat).
% 12.20/12.17 0 [] preorder(nat).
% 12.20/12.17 0 [] linorder(nat).
% 12.20/12.17 0 [] monoid_add(nat).
% 12.20/12.17 0 [] order(nat).
% 12.20/12.17 0 [] ord(nat).
% 12.20/12.17 0 [] bot(nat).
% 12.20/12.17 0 [] minus(nat).
% 12.20/12.17 0 [] zero(nat).
% 12.20/12.17 0 [] one(nat).
% 12.20/12.17 0 [] cl_HOL_Oe_qual(nat).
% 12.20/12.17 0 [] preorder(bool).
% 12.20/12.17 0 [] order(bool).
% 12.20/12.17 0 [] ord(bool).
% 12.20/12.17 0 [] bot(bool).
% 12.20/12.17 0 [] minus(bool).
% 12.20/12.17 0 [] cl_HOL_Oe_qual(bool).
% 12.20/12.17 0 [] cl_HOL_Oe_qual(list(T_1)).
% 12.20/12.17 0 [] ti(T,ti(T,A))=ti(T,A).
% 12.20/12.17 0 [] -hBOOL(hAPP(bool,bool,fNot,P))| -hBOOL(P).
% 12.20/12.17 0 [] hBOOL(P)|hBOOL(hAPP(bool,bool,fNot,P)).
% 12.20/12.17 0 [] hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R)=hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R)).
% 12.20/12.17 0 [] hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R)=hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q).
% 12.20/12.17 0 [] hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q)=ti(X_a,P).
% 12.20/12.17 0 [] hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R)=hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R)).
% 12.20/12.17 0 [] -hBOOL(P)| -hBOOL(Q)|hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)).
% 12.20/12.17 0 [] -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(P).
% 12.20/12.17 0 [] -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))|hBOOL(Q).
% 12.20/12.17 0 [] -hBOOL(fFalse).
% 12.20/12.17 0 [] ti(bool,P)=fTrue|ti(bool,P)=fFalse.
% 12.20/12.17 0 [] -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fe_qual(X_a),X),Y))|ti(X_a,X)=ti(X_a,Y).
% 12.20/12.17 0 [] ti(X_a,X)!=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fe_qual(X_a),X),Y)).
% 12.20/12.17 0 [] a!=b.
% 12.20/12.17 0 [] -hBOOL(hAPP(list(arrow_490897120le_alt),bool,distinct(arrow_490897120le_alt),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),a),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),b),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),C),nil(arrow_490897120le_alt)))))).
% 12.20/12.17 end_of_list.
% 12.20/12.17
% 12.20/12.17 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 12.20/12.17
% 12.20/12.17 This ia a non-Horn set with equality. The strategy will be
% 12.20/12.17 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 12.20/12.17 deletion, with positive clauses in sos and nonpositive
% 12.20/12.17 clauses in usable.
% 12.20/12.17
% 12.20/12.17 dependent: set(knuth_bendix).
% 12.20/12.17 dependent: set(anl_eq).
% 12.20/12.17 dependent: set(para_from).
% 12.20/12.17 dependent: set(para_into).
% 12.20/12.17 dependent: clear(para_from_right).
% 12.20/12.17 dependent: clear(para_into_right).
% 12.20/12.17 dependent: set(para_from_vars).
% 12.20/12.17 dependent: set(eq_units_both_ways).
% 12.20/12.17 dependent: set(dynamic_demod_all).
% 12.20/12.17 dependent: set(dynamic_demod).
% 12.20/12.17 dependent: set(order_eq).
% 12.20/12.17 dependent: set(back_demod).
% 12.20/12.17 dependent: set(lrpo).
% 12.20/12.17 dependent: set(hyper_res).
% 12.20/12.17 dependent: set(unit_deletion).
% 12.20/12.17 dependent: set(factor).
% 12.20/12.17
% 12.20/12.17 ------------> process usable:
% 12.20/12.17 ** KEPT (pick-wt=13): 1 [] -minus(A)|ti(fun(A,fun(A,A)),minus_minus(A))=minus_minus(A).
% 12.20/12.17 ** KEPT (pick-wt=9): 2 [] -one(A)|ti(A,one_one(A))=one_one(A).
% 12.20/12.17 ** KEPT (pick-wt=13): 3 [] -monoid_add(A)|ti(fun(A,fun(A,A)),plus_plus(A))=plus_plus(A).
% 12.20/12.17 ** KEPT (pick-wt=13): 4 [] -ab_semigroup_add(A)|ti(fun(A,fun(A,A)),plus_plus(A))=plus_plus(A).
% 12.20/12.17 ** KEPT (pick-wt=13): 5 [] -cancel_semigroup_add(A)|ti(fun(A,fun(A,A)),plus_plus(A))=plus_plus(A).
% 12.20/12.17 ** KEPT (pick-wt=9): 6 [] -zero(A)|ti(A,zero_zero(A))=zero_zero(A).
% 12.20/12.17 ** KEPT (pick-wt=13): 7 [] -cl_HOL_Oe_qual(A)|ti(fun(A,fun(A,bool)),e_qual_e_qual(A))=e_qual_e_qual(A).
% 12.20/12.17 ** KEPT (pick-wt=11): 8 [] -number_ring(A)|ti(fun(int,A),number_number_of(A))=number_number_of(A).
% 12.20/12.17 ** KEPT (pick-wt=11): 9 [] -ring_1(A)|ti(fun(A,bool),ring_1_Ints(A))=ring_1_Ints(A).
% 12.20/12.17 ** KEPT (pick-wt=12): 10 [] -linorder(A)|ti(fun(list(A),bool),linorder_sorted(A))=linorder_sorted(A).
% 12.20/12.17 ** KEPT (pick-wt=14): 11 [] -linorder(A)|ti(fun(fun(A,bool),list(A)),linord467138063of_set(A))=linord467138063of_set(A).
% 12.20/12.17 ** KEPT (pick-wt=9): 12 [] -bot(A)|ti(A,bot_bot(A))=bot_bot(A).
% 12.20/12.17 ** KEPT (pick-wt=13): 13 [] -ord(A)|ti(fun(A,fun(A,bool)),ord_less(A))=ord_less(A).
% 12.20/12.17 ** KEPT (pick-wt=13): 14 [] -ordere236663937imp_le(A)|ti(fun(A,fun(A,A)),ord_max(A))=ord_max(A).
% 12.20/12.17 ** KEPT (pick-wt=13): 15 [] -linorder(A)|ti(fun(A,fun(A,A)),ord_max(A))=ord_max(A).
% 12.20/12.17 ** KEPT (pick-wt=6): 16 [] -hBOOL(ti(bool,A))|hBOOL(A).
% 12.20/12.17 ** KEPT (pick-wt=6): 17 [] hBOOL(ti(bool,A))| -hBOOL(A).
% 12.20/12.17 ** KEPT (pick-wt=19): 18 [] nil(A)!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C).
% 12.20/12.17 ** KEPT (pick-wt=19): 19 [] hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)!=nil(A).
% 12.20/12.17 ** KEPT (pick-wt=22): 20 [] A!=nil(B)|A!=hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),C),D).
% 12.20/12.17 ** KEPT (pick-wt=18): 22 [copy,21,flip.1] hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)!=C.
% 12.20/12.17 Following clause subsumed by 22 during input processing: 0 [] hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)!=C.
% 12.20/12.17 ** KEPT (pick-wt=40): 23 [] hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E)|ti(A,B)=ti(A,D).
% 12.20/12.17 ** KEPT (pick-wt=36): 24 [] hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E)|C=E.
% 12.20/12.17 ** KEPT (pick-wt=43): 25 [] hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E)|ti(A,B)!=ti(A,D)|C!=E.
% 12.20/12.17 ** KEPT (pick-wt=44): 26 [] A=nil(B)| -hBOOL(hAPP(list(B),bool,C,hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),$f5(B,C,A)),nil(B))))|$f6(B,C,A)!=nil(B)|hBOOL(hAPP(list(B),bool,C,A)).
% 12.20/12.17 ** KEPT (pick-wt=47): 27 [] A=nil(B)| -hBOOL(hAPP(list(B),bool,C,hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),$f5(B,C,A)),nil(B))))|hBOOL(hAPP(list(B),bool,C,$f6(B,C,A)))|hBOOL(hAPP(list(B),bool,C,A)).
% 12.20/12.17 ** KEPT (pick-wt=65): 28 [] A=nil(B)| -hBOOL(hAPP(list(B),bool,C,hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),$f5(B,C,A)),nil(B))))| -hBOOL(hAPP(list(B),bool,C,hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),$f7(B,C,A)),$f6(B,C,A))))|hBOOL(hAPP(list(B),bool,C,A)).
% 12.20/12.17 ** KEPT (pick-wt=27): 29 [] A=nil(B)| -hBOOL(hAPP(list(B),bool,distinct(B),A))|hBOOL(hAPP(list(B),bool,distinct(B),hAPP(list(B),list(B),butlast(B),A))).
% 12.20/12.17 ** KEPT (pick-wt=31): 30 [] -hBOOL(hAPP(list(A),bool,distinct(A),B))|hBOOL(hAPP(list(A),bool,distinct(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),insert(A),C),B))).
% 12.20/12.17 ** KEPT (pick-wt=30): 31 [] A!=nil(B)|hAPP(list(B),list(B),butlast(B),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),C),A))=nil(B).
% 12.20/12.17 ** KEPT (pick-wt=12): 32 [] A!=nil(B)|hBOOL(hAPP(list(B),bool,null(B),A)).
% 12.20/12.17 ** KEPT (pick-wt=12): 33 [] A=nil(B)| -hBOOL(hAPP(list(B),bool,null(B),A)).
% 12.20/12.17 Following clause subsumed by 33 during input processing: 0 [] -hBOOL(hAPP(list(A),bool,null(A),B))|B=nil(A).
% 12.20/12.17 Following clause subsumed by 32 during input processing: 0 [] hBOOL(hAPP(list(A),bool,null(A),B))|B!=nil(A).
% 12.20/12.17 ** KEPT (pick-wt=23): 34 [] -hBOOL(hAPP(list(A),bool,null(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))).
% 12.20/12.17 ** KEPT (pick-wt=26): 35 [] -linorder(A)|hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),nil(A)))).
% 12.20/12.17 ** KEPT (pick-wt=11): 36 [] -linorder(A)|hBOOL(hAPP(list(A),bool,linorder_sorted(A),nil(A))).
% 12.20/12.17 ** KEPT (pick-wt=83): 38 [copy,37,flip.2] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),E)|hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),$f8(A,B,C,D,E))=B|hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),$f8(A,B,C,D,E))=D.
% 12.20/12.17 ** KEPT (pick-wt=83): 40 [copy,39,flip.2,flip.3] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),E)|hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),$f8(A,B,C,D,E))=B|hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),$f8(A,B,C,D,E)),E)=C.
% 12.20/12.17 ** KEPT (pick-wt=83): 41 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),E)|hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),$f8(A,B,C,D,E)),C)=E|hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),$f8(A,B,C,D,E))=D.
% 12.20/12.17 ** KEPT (pick-wt=83): 43 [copy,42,flip.3] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),E)|hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),$f8(A,B,C,D,E)),C)=E|hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),$f8(A,B,C,D,E)),E)=C.
% 12.20/12.17 ** KEPT (pick-wt=73): 44 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),E)|B!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),F)|hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),F),C)!=E.
% 12.20/12.17 ** KEPT (pick-wt=73): 45 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),E)|hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),F)!=D|C!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),F),E).
% 12.20/12.17 ** KEPT (pick-wt=38): 46 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),D)|C=D.
% 12.20/12.17 ** KEPT (pick-wt=38): 47 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),D)|C!=D.
% 12.20/12.17 ** KEPT (pick-wt=38): 48 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),C)|B=D.
% 12.20/12.17 ** KEPT (pick-wt=38): 49 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),C)|B!=D.
% 12.20/12.17 Following clause subsumed by 45 during input processing: 0 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)!=D|E!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),C),F)|hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),E)=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),F).
% 12.20/12.17 ** KEPT (pick-wt=71): 50 [] hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)!=D|E!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),C),F)|hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),E)=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),F).
% 12.20/12.17 ** KEPT (pick-wt=24): 51 [] nil(A)!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)|B=nil(A).
% 12.20/12.17 ** KEPT (pick-wt=24): 52 [] nil(A)!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)|C=nil(A).
% 12.20/12.17 ** KEPT (pick-wt=28): 53 [] nil(A)=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)|B!=nil(A)|C!=nil(A).
% 12.20/12.17 ** KEPT (pick-wt=23): 55 [copy,54,flip.1] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)!=B|C=nil(A).
% 12.20/12.17 ** KEPT (pick-wt=23): 57 [copy,56,flip.1] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)=B|C!=nil(A).
% 12.20/12.17 ** KEPT (pick-wt=23): 59 [copy,58,flip.1] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)!=C|B=nil(A).
% 12.20/12.17 ** KEPT (pick-wt=23): 61 [copy,60,flip.1] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)=C|B!=nil(A).
% 12.20/12.17 ** KEPT (pick-wt=24): 62 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)!=nil(A)|B=nil(A).
% 12.20/12.17 ** KEPT (pick-wt=24): 63 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)!=nil(A)|C=nil(A).
% 12.20/12.17 ** KEPT (pick-wt=28): 64 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)=nil(A)|B!=nil(A)|C!=nil(A).
% 12.20/12.17 Following clause subsumed by 55 during input processing: 0 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)!=B|C=nil(A).
% 12.20/12.17 Following clause subsumed by 57 during input processing: 0 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)=B|C!=nil(A).
% 12.20/12.17 Following clause subsumed by 59 during input processing: 0 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)!=C|B=nil(A).
% 12.20/12.17 Following clause subsumed by 61 during input processing: 0 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)=C|B!=nil(A).
% 12.20/12.17 ** KEPT (pick-wt=23): 65 [] A!=B|A=hAPP(list(C),list(C),hAPP(list(C),fun(list(C),list(C)),append(C),nil(C)),B).
% 12.20/12.17 ** KEPT (pick-wt=61): 67 [copy,66,flip.3] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E)|B=nil(A)|hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),$f9(A,B,C,D,E))=B.
% 12.20/12.17 ** KEPT (pick-wt=62): 68 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E)|B=nil(A)|hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),$f9(A,B,C,D,E)),C)=E.
% 12.20/12.17 ** KEPT (pick-wt=75): 70 [copy,69,flip.3] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E)|C=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E)|hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),$f9(A,B,C,D,E))=B.
% 12.20/12.17 ** KEPT (pick-wt=76): 71 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E)|C=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E)|hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),$f9(A,B,C,D,E)),C)=E.
% 12.20/12.17 ** KEPT (pick-wt=56): 72 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E)|B!=nil(A)|C!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E).
% 12.20/12.17 ** KEPT (pick-wt=71): 73 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C)=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E)|B!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),F)|hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),F),C)!=E.
% 12.20/12.17 ** KEPT (pick-wt=61): 74 [] hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),E)|D=nil(A)|hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),$f10(A,B,C,D,E))=D.
% 12.20/12.17 ** KEPT (pick-wt=62): 76 [copy,75,flip.3] hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),E)|D=nil(A)|hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),$f10(A,B,C,D,E)),E)=C.
% 12.20/12.17 ** KEPT (pick-wt=75): 77 [] hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),E)|hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)=E|hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),$f10(A,B,C,D,E))=D.
% 12.20/12.17 ** KEPT (pick-wt=76): 79 [copy,78,flip.3] hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),E)|hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)=E|hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),$f10(A,B,C,D,E)),E)=C.
% 12.20/12.17 ** KEPT (pick-wt=56): 80 [] hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),E)|D!=nil(A)|hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)!=E.
% 12.20/12.17 Following clause subsumed by 50 during input processing: 0 [] hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),E)|hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),F)!=D|C!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),F),E).
% 12.20/12.17 ** KEPT (pick-wt=70): 81 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),nil(A)))!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),E),nil(A)))|B=D.
% 12.20/12.17 ** KEPT (pick-wt=74): 82 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),nil(A)))!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),E),nil(A)))|ti(A,C)=ti(A,E).
% 12.20/12.17 ** KEPT (pick-wt=77): 83 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),nil(A)))=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),D),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),E),nil(A)))|B!=D|ti(A,C)!=ti(A,E).
% 12.20/12.17 ** KEPT (pick-wt=37): 84 [] A!=nil(B)|hAPP(list(B),list(B),butlast(B),hAPP(list(B),list(B),hAPP(list(B),fun(list(B),list(B)),append(B),C),A))=hAPP(list(B),list(B),butlast(B),C).
% 12.20/12.17 ** KEPT (pick-wt=29): 85 [] -linorder(A)|B=nil(A)| -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B))|hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),butlast(A),B))).
% 12.20/12.17 ** KEPT (pick-wt=25): 86 [] -hBOOL(hAPP(list(A),bool,B,nil(A)))|hBOOL(hAPP(list(A),bool,B,$f11(A,C,B)))|hBOOL(hAPP(list(A),bool,B,C)).
% 12.20/12.17 ** KEPT (pick-wt=60): 87 [] -hBOOL(hAPP(list(A),bool,B,nil(A)))| -hBOOL(hAPP(list(A),bool,B,hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),$f11(A,C,B)),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),$f12(A,C,B)),nil(A)))))|hBOOL(hAPP(list(A),bool,B,C)).
% 12.20/12.17 ** KEPT (pick-wt=26): 88 [] -hBOOL(hAPP(list(A),bool,hAPP(list(A),fun(list(A),bool),e_qual_e_qual(list(A)),B),nil(A)))|hBOOL(hAPP(list(A),bool,null(A),B)).
% 12.20/12.17 ** KEPT (pick-wt=26): 89 [] hBOOL(hAPP(list(A),bool,hAPP(list(A),fun(list(A),bool),e_qual_e_qual(list(A)),B),nil(A)))| -hBOOL(hAPP(list(A),bool,null(A),B)).
% 12.20/12.17 ** KEPT (pick-wt=39): 90 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),nil(A)))!=D|D!=nil(A).
% 12.20/12.17 ** KEPT (pick-wt=45): 91 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),nil(A)))!=D|hAPP(list(A),list(A),butlast(A),D)=B.
% 12.20/12.17 ** KEPT (pick-wt=46): 92 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),nil(A)))!=D|hAPP(list(A),A,last(A),D)=ti(A,C).
% 12.20/12.17 ** KEPT (pick-wt=60): 93 [] hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),nil(A)))=D|D=nil(A)|hAPP(list(A),list(A),butlast(A),D)!=B|hAPP(list(A),A,last(A),D)!=ti(A,C).
% 12.20/12.17 ** KEPT (pick-wt=20): 94 [] hAPP(list(A),list(A),rev(A),B)!=hAPP(list(A),list(A),rev(A),C)|B=C.
% 12.20/12.17 ** KEPT (pick-wt=20): 95 [] hAPP(list(A),list(A),rev(A),B)=hAPP(list(A),list(A),rev(A),C)|B!=C.
% 12.20/12.17 ** KEPT (pick-wt=20): 96 [] hAPP(list(A),list(A),rev(A),B)!=C|B=hAPP(list(A),list(A),rev(A),C).
% 12.20/12.17 ** KEPT (pick-wt=20): 97 [] hAPP(list(A),list(A),rev(A),B)=C|B!=hAPP(list(A),list(A),rev(A),C).
% 12.20/12.17 ** KEPT (pick-wt=20): 98 [] -hBOOL(hAPP(list(A),bool,hAPP(list(A),fun(list(A),bool),e_qual_e_qual(list(A)),B),C))|B=C.
% 12.20/12.17 ** KEPT (pick-wt=20): 99 [] hBOOL(hAPP(list(A),bool,hAPP(list(A),fun(list(A),bool),e_qual_e_qual(list(A)),B),C))|B!=C.
% 12.20/12.17 ** KEPT (pick-wt=15): 100 [] hAPP(list(A),list(A),rev(A),B)!=nil(A)|B=nil(A).
% 12.20/12.17 ** KEPT (pick-wt=15): 101 [] hAPP(list(A),list(A),rev(A),B)=nil(A)|B!=nil(A).
% 12.20/12.17 Following clause subsumed by 100 during input processing: 0 [flip.1] hAPP(list(A),list(A),rev(A),B)!=nil(A)|B=nil(A).
% 12.20/12.17 Following clause subsumed by 101 during input processing: 0 [flip.1] hAPP(list(A),list(A),rev(A),B)=nil(A)|B!=nil(A).
% 12.20/12.17 ** KEPT (pick-wt=23): 102 [] -hBOOL(hAPP(list(A),bool,distinct(A),hAPP(list(A),list(A),rev(A),B)))|hBOOL(hAPP(list(A),bool,distinct(A),B)).
% 12.20/12.17 ** KEPT (pick-wt=23): 103 [] hBOOL(hAPP(list(A),bool,distinct(A),hAPP(list(A),list(A),rev(A),B)))| -hBOOL(hAPP(list(A),bool,distinct(A),B)).
% 12.20/12.17 ** KEPT (pick-wt=15): 104 [] hAPP(list(A),list(A),rotate1(A),B)!=nil(A)|B=nil(A).
% 12.20/12.17 ** KEPT (pick-wt=15): 105 [] hAPP(list(A),list(A),rotate1(A),B)=nil(A)|B!=nil(A).
% 12.20/12.17 ** KEPT (pick-wt=30): 106 [] hAPP(A,B,C,$f19(A,B,C,D))!=hAPP(A,B,D,$f19(A,B,C,D))|ti(fun(A,B),C)=ti(fun(A,B),D).
% 12.20/12.17 ** KEPT (pick-wt=23): 107 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))|hBOOL(hAPP(A,bool,C,B)).
% 12.20/12.17 ** KEPT (pick-wt=23): 108 [] hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))| -hBOOL(hAPP(A,bool,C,B)).
% 12.20/12.17 ** KEPT (pick-wt=23): 109 [] -hBOOL(hAPP(list(A),bool,distinct(A),hAPP(list(A),list(A),rotate1(A),B)))|hBOOL(hAPP(list(A),bool,distinct(A),B)).
% 12.20/12.17 ** KEPT (pick-wt=23): 110 [] hBOOL(hAPP(list(A),bool,distinct(A),hAPP(list(A),list(A),rotate1(A),B)))| -hBOOL(hAPP(list(A),bool,distinct(A),B)).
% 12.20/12.17 ** KEPT (pick-wt=45): 111 [] hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),nil(A))!=hAPP(list(A),list(A),rev(A),C)|C=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),nil(A)).
% 12.20/12.17 ** KEPT (pick-wt=45): 112 [] hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),nil(A))=hAPP(list(A),list(A),rev(A),C)|C!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),nil(A)).
% 12.20/12.17 ** KEPT (pick-wt=45): 113 [] hAPP(list(A),list(A),rev(A),B)!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),nil(A))|B=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),nil(A)).
% 12.20/12.17 ** KEPT (pick-wt=45): 114 [] hAPP(list(A),list(A),rev(A),B)=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),nil(A))|B!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),nil(A)).
% 12.20/12.17 ** KEPT (pick-wt=30): 115 [] A!=nil(B)|hAPP(list(B),B,last(B),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),C),A))=ti(B,C).
% 12.20/12.17 Following clause subsumed by 115 during input processing: 0 [] A!=nil(B)|hAPP(list(B),B,last(B),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),C),A))=ti(B,C).
% 12.20/12.17 ** KEPT (pick-wt=35): 116 [] A!=nil(B)|hAPP(list(B),B,last(B),hAPP(list(B),list(B),hAPP(list(B),fun(list(B),list(B)),append(B),C),A))=hAPP(list(B),B,last(B),C).
% 12.20/12.17 Following clause subsumed by 116 during input processing: 0 [] A!=nil(B)|hAPP(list(B),B,last(B),hAPP(list(B),list(B),hAPP(list(B),fun(list(B),list(B)),append(B),C),A))=hAPP(list(B),B,last(B),C).
% 12.20/12.18 ** KEPT (pick-wt=67): 117 [] hAPP(list(A),list(A),rev(A),B)!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D)|B=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),hAPP(list(A),list(A),rev(A),D)),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),nil(A))).
% 12.20/12.18 ** KEPT (pick-wt=67): 118 [] hAPP(list(A),list(A),rev(A),B)=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D)|B!=hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),hAPP(list(A),list(A),rev(A),D)),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),nil(A))).
% 12.20/12.18 ** KEPT (pick-wt=7): 120 [copy,119,flip.2] -cl_HOL_Oe_qual(A)|fe_qual(A)=e_qual_e_qual(A).
% 12.20/12.18 ** KEPT (pick-wt=15): 121 [] -cl_HOL_Oe_qual(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),e_qual_e_qual(A),B),B)).
% 12.20/12.18 ** KEPT (pick-wt=22): 122 [] -cl_HOL_Oe_qual(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),e_qual_e_qual(A),B),C))|ti(A,B)=ti(A,C).
% 12.20/12.18 ** KEPT (pick-wt=22): 123 [] -cl_HOL_Oe_qual(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),e_qual_e_qual(A),B),C))|ti(A,B)!=ti(A,C).
% 12.20/12.18 Following clause subsumed by 120 during input processing: 0 [] -cl_HOL_Oe_qual(A)|fe_qual(A)=e_qual_e_qual(A).
% 12.20/12.18 ** KEPT (pick-wt=35): 124 [] A!=nil(B)|hAPP(list(B),B,hd(B),hAPP(list(B),list(B),hAPP(list(B),fun(list(B),list(B)),append(B),A),C))=hAPP(list(B),B,hd(B),C).
% 12.20/12.18 ** KEPT (pick-wt=23): 125 [] -hBOOL(hAPP(list(A),bool,distinct(A),B))|hBOOL(hAPP(list(A),bool,distinct(A),hAPP(list(A),list(A),tl(A),B))).
% 12.20/12.18 ** KEPT (pick-wt=25): 126 [] -linorder(A)| -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B))|hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),tl(A),B))).
% 12.20/12.18 ** KEPT (pick-wt=50): 127 [] hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),dropWhile(A),B),C)=nil(A)| -hBOOL(hAPP(A,bool,B,hAPP(list(A),A,hd(A),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),dropWhile(A),B),C)))).
% 12.20/12.18 ** KEPT (pick-wt=15): 128 [] -hBOOL(hAPP(A,bool,hAPP(list(A),fun(A,bool),member_1(A),nil(A)),B)).
% 12.20/12.18 ** KEPT (pick-wt=18): 129 [] -hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex1(A),B),nil(A))).
% 12.20/12.18 ** KEPT (pick-wt=50): 130 [] -hBOOL(hAPP(A,bool,hAPP(list(A),fun(A,bool),member_1(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)),D))|ti(A,B)=ti(A,D)|hBOOL(hAPP(A,bool,hAPP(list(A),fun(A,bool),member_1(A),C),D)).
% 12.20/12.18 ** KEPT (pick-wt=36): 131 [] hBOOL(hAPP(A,bool,hAPP(list(A),fun(A,bool),member_1(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)),D))|ti(A,B)!=ti(A,D).
% 12.20/12.18 ** KEPT (pick-wt=43): 132 [] hBOOL(hAPP(A,bool,hAPP(list(A),fun(A,bool),member_1(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)),D))| -hBOOL(hAPP(A,bool,hAPP(list(A),fun(A,bool),member_1(A),C),D)).
% 12.20/12.18 ** KEPT (pick-wt=45): 133 [] -hBOOL(hAPP(list(A),bool,hAPP(A,fun(list(A),bool),listMem(A),B),C))|hBOOL(hAPP(list(A),bool,hAPP(A,fun(list(A),bool),listMem(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),C))).
% 12.20/12.18 ** KEPT (pick-wt=32): 134 [] hAPP(A,list(A),hAPP(nat,fun(A,list(A)),replicate(A),B),C)!=hAPP(A,list(A),hAPP(nat,fun(A,list(A)),replicate(A),D),E)|B=D.
% 12.20/12.18 ** KEPT (pick-wt=40): 135 [] hAPP(A,list(A),hAPP(nat,fun(A,list(A)),replicate(A),B),C)!=hAPP(A,list(A),hAPP(nat,fun(A,list(A)),replicate(A),D),E)|B=zero_zero(nat)|ti(A,C)=ti(A,E).
% 12.20/12.18 ** KEPT (pick-wt=36): 136 [] hAPP(A,list(A),hAPP(nat,fun(A,list(A)),replicate(A),B),C)=hAPP(A,list(A),hAPP(nat,fun(A,list(A)),replicate(A),D),E)|B!=D|B!=zero_zero(nat).
% 12.20/12.18 ** KEPT (pick-wt=39): 137 [] hAPP(A,list(A),hAPP(nat,fun(A,list(A)),replicate(A),B),C)=hAPP(A,list(A),hAPP(nat,fun(A,list(A)),replicate(A),D),E)|B!=D|ti(A,C)!=ti(A,E).
% 12.20/12.18 ** KEPT (pick-wt=58): 138 [] -hBOOL(hAPP(A,bool,B,C))|hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),dropWhile(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D))=hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),dropWhile(A),B),D).
% 12.20/12.18 ** KEPT (pick-wt=33): 139 [] -hBOOL(hAPP(list(A),bool,distinct(A),B))|hBOOL(hAPP(list(A),bool,distinct(A),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),dropWhile(A),C),B))).
% 12.20/12.18 ** KEPT (pick-wt=35): 140 [] -linorder(A)| -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B))|hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),dropWhile(A),C),B))).
% 12.20/12.18 ** KEPT (pick-wt=21): 142 [copy,141,flip.1] hAPP(A,list(A),hAPP(nat,fun(A,list(A)),replicate(A),B),C)!=nil(A)|B=zero_zero(nat).
% 12.20/12.18 ** KEPT (pick-wt=21): 144 [copy,143,flip.1] hAPP(A,list(A),hAPP(nat,fun(A,list(A)),replicate(A),B),C)=nil(A)|B!=zero_zero(nat).
% 12.20/12.18 Following clause subsumed by 142 during input processing: 0 [] hAPP(A,list(A),hAPP(nat,fun(A,list(A)),replicate(A),B),C)!=nil(A)|B=zero_zero(nat).
% 12.20/12.18 Following clause subsumed by 144 during input processing: 0 [] hAPP(A,list(A),hAPP(nat,fun(A,list(A)),replicate(A),B),C)=nil(A)|B!=zero_zero(nat).
% 12.20/12.18 ** KEPT (pick-wt=71): 145 [] -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),A))|hAPP(fun(nat,bool),list(B),hAPP(list(B),fun(fun(nat,bool),list(B)),sublist(B),hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),C),nil(B))),A)=hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),C),nil(B)).
% 12.20/12.18 ** KEPT (pick-wt=86): 147 [copy,146,flip.2] hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),dropWhile(A),B),C)!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E)|hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),takeWhile(A),B),C)),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E))=C.
% 12.20/12.18 ** KEPT (pick-wt=41): 148 [] hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),dropWhile(A),B),C)!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E)| -hBOOL(hAPP(A,bool,B,D)).
% 12.20/12.18 ** KEPT (pick-wt=92): 150 [copy,149,flip.2] hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),dropWhile(A),B),C)=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E)|hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),takeWhile(A),B),C)),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E))!=C|hBOOL(hAPP(A,bool,B,D)).
% 12.20/12.18 ** KEPT (pick-wt=35): 152 [copy,151,flip.2,flip.3] -hBOOL(hAPP(list(A),bool,hAPP(A,fun(list(A),bool),listMem(A),B),C))|ti(A,$f21(A,B,C))=ti(A,B)|ti(A,$f24(A,B,C))=ti(A,B).
% 12.20/12.18 ** KEPT (pick-wt=49): 154 [copy,153,flip.2,flip.3] -hBOOL(hAPP(list(A),bool,hAPP(A,fun(list(A),bool),listMem(A),B),C))|ti(A,$f21(A,B,C))=ti(A,B)|hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),$f22(A,B,C)),$f23(A,B,C))=C.
% 12.20/12.18 ** KEPT (pick-wt=46): 156 [copy,155,flip.2] -hBOOL(hAPP(list(A),bool,hAPP(A,fun(list(A),bool),listMem(A),B),C))|ti(A,$f21(A,B,C))=ti(A,B)|hBOOL(hAPP(list(A),bool,hAPP(A,fun(list(A),bool),listMem(A),$f24(A,B,C)),$f23(A,B,C))).
% 12.20/12.18 ** KEPT (pick-wt=49): 158 [copy,157,flip.2,flip.3] -hBOOL(hAPP(list(A),bool,hAPP(A,fun(list(A),bool),listMem(A),B),C))|hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),$f21(A,B,C)),$f20(A,B,C))=C|ti(A,$f24(A,B,C))=ti(A,B).
% 12.20/12.18 ** KEPT (pick-wt=63): 160 [copy,159,flip.2,flip.3] -hBOOL(hAPP(list(A),bool,hAPP(A,fun(list(A),bool),listMem(A),B),C))|hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),$f21(A,B,C)),$f20(A,B,C))=C|hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),$f22(A,B,C)),$f23(A,B,C))=C.
% 12.20/12.18 ** KEPT (pick-wt=60): 162 [copy,161,flip.2] -hBOOL(hAPP(list(A),bool,hAPP(A,fun(list(A),bool),listMem(A),B),C))|hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),$f21(A,B,C)),$f20(A,B,C))=C|hBOOL(hAPP(list(A),bool,hAPP(A,fun(list(A),bool),listMem(A),$f24(A,B,C)),$f23(A,B,C))).
% 12.20/12.18 ** KEPT (pick-wt=40): 163 [] hBOOL(hAPP(list(A),bool,hAPP(A,fun(list(A),bool),listMem(A),B),C))|ti(A,B)!=ti(A,D)|C!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E).
% 12.20/12.18 ** KEPT (pick-wt=55): 164 [] hBOOL(hAPP(list(A),bool,hAPP(A,fun(list(A),bool),listMem(A),B),C))|ti(A,B)!=ti(A,D)|C!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),E),F)| -hBOOL(hAPP(list(A),bool,hAPP(A,fun(list(A),bool),listMem(A),D),F)).
% 12.20/12.18 ** KEPT (pick-wt=14): 165 [] -zero(A)|zero_zero(A)!=ti(A,B)|ti(A,B)=zero_zero(A).
% 12.20/12.18 ** KEPT (pick-wt=14): 166 [] -zero(A)|zero_zero(A)=ti(A,B)|ti(A,B)!=zero_zero(A).
% 12.20/12.18 ** KEPT (pick-wt=33): 167 [] -hBOOL(hAPP(list(A),bool,distinct(A),B))|hBOOL(hAPP(list(A),bool,distinct(A),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),takeWhile(A),C),B))).
% 12.20/12.18 ** KEPT (pick-wt=35): 168 [] -linorder(A)| -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B))|hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),takeWhile(A),C),B))).
% 12.20/12.18 ** KEPT (pick-wt=34): 169 [] -hBOOL(hAPP(list(A),bool,distinct(A),B))|hBOOL(hAPP(list(A),bool,distinct(A),hAPP(fun(nat,bool),list(A),hAPP(list(A),fun(fun(nat,bool),list(A)),sublist(A),B),C))).
% 12.20/12.18 ** KEPT (pick-wt=73): 170 [] -hBOOL(hAPP(A,bool,B,C))|hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),takeWhile(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D))=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),takeWhile(A),B),D)).
% 12.20/12.18 ** KEPT (pick-wt=53): 171 [] -linorder(A)| -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),rev(A),B)))|B!=nil(A)|hAPP(A,A,hAPP(list(A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(list(A),fun(A,A)),foldr(A,A),ord_max(A)),B),C)=ti(A,C).
% 12.20/12.18 ** KEPT (pick-wt=75): 172 [] -linorder(A)| -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),rev(A),B)))|B=nil(A)|hAPP(A,A,hAPP(list(A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(list(A),fun(A,A)),foldr(A,A),ord_max(A)),B),C)=hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),zero_zero(nat))),C).
% 12.20/12.18 ** KEPT (pick-wt=139): 173 [] -hBOOL(hAPP(list(A),bool,hAPP(list(B),fun(list(A),bool),C,nil(B)),nil(A)))| -hBOOL(hAPP(list(A),bool,hAPP(list(B),fun(list(A),bool),C,hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),$f26(A,B,D,E,C)),$f25(A,B,D,E,C))),nil(A)))| -hBOOL(hAPP(list(A),bool,hAPP(list(B),fun(list(A),bool),C,nil(B)),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),$f28(A,B,D,E,C)),$f27(A,B,D,E,C))))|hBOOL(hAPP(list(A),bool,hAPP(list(B),fun(list(A),bool),C,$f31(A,B,D,E,C)),$f29(A,B,D,E,C)))|hBOOL(hAPP(list(A),bool,hAPP(list(B),fun(list(A),bool),C,D),E)).
% 12.20/12.18 ** KEPT (pick-wt=179): 174 [] -hBOOL(hAPP(list(A),bool,hAPP(list(B),fun(list(A),bool),C,nil(B)),nil(A)))| -hBOOL(hAPP(list(A),bool,hAPP(list(B),fun(list(A),bool),C,hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),$f26(A,B,D,E,C)),$f25(A,B,D,E,C))),nil(A)))| -hBOOL(hAPP(list(A),bool,hAPP(list(B),fun(list(A),bool),C,nil(B)),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),$f28(A,B,D,E,C)),$f27(A,B,D,E,C))))| -hBOOL(hAPP(list(A),bool,hAPP(list(B),fun(list(A),bool),C,hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),$f32(A,B,D,E,C)),$f31(A,B,D,E,C))),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),$f30(A,B,D,E,C)),$f29(A,B,D,E,C))))|hBOOL(hAPP(list(A),bool,hAPP(list(B),fun(list(A),bool),C,D),E)).
% 12.20/12.18 ** KEPT (pick-wt=102): 175 [] -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,C),D))| -hBOOL(hAPP(list(A),bool,hAPP(list(A),fun(list(A),bool),hAPP(fun(A,fun(A,bool)),fun(list(A),fun(list(A),bool)),listrelp(A),B),E),F))|hBOOL(hAPP(list(A),bool,hAPP(list(A),fun(list(A),bool),hAPP(fun(A,fun(A,bool)),fun(list(A),fun(list(A),bool)),listrelp(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),E)),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),F))).
% 12.20/12.18 ** KEPT (pick-wt=20): 176 [] hAPP(list(A),nat,size_size(list(A)),B)=hAPP(list(A),nat,size_size(list(A)),C)|B!=C.
% 12.20/12.18 ** KEPT (pick-wt=15): 177 [] hAPP(list(A),nat,size_size(list(A)),B)!=zero_zero(nat)|B=nil(A).
% 12.20/12.18 ** KEPT (pick-wt=15): 178 [] hAPP(list(A),nat,size_size(list(A)),B)=zero_zero(nat)|B!=nil(A).
% 12.20/12.18 ** KEPT (pick-wt=76): 179 [] hAPP(list(A),nat,size_size(list(A)),B)!=hAPP(list(C),nat,size_size(list(C)),D)| -hBOOL(hAPP(list(C),bool,hAPP(list(A),fun(list(C),bool),E,nil(A)),nil(C)))|hAPP(list(A),nat,size_size(list(A)),$f35(A,C,E,B,D))=hAPP(list(C),nat,size_size(list(C)),$f33(A,C,E,B,D))|hBOOL(hAPP(list(C),bool,hAPP(list(A),fun(list(C),bool),E,B),D)).
% 12.20/12.18 ** KEPT (pick-wt=74): 180 [] hAPP(list(A),nat,size_size(list(A)),B)!=hAPP(list(C),nat,size_size(list(C)),D)| -hBOOL(hAPP(list(C),bool,hAPP(list(A),fun(list(C),bool),E,nil(A)),nil(C)))|hBOOL(hAPP(list(C),bool,hAPP(list(A),fun(list(C),bool),E,$f35(A,C,E,B,D)),$f33(A,C,E,B,D)))|hBOOL(hAPP(list(C),bool,hAPP(list(A),fun(list(C),bool),E,B),D)).
% 12.20/12.18 ** KEPT (pick-wt=114): 181 [] hAPP(list(A),nat,size_size(list(A)),B)!=hAPP(list(C),nat,size_size(list(C)),D)| -hBOOL(hAPP(list(C),bool,hAPP(list(A),fun(list(C),bool),E,nil(A)),nil(C)))| -hBOOL(hAPP(list(C),bool,hAPP(list(A),fun(list(C),bool),E,hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),$f36(A,C,E,B,D)),$f35(A,C,E,B,D))),hAPP(list(C),list(C),hAPP(C,fun(list(C),list(C)),cons(C),$f34(A,C,E,B,D)),$f33(A,C,E,B,D))))|hBOOL(hAPP(list(C),bool,hAPP(list(A),fun(list(C),bool),E,B),D)).
% 12.20/12.18 ** KEPT (pick-wt=20): 182 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),bot_bot(fun(A,bool)))).
% 12.20/12.18 ** KEPT (pick-wt=13): 183 [] -bot(A)|hAPP(B,A,bot_bot(fun(B,A)),C)=bot_bot(A).
% 12.20/12.18 Following clause subsumed by 183 during input processing: 0 [] -bot(A)|hAPP(B,A,bot_bot(fun(B,A)),C)=bot_bot(A).
% 12.20/12.18 ** KEPT (pick-wt=60): 185 [copy,184,flip.3] -hBOOL(hAPP(list(A),bool,hAPP(list(A),fun(list(A),bool),hAPP(fun(A,fun(A,bool)),fun(list(A),fun(list(A),bool)),listrelp(A),B),C),D))|C=nil(A)|hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),$f41(A,B,C,D)),$f39(A,B,C,D))=C.
% 12.20/12.18 ** KEPT (pick-wt=60): 187 [copy,186,flip.3] -hBOOL(hAPP(list(A),bool,hAPP(list(A),fun(list(A),bool),hAPP(fun(A,fun(A,bool)),fun(list(A),fun(list(A),bool)),listrelp(A),B),C),D))|C=nil(A)|hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),$f40(A,B,C,D)),$f38(A,B,C,D))=D.
% 12.20/12.18 ** KEPT (pick-wt=54): 188 [] -hBOOL(hAPP(list(A),bool,hAPP(list(A),fun(list(A),bool),hAPP(fun(A,fun(A,bool)),fun(list(A),fun(list(A),bool)),listrelp(A),B),C),D))|C=nil(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,$f41(A,B,C,D)),$f40(A,B,C,D))).
% 12.20/12.18 ** KEPT (pick-wt=72): 189 [] -hBOOL(hAPP(list(A),bool,hAPP(list(A),fun(list(A),bool),hAPP(fun(A,fun(A,bool)),fun(list(A),fun(list(A),bool)),listrelp(A),B),C),D))|C=nil(A)|hBOOL(hAPP(list(A),bool,hAPP(list(A),fun(list(A),bool),hAPP(fun(A,fun(A,bool)),fun(list(A),fun(list(A),bool)),listrelp(A),B),$f39(A,B,C,D)),$f38(A,B,C,D))).
% 12.20/12.18 ** KEPT (pick-wt=60): 191 [copy,190,flip.3] -hBOOL(hAPP(list(A),bool,hAPP(list(A),fun(list(A),bool),hAPP(fun(A,fun(A,bool)),fun(list(A),fun(list(A),bool)),listrelp(A),B),C),D))|D=nil(A)|hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),$f41(A,B,C,D)),$f39(A,B,C,D))=C.
% 12.20/12.18 ** KEPT (pick-wt=60): 193 [copy,192,flip.3] -hBOOL(hAPP(list(A),bool,hAPP(list(A),fun(list(A),bool),hAPP(fun(A,fun(A,bool)),fun(list(A),fun(list(A),bool)),listrelp(A),B),C),D))|D=nil(A)|hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),$f40(A,B,C,D)),$f38(A,B,C,D))=D.
% 12.20/12.18 ** KEPT (pick-wt=54): 194 [] -hBOOL(hAPP(list(A),bool,hAPP(list(A),fun(list(A),bool),hAPP(fun(A,fun(A,bool)),fun(list(A),fun(list(A),bool)),listrelp(A),B),C),D))|D=nil(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,$f41(A,B,C,D)),$f40(A,B,C,D))).
% 12.20/12.18 ** KEPT (pick-wt=72): 195 [] -hBOOL(hAPP(list(A),bool,hAPP(list(A),fun(list(A),bool),hAPP(fun(A,fun(A,bool)),fun(list(A),fun(list(A),bool)),listrelp(A),B),C),D))|D=nil(A)|hBOOL(hAPP(list(A),bool,hAPP(list(A),fun(list(A),bool),hAPP(fun(A,fun(A,bool)),fun(list(A),fun(list(A),bool)),listrelp(A),B),$f39(A,B,C,D)),$f38(A,B,C,D))).
% 12.20/12.18 ** KEPT (pick-wt=38): 196 [] hBOOL(hAPP(list(A),bool,hAPP(list(A),fun(list(A),bool),hAPP(fun(A,fun(A,bool)),fun(list(A),fun(list(A),bool)),listrelp(A),B),C),D))|C!=nil(A)|D!=nil(A).
% 12.20/12.18 ** KEPT (pick-wt=108): 197 [] hBOOL(hAPP(list(A),bool,hAPP(list(A),fun(list(A),bool),hAPP(fun(A,fun(A,bool)),fun(list(A),fun(list(A),bool)),listrelp(A),B),C),D))|C!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),E),F)|D!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),G),H)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,E),G))| -hBOOL(hAPP(list(A),bool,hAPP(list(A),fun(list(A),bool),hAPP(fun(A,fun(A,bool)),fun(list(A),fun(list(A),bool)),listrelp(A),B),F),H)).
% 12.20/12.18 ** KEPT (pick-wt=27): 198 [] ti(fun(A,bool),B)!=bot_bot(fun(A,bool))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)).
% 12.20/12.18 ** KEPT (pick-wt=21): 199 [] hAPP(fun(A,bool),fun(A,bool),collect(A),B)!=bot_bot(fun(A,bool))| -hBOOL(hAPP(A,bool,B,C)).
% 12.20/12.18 Following clause subsumed by 182 during input processing: 0 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),bot_bot(fun(A,bool)))).
% 12.20/12.18 Following clause subsumed by 199 during input processing: 0 [flip.1] hAPP(fun(A,bool),fun(A,bool),collect(A),B)!=bot_bot(fun(A,bool))| -hBOOL(hAPP(A,bool,B,C)).
% 12.20/12.18 Following clause subsumed by 198 during input processing: 0 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))|ti(fun(A,bool),C)!=bot_bot(fun(A,bool)).
% 12.20/12.18 Following clause subsumed by 198 during input processing: 0 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))|ti(fun(A,bool),C)!=bot_bot(fun(A,bool)).
% 12.20/12.18 ** KEPT (pick-wt=17): 201 [copy,200,flip.2] -linorder(A)|nil(A)=hAPP(fun(A,bool),list(A),linord467138063of_set(A),bot_bot(fun(A,bool))).
% 12.20/12.18 ** KEPT (pick-wt=49): 202 [] -linorder(A)|hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)).
% 12.20/12.18 Following clause subsumed by 202 during input processing: 0 [] -linorder(A)|hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)).
% 12.20/12.18 ** KEPT (pick-wt=49): 203 [] -linorder(A)|hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))=hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)).
% 12.20/12.18 Following clause subsumed by 203 during input processing: 0 [] -linorder(A)|hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))=hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)).
% 12.20/12.18 ** KEPT (pick-wt=18): 204 [] -linorder(A)|hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),B)=ti(A,B).
% 12.20/12.18 ** KEPT (pick-wt=27): 205 [] -linorder(A)|hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)=hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B).
% 12.20/12.18 Following clause subsumed by 205 during input processing: 0 [] -linorder(A)|hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)=hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B).
% 12.20/12.18 ** KEPT (pick-wt=38): 206 [] -linorder(A)|hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C))=hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C).
% 12.20/12.18 Following clause subsumed by 206 during input processing: 0 [] -linorder(A)|hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C))=hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C).
% 12.20/12.18 Following clause subsumed by 204 during input processing: 0 [] -linorder(A)|hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),B)=ti(A,B).
% 12.20/12.18 ** KEPT (pick-wt=86): 207 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(list(A),nat,size_size(list(A)),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),takeWhile(A),B),C))),hAPP(list(A),nat,size_size(list(A)),C)))| -hBOOL(hAPP(A,bool,B,hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),C),hAPP(list(A),nat,size_size(list(A)),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),takeWhile(A),B),C))))).
% 12.20/12.18 ** KEPT (pick-wt=81): 208 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(list(B),nat,size_size(list(B)),hAPP(list(B),list(B),hAPP(fun(B,bool),fun(list(B),list(B)),takeWhile(B),C),D))))|hAPP(nat,B,hAPP(list(B),fun(nat,B),nth(B),hAPP(list(B),list(B),hAPP(fun(B,bool),fun(list(B),list(B)),takeWhile(B),C),D)),A)=hAPP(nat,B,hAPP(list(B),fun(nat,B),nth(B),D),A).
% 12.20/12.18 ** KEPT (pick-wt=14): 209 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))).
% 12.20/12.18 ** KEPT (pick-wt=16): 210 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|A!=B.
% 12.20/12.18 ** KEPT (pick-wt=16): 211 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|B!=A.
% 12.20/12.18 ** KEPT (pick-wt=13): 212 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),A)).
% 12.20/12.18 Following clause subsumed by 210 during input processing: 0 [] A!=B| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).
% 12.20/12.18 Following clause subsumed by 211 during input processing: 0 [] A!=B| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)).
% 12.20/12.18 Following clause subsumed by 212 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),A)).
% 12.20/12.18 ** KEPT (pick-wt=17): 213 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|B!=zero_zero(nat).
% 12.20/12.18 Following clause subsumed by 209 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))).
% 12.20/12.18 Following clause subsumed by 213 during input processing: 0 [] A!=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).
% 12.20/12.18 Following clause subsumed by 209 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))).
% 12.20/12.18 ** KEPT (pick-wt=15): 214 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),B)).
% 12.20/12.18 ** KEPT (pick-wt=35): 215 [] -linorder(A)|ti(A,B)=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 12.20/12.18 ** KEPT (pick-wt=22): 216 [] -linorder(A)|ti(A,B)!=ti(A,C)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)).
% 12.20/12.18 ** KEPT (pick-wt=22): 217 [] -linorder(A)|ti(A,B)!=ti(A,C)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 12.20/12.18 Following clause subsumed by 215 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B))|ti(A,B)=ti(A,C).
% 12.20/12.18 ** KEPT (pick-wt=28): 218 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 12.20/12.18 Following clause subsumed by 216 during input processing: 0 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)!=ti(A,C).
% 12.20/12.18 Following clause subsumed by 215 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 12.20/12.18 Following clause subsumed by 215 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B))|ti(A,C)=ti(A,B).
% 12.20/12.18 Following clause subsumed by 216 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B))|ti(A,C)!=ti(A,B).
% 12.20/12.18 Following clause subsumed by 215 during input processing: 0 [] -linorder(A)|ti(A,B)=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 12.20/12.18 ** KEPT (pick-wt=18): 219 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|B!=C.
% 12.20/12.18 ** KEPT (pick-wt=28): 220 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 12.20/12.18 Following clause subsumed by 220 during input processing: 0 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 12.20/12.18 Following clause subsumed by 219 during input processing: 0 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|B!=C.
% 12.20/12.18 ** KEPT (pick-wt=18): 221 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|C!=B.
% 12.20/12.18 Following clause subsumed by 220 during input processing: 0 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B))|hBOOL(D).
% 12.20/12.18 Following clause subsumed by 220 during input processing: 0 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 12.20/12.18 ** KEPT (pick-wt=28): 222 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 12.20/12.18 ** KEPT (pick-wt=31): 223 [] -ord(A)|B!=C| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 12.20/12.18 ** KEPT (pick-wt=31): 224 [] -order(A)|B!=C| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B)).
% 12.20/12.18 ** KEPT (pick-wt=31): 225 [] -ord(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|C!=D|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 12.20/12.18 ** KEPT (pick-wt=31): 226 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|B!=D|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)).
% 12.20/12.18 ** KEPT (pick-wt=41): 227 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 12.20/12.18 ** KEPT (pick-wt=41): 228 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)).
% 12.20/12.18 Following clause subsumed by 220 during input processing: 0 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 12.20/12.18 Following clause subsumed by 215 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)).
% 12.20/12.18 ** KEPT (pick-wt=101): 229 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(list(B),nat,size_size(list(B)),C)))|hAPP(B,list(B),hAPP(nat,fun(B,list(B)),hAPP(list(B),fun(nat,fun(B,list(B))),list_update(B),hAPP(list(B),list(B),hAPP(list(B),fun(list(B),list(B)),append(B),C),D)),A),E)=hAPP(list(B),list(B),hAPP(list(B),fun(list(B),list(B)),append(B),hAPP(B,list(B),hAPP(nat,fun(B,list(B)),hAPP(list(B),fun(nat,fun(B,list(B))),list_update(B),C),A),E)),D).
% 12.20/12.18 ** KEPT (pick-wt=63): 230 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(list(B),nat,size_size(list(B)),C)))|A!=D|hAPP(nat,B,hAPP(list(B),fun(nat,B),nth(B),hAPP(B,list(B),hAPP(nat,fun(B,list(B)),hAPP(list(B),fun(nat,fun(B,list(B))),list_update(B),C),A),E)),D)=ti(B,E).
% 12.20/12.18 ** KEPT (pick-wt=73): 231 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(list(B),nat,size_size(list(B)),C)))|A=D|hAPP(nat,B,hAPP(list(B),fun(nat,B),nth(B),hAPP(B,list(B),hAPP(nat,fun(B,list(B)),hAPP(list(B),fun(nat,fun(B,list(B))),list_update(B),C),A),E)),D)=hAPP(nat,B,hAPP(list(B),fun(nat,B),nth(B),C),D).
% 12.20/12.18 ** KEPT (pick-wt=63): 232 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(list(B),nat,size_size(list(B)),C)))|hAPP(B,list(B),hAPP(nat,fun(B,list(B)),hAPP(list(B),fun(nat,fun(B,list(B))),list_update(B),C),A),D)!=C|hAPP(nat,B,hAPP(list(B),fun(nat,B),nth(B),C),A)=ti(B,D).
% 12.20/12.18 ** KEPT (pick-wt=63): 233 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(list(B),nat,size_size(list(B)),C)))|hAPP(B,list(B),hAPP(nat,fun(B,list(B)),hAPP(list(B),fun(nat,fun(B,list(B))),list_update(B),C),A),D)=C|hAPP(nat,B,hAPP(list(B),fun(nat,B),nth(B),C),A)!=ti(B,D).
% 12.20/12.18 ** KEPT (pick-wt=60): 234 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(list(B),nat,size_size(list(B)),C)))|hAPP(nat,B,hAPP(list(B),fun(nat,B),nth(B),hAPP(B,list(B),hAPP(nat,fun(B,list(B)),hAPP(list(B),fun(nat,fun(B,list(B))),list_update(B),C),A),D)),A)=ti(B,D).
% 12.20/12.18 ** KEPT (pick-wt=50): 235 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(list(B),nat,size_size(list(B)),C)))|hAPP(list(B),B,last(B),hAPP(list(B),list(B),hAPP(nat,fun(list(B),list(B)),drop(B),A),C))=hAPP(list(B),B,last(B),C).
% 12.20/12.18 ** KEPT (pick-wt=16): 236 [] -bot(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),bot_bot(A))).
% 12.20/12.18 ** KEPT (pick-wt=22): 237 [] -bot(A)|ti(A,B)=bot_bot(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),bot_bot(A)),B)).
% 12.20/12.18 ** KEPT (pick-wt=22): 238 [] -bot(A)|ti(A,B)!=bot_bot(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),bot_bot(A)),B)).
% 12.20/12.18 ** KEPT (pick-wt=52): 239 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 12.20/12.19 ** KEPT (pick-wt=39): 240 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)).
% 12.20/12.19 ** KEPT (pick-wt=39): 241 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 12.20/12.19 ** KEPT (pick-wt=39): 242 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 12.20/12.19 ** KEPT (pick-wt=39): 243 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)).
% 12.20/12.19 ** KEPT (pick-wt=52): 244 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)).
% 12.20/12.19 Following clause subsumed by 240 during input processing: 0 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))).
% 12.20/12.19 Following clause subsumed by 241 during input processing: 0 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))).
% 12.20/12.19 ** KEPT (pick-wt=31): 245 [] -hBOOL(hAPP(list(A),bool,distinct(A),B))|hBOOL(hAPP(list(A),bool,distinct(A),hAPP(list(A),list(A),hAPP(nat,fun(list(A),list(A)),drop(A),C),B))).
% 12.20/12.19 ** KEPT (pick-wt=33): 246 [] -linorder(A)| -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B))|hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(nat,fun(list(A),list(A)),drop(A),C),B))).
% 12.20/12.19 ** KEPT (pick-wt=31): 247 [] hAPP(A,list(A),hAPP(nat,fun(A,list(A)),hAPP(list(A),fun(nat,fun(A,list(A))),list_update(A),B),C),D)!=nil(A)|B=nil(A).
% 12.20/12.19 ** KEPT (pick-wt=31): 248 [] hAPP(A,list(A),hAPP(nat,fun(A,list(A)),hAPP(list(A),fun(nat,fun(A,list(A))),list_update(A),B),C),D)=nil(A)|B!=nil(A).
% 12.20/12.19 ** KEPT (pick-wt=60): 249 [] A=nil(B)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),hAPP(list(B),nat,size_size(list(B)),A)))|hAPP(list(B),B,hd(B),hAPP(list(B),list(B),hAPP(nat,fun(list(B),list(B)),drop(B),C),A))=hAPP(nat,B,hAPP(list(B),fun(nat,B),nth(B),A),C).
% 12.20/12.19 ** KEPT (pick-wt=50): 250 [] hAPP(list(A),list(A),hAPP(nat,fun(list(A),list(A)),drop(A),B),C)!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E)|hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),C),B)=ti(A,D).
% 12.20/12.19 Following clause subsumed by 176 during input processing: 0 [] A!=B|hAPP(list(C),nat,size_size(list(C)),A)=hAPP(list(C),nat,size_size(list(C)),B).
% 12.20/12.19 ** KEPT (pick-wt=50): 251 [] A!=B| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),hAPP(list(D),nat,size_size(list(D)),A)))|hAPP(nat,D,hAPP(list(D),fun(nat,D),nth(D),A),C)=hAPP(nat,D,hAPP(list(D),fun(nat,D),nth(D),B),C).
% 12.20/12.19 ** KEPT (pick-wt=43): 252 [] A=B|hAPP(list(C),nat,size_size(list(C)),A)!=hAPP(list(C),nat,size_size(list(C)),B)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f47(C,A,B)),hAPP(list(C),nat,size_size(list(C)),A))).
% 12.20/12.19 ** KEPT (pick-wt=53): 253 [] A=B|hAPP(list(C),nat,size_size(list(C)),A)!=hAPP(list(C),nat,size_size(list(C)),B)|hAPP(nat,C,hAPP(list(C),fun(nat,C),nth(C),A),$f47(C,A,B))!=hAPP(nat,C,hAPP(list(C),fun(nat,C),nth(C),B),$f47(C,A,B)).
% 12.20/12.19 ** KEPT (pick-wt=43): 254 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hAPP(nat,C,hAPP(list(C),fun(nat,C),nth(C),hAPP(C,list(C),hAPP(nat,fun(C,list(C)),replicate(C),B),D)),A)=ti(C,D).
% 12.20/12.19 ** KEPT (pick-wt=25): 255 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(list(A),nat,size_size(list(A)),B)))|B!=nil(A).
% 12.20/12.19 ** KEPT (pick-wt=78): 256 [] -hBOOL(hAPP(list(A),bool,distinct(A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),hAPP(list(A),nat,size_size(list(A)),B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),D),hAPP(list(A),nat,size_size(list(A)),B)))|C=D|hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),C)!=hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),D).
% 12.20/12.19 ** KEPT (pick-wt=15): 257 [] hBOOL(hAPP(list(A),bool,distinct(A),B))|$f49(A,B)!=$f48(A,B).
% 12.20/12.19 Following clause subsumed by 256 during input processing: 0 [] -hBOOL(hAPP(list(A),bool,distinct(A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),hAPP(list(A),nat,size_size(list(A)),B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),D),hAPP(list(A),nat,size_size(list(A)),B)))|hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),C)!=hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),D)|C=D.
% 12.20/12.19 ** KEPT (pick-wt=78): 258 [] -hBOOL(hAPP(list(A),bool,distinct(A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),hAPP(list(A),nat,size_size(list(A)),B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),D),hAPP(list(A),nat,size_size(list(A)),B)))|hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),C)=hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),D)|C!=D.
% 12.20/12.19 ** KEPT (pick-wt=43): 259 [] hAPP(list(A),nat,size_size(list(A)),B)!=hAPP(list(A),nat,size_size(list(A)),C)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f50(A,B,C)),hAPP(list(A),nat,size_size(list(A)),B)))|B=C.
% 12.20/12.19 ** KEPT (pick-wt=53): 260 [] hAPP(list(A),nat,size_size(list(A)),B)!=hAPP(list(A),nat,size_size(list(A)),C)|hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),B),$f50(A,B,C))!=hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),C),$f50(A,B,C))|B=C.
% 12.20/12.19 ** KEPT (pick-wt=56): 261 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f51(A,B,C)),C))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),D),C))|hBOOL(hAPP(A,bool,hAPP(nat,fun(A,bool),B,D),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),$f52(A,B,C)),D))).
% 12.20/12.19 ** KEPT (pick-wt=28): 262 [] -hBOOL(hAPP(A,bool,hAPP(nat,fun(A,bool),B,$f51(A,B,C)),D))|hAPP(list(A),nat,size_size(list(A)),$f52(A,B,C))=C.
% 12.20/12.19 ** KEPT (pick-wt=55): 263 [] -hBOOL(hAPP(A,bool,hAPP(nat,fun(A,bool),B,$f51(A,B,C)),D))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),E),C))|hBOOL(hAPP(A,bool,hAPP(nat,fun(A,bool),B,E),hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),$f52(A,B,C)),E))).
% 12.20/12.19 ** KEPT (pick-wt=56): 264 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hBOOL(hAPP(C,bool,hAPP(nat,fun(C,bool),D,A),$f53(C,D,B,A)))|hAPP(list(C),nat,size_size(list(C)),E)!=B|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f54(C,D,B,E)),B)).
% 12.20/12.19 ** KEPT (pick-wt=71): 265 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hBOOL(hAPP(C,bool,hAPP(nat,fun(C,bool),D,A),$f53(C,D,B,A)))|hAPP(list(C),nat,size_size(list(C)),E)!=B| -hBOOL(hAPP(C,bool,hAPP(nat,fun(C,bool),D,$f54(C,D,B,E)),hAPP(nat,C,hAPP(list(C),fun(nat,C),nth(C),E),$f54(C,D,B,E)))).
% 12.20/12.19 ** KEPT (pick-wt=116): 266 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(list(B),nat,size_size(list(B)),hAPP(list(B),list(B),hAPP(fun(B,bool),fun(list(B),list(B)),dropWhile(B),C),D))))|hAPP(nat,B,hAPP(list(B),fun(nat,B),nth(B),hAPP(list(B),list(B),hAPP(fun(B,bool),fun(list(B),list(B)),dropWhile(B),C),D)),A)=hAPP(nat,B,hAPP(list(B),fun(nat,B),nth(B),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(list(B),nat,size_size(list(B)),hAPP(list(B),list(B),hAPP(fun(B,bool),fun(list(B),list(B)),takeWhile(B),C),D)))).
% 12.20/12.19 ** KEPT (pick-wt=84): 267 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(list(B),nat,size_size(list(B)),C)))|hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),hAPP(nat,B,hAPP(list(B),fun(nat,B),nth(B),C),A)),hAPP(list(B),list(B),hAPP(nat,fun(list(B),list(B)),drop(B),hAPP(nat,nat,suc,A)),C))=hAPP(list(B),list(B),hAPP(nat,fun(list(B),list(B)),drop(B),A),C).
% 12.20/12.19 ** KEPT (pick-wt=40): 268 [] -hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f55(A,B,C)),hAPP(list(A),nat,size_size(list(A)),C))).
% 12.20/12.19 ** KEPT (pick-wt=38): 269 [] -hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),C))|hBOOL(hAPP(A,bool,B,hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),C),$f55(A,B,C)))).
% 12.20/12.19 ** KEPT (pick-wt=55): 270 [] hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),C))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),D),hAPP(list(A),nat,size_size(list(A)),C)))| -hBOOL(hAPP(A,bool,B,hAPP(nat,A,hAPP(list(A),fun(nat,A),nth(A),C),D))).
% 12.20/12.19 ** KEPT (pick-wt=34): 271 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),hAPP(nat,nat,suc,B))).
% 12.20/12.19 ** KEPT (pick-wt=14): 272 [] hAPP(nat,nat,suc,A)!=hAPP(nat,nat,suc,B)|A=B.
% 12.20/12.19 ** KEPT (pick-wt=28): 273 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)|A=C.
% 12.20/12.19 ** KEPT (pick-wt=28): 274 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)|A!=C.
% 12.20/12.19 ** KEPT (pick-wt=28): 275 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)|B=C.
% 12.20/12.19 ** KEPT (pick-wt=28): 276 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)|B!=C.
% 12.20/12.19 Following clause subsumed by 272 during input processing: 0 [] hAPP(nat,nat,suc,A)!=hAPP(nat,nat,suc,B)|A=B.
% 12.20/12.19 ** KEPT (pick-wt=14): 277 [] hAPP(nat,nat,suc,A)=hAPP(nat,nat,suc,B)|A!=B.
% 12.20/12.19 ** KEPT (pick-wt=33): 279 [copy,278,flip.2] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),$f56(A,B)))=B.
% 12.20/12.19 ** KEPT (pick-wt=31): 280 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|B!=hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)).
% 12.20/12.19 ** KEPT (pick-wt=7): 281 [] hAPP(nat,nat,suc,A)!=A.
% 12.20/12.19 Following clause subsumed by 281 during input processing: 0 [flip.1] hAPP(nat,nat,suc,A)!=A.
% 12.20/12.19 ** KEPT (pick-wt=31): 282 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)!=hAPP(nat,nat,suc,zero_zero(nat))|A=hAPP(nat,nat,suc,zero_zero(nat))|A=zero_zero(nat).
% 12.20/12.19 ** KEPT (pick-wt=35): 283 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)!=hAPP(nat,nat,suc,zero_zero(nat))|A=hAPP(nat,nat,suc,zero_zero(nat))|B=hAPP(nat,nat,suc,zero_zero(nat)).
% 12.20/12.19 ** KEPT (pick-wt=27): 284 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)!=hAPP(nat,nat,suc,zero_zero(nat))|B=zero_zero(nat)|A=zero_zero(nat).
% 12.20/12.19 ** KEPT (pick-wt=31): 285 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)!=hAPP(nat,nat,suc,zero_zero(nat))|B=zero_zero(nat)|B=hAPP(nat,nat,suc,zero_zero(nat)).
% 12.20/12.19 ** KEPT (pick-wt=31): 286 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)=hAPP(nat,nat,suc,zero_zero(nat))|A!=hAPP(nat,nat,suc,zero_zero(nat))|B!=zero_zero(nat).
% 12.20/12.19 ** KEPT (pick-wt=31): 287 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)=hAPP(nat,nat,suc,zero_zero(nat))|A!=zero_zero(nat)|B!=hAPP(nat,nat,suc,zero_zero(nat)).
% 12.20/12.19 ** KEPT (pick-wt=31): 288 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)|A=hAPP(nat,nat,suc,zero_zero(nat))|A=zero_zero(nat).
% 12.20/12.19 ** KEPT (pick-wt=35): 289 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)|A=hAPP(nat,nat,suc,zero_zero(nat))|B=hAPP(nat,nat,suc,zero_zero(nat)).
% 12.20/12.19 ** KEPT (pick-wt=27): 290 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)|B=zero_zero(nat)|A=zero_zero(nat).
% 12.20/12.19 ** KEPT (pick-wt=31): 291 [] hAPP(nat,nat,suc,zero_zero(nat))!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)|B=zero_zero(nat)|B=hAPP(nat,nat,suc,zero_zero(nat)).
% 12.20/12.19 ** KEPT (pick-wt=31): 292 [] hAPP(nat,nat,suc,zero_zero(nat))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)|A!=hAPP(nat,nat,suc,zero_zero(nat))|B!=zero_zero(nat).
% 12.20/12.19 ** KEPT (pick-wt=31): 293 [] hAPP(nat,nat,suc,zero_zero(nat))=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)|A!=zero_zero(nat)|B!=hAPP(nat,nat,suc,zero_zero(nat)).
% 12.20/12.19 ** KEPT (pick-wt=34): 294 [] -cancel_semigroup_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)!=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C)|ti(A,B)=ti(A,D).
% 12.20/12.19 ** KEPT (pick-wt=34): 295 [] -cancel146912293up_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)!=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)|ti(A,C)=ti(A,D).
% 12.20/12.19 ** KEPT (pick-wt=34): 296 [] -cancel_semigroup_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)!=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)|ti(A,C)=ti(A,D).
% 12.20/12.19 Following clause subsumed by 294 during input processing: 0 [] -cancel_semigroup_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)!=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C)|ti(A,B)=ti(A,D).
% 12.20/12.19 ** KEPT (pick-wt=34): 297 [] -cancel_semigroup_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C)|ti(A,B)!=ti(A,D).
% 12.20/12.19 Following clause subsumed by 296 during input processing: 0 [] -cancel_semigroup_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)!=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)|ti(A,C)=ti(A,D).
% 12.20/12.19 ** KEPT (pick-wt=34): 298 [] -cancel_semigroup_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)|ti(A,C)!=ti(A,D).
% 12.20/12.19 ** KEPT (pick-wt=49): 299 [] -ab_semigroup_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)).
% 12.20/12.19 ** KEPT (pick-wt=19): 300 [] -comm_monoid_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A))=ti(A,B).
% 12.20/12.19 ** KEPT (pick-wt=19): 301 [] -monoid_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A))=ti(A,B).
% 12.20/12.19 ** KEPT (pick-wt=23): 302 [] -linord219039673up_add(A)|zero_zero(A)!=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)|ti(A,B)=zero_zero(A).
% 12.20/12.19 ** KEPT (pick-wt=23): 303 [] -linord219039673up_add(A)|zero_zero(A)=hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)|ti(A,B)!=zero_zero(A).
% 12.20/12.19 ** KEPT (pick-wt=19): 304 [] -comm_monoid_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B)=ti(A,B).
% 12.20/12.19 ** KEPT (pick-wt=19): 305 [] -monoid_add(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B)=ti(A,B).
% 12.20/12.19 ** KEPT (pick-wt=50): 306 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)).
% 12.20/12.19 ** KEPT (pick-wt=50): 307 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 12.20/12.19 ** KEPT (pick-wt=63): 308 [] -ordere223160158up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))).
% 12.20/12.19 ** KEPT (pick-wt=50): 309 [] -ordere223160158up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))).
% 12.20/12.19 ** KEPT (pick-wt=50): 310 [] -ordere223160158up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))).
% 12.20/12.19 Following clause subsumed by 306 during input processing: 0 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)).
% 12.20/12.19 ** KEPT (pick-wt=50): 311 [] -ordere236663937imp_le(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)).
% 12.20/12.19 Following clause subsumed by 307 during input processing: 0 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 12.20/12.19 ** KEPT (pick-wt=50): 312 [] -ordere236663937imp_le(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)).
% 12.20/12.19 ** KEPT (pick-wt=8): 313 [] zero_zero(nat)!=hAPP(nat,nat,suc,A).
% 12.20/12.19 Following clause subsumed by 313 during input processing: 0 [] zero_zero(nat)!=hAPP(nat,nat,suc,A).
% 12.20/12.19 ** KEPT (pick-wt=8): 314 [] hAPP(nat,nat,suc,A)!=zero_zero(nat).
% 12.20/12.19 Following clause subsumed by 314 during input processing: 0 [] hAPP(nat,nat,suc,A)!=zero_zero(nat).
% 12.20/12.19 Following clause subsumed by 313 during input processing: 0 [] zero_zero(nat)!=hAPP(nat,nat,suc,A).
% 12.20/12.19 Following clause subsumed by 314 during input processing: 0 [] hAPP(nat,nat,suc,A)!=zero_zero(nat).
% 12.20/12.19 ** KEPT (pick-wt=30): 315 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,suc,A))).
% 12.20/12.19 ** KEPT (pick-wt=33): 316 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,suc,B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|A=B.
% 12.20/12.19 ** KEPT (pick-wt=30): 317 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,suc,B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).
% 12.20/12.19 ** KEPT (pick-wt=20): 318 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,suc,B)))|A!=B.
% 12.20/12.19 ** KEPT (pick-wt=34): 319 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),hAPP(nat,nat,suc,B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).
% 12.20/12.19 Following clause subsumed by 271 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),hAPP(nat,nat,suc,B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).
% 12.20/12.19 Following clause subsumed by 316 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,suc,B)))|A=B.
% 12.20/12.19 Following clause subsumed by 318 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,suc,B)))|A!=B.
% 12.20/12.19 ** KEPT (pick-wt=33): 320 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,suc,B)))|B=A.
% 12.20/12.19 Following clause subsumed by 317 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,suc,B))).
% 12.20/12.19 ** KEPT (pick-wt=37): 321 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hAPP(nat,nat,suc,A)=B|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B)).
% 12.20/12.19 ** KEPT (pick-wt=43): 322 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),C)).
% 12.20/12.19 Following clause subsumed by 316 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,suc,B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|A=B.
% 12.20/12.19 ** KEPT (pick-wt=30): 323 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).
% 12.20/12.19 Following clause subsumed by 319 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,A)),hAPP(nat,nat,suc,B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)).
% 12.20/12.19 ** KEPT (pick-wt=24): 324 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less(fun(A,bool)),B),bot_bot(fun(A,bool)))).
% 12.20/12.19 ** KEPT (pick-wt=19): 325 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)!=zero_zero(nat)|A=zero_zero(nat).
% 12.20/12.19 ** KEPT (pick-wt=19): 326 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)!=zero_zero(nat)|B=zero_zero(nat).
% 12.20/12.19 ** KEPT (pick-wt=23): 327 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)=zero_zero(nat)|A!=zero_zero(nat)|B!=zero_zero(nat).
% 12.20/12.19 ** KEPT (pick-wt=18): 328 [] hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)!=A|B=zero_zero(nat).
% 12.20/12.19 ** KEPT (pick-wt=24): 329 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),A)).
% 12.20/12.19 ** KEPT (pick-wt=24): 330 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),B)).
% 12.20/12.19 ** KEPT (pick-wt=48): 331 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).
% 12.20/12.19 ** KEPT (pick-wt=48): 332 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)).
% 12.20/12.19 ** KEPT (pick-wt=37): 333 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))).
% 12.20/12.19 ** KEPT (pick-wt=37): 334 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))).
% 12.20/12.19 ** KEPT (pick-wt=48): 335 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))).
% 12.20/12.19 ** KEPT (pick-wt=61): 336 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))).
% 12.20/12.19 ** KEPT (pick-wt=51): 337 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)!=hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),D)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)).
% 12.20/12.19 ** KEPT (pick-wt=37): 338 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)).
% 12.20/12.19 ** KEPT (pick-wt=60): 339 [] -ordere236663937imp_le(A)|hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)=hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)).
% 12.20/12.19 ** KEPT (pick-wt=55): 340 [] -hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D)))|hBOOL(hAPP(A,bool,B,C))|hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),D)).
% 12.20/12.19 ** KEPT (pick-wt=38): 341 [] hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D)))| -hBOOL(hAPP(A,bool,B,C)).
% 12.20/12.19 ** KEPT (pick-wt=49): 342 [] hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D)))| -hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),D)).
% 12.20/12.19 ** KEPT (pick-wt=18): 343 [] -hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),nil(A))).
% 12.20/12.19 ** KEPT (pick-wt=67): 344 [] -hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),C),D)))|hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),C))|hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),D)).
% 12.20/12.19 ** KEPT (pick-wt=50): 345 [] hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),C),D)))| -hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),C)).
% 12.20/12.19 ** KEPT (pick-wt=50): 346 [] hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),C),D)))| -hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),D)).
% 12.20/12.19 ** KEPT (pick-wt=41): 347 [] -linord219039673up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)).
% 12.20/12.19 ** KEPT (pick-wt=41): 348 [] -linord219039673up_add(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)).
% 12.20/12.19 ** KEPT (pick-wt=41): 349 [] -linord219039673up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))).
% 12.20/12.19 ** KEPT (pick-wt=41): 350 [] -linord219039673up_add(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))).
% 12.20/12.19 ** KEPT (pick-wt=55): 351 [] -ordere216010020id_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))).
% 12.20/12.19 ** KEPT (pick-wt=55): 352 [] -ordere216010020id_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))).
% 12.20/12.19 ** KEPT (pick-wt=41): 353 [] -hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),hAPP(list(A),list(A),rev(A),C)))|hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),C)).
% 12.20/12.19 ** KEPT (pick-wt=41): 354 [] hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),hAPP(list(A),list(A),rev(A),C)))| -hBOOL(hAPP(list(A),bool,hAPP(fun(A,bool),fun(list(A),bool),list_ex(A),B),C)).
% 12.20/12.19 ** KEPT (pick-wt=22): 356 [copy,355,flip.2] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A))|hAPP(nat,nat,suc,$f57(A))=A.
% 12.20/12.19 ** KEPT (pick-wt=21): 357 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A))|A!=hAPP(nat,nat,suc,B).
% 12.20/12.19 ** KEPT (pick-wt=22): 358 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,suc,zero_zero(nat))))|A=zero_zero(nat).
% 12.20/12.19 Following clause subsumed by 318 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,suc,zero_zero(nat))))|A!=zero_zero(nat).
% 12.20/12.19 ** KEPT (pick-wt=30): 360 [copy,359,flip.3] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,suc,B)))|A=zero_zero(nat)|hAPP(nat,nat,suc,$f58(A,B))=A.
% 12.20/12.19 ** KEPT (pick-wt=36): 361 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,suc,B)))|A=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f58(A,B)),B)).
% 12.20/12.19 ** KEPT (pick-wt=21): 362 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,suc,B)))|A!=zero_zero(nat).
% 12.20/12.19 ** KEPT (pick-wt=37): 363 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,suc,B)))|A!=hAPP(nat,nat,suc,C)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),B)).
% 12.20/12.19 ** KEPT (pick-wt=53): 364 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B))
% 12.20/12.19 Search stopped in tp_alloc by max_mem option.
% 12.20/12.19 .
% 12.20/12.19 Following clause subsumed by 333 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)).
% 12.20/12.19 Following clause subsumed by 334 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)).
% 12.20/12.19 ** KEPT (pick-wt=33): 366 [copy,365,flip.2] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),$f59(A,B)))=B.
% 12.20/12.19 ** KEPT (pick-wt=38): 368 [copy,367,flip.2] hAPP(list(A),nat,size_size(list(A)),B)!=hAPP(nat,nat,suc,C)|hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),$f61(A,B,C)),$f60(A,B,C))=B.
% 12.20/12.19 ** KEPT (pick-wt=27): 369 [] hAPP(list(A),nat,size_size(list(A)),B)!=hAPP(nat,nat,suc,C)|hAPP(list(A),nat,size_size(list(A)),$f60(A,B,C))=C.
% 12.20/12.19 ** KEPT (pick-wt=42): 370 [] hAPP(list(A),nat,size_size(list(A)),B)=hAPP(nat,nat,suc,C)|B!=hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),E)|hAPP(list(A),nat,size_size(list(A)),E)!=C.
% 12.20/12.19 ** KEPT (pick-wt=38): 372 [copy,371,flip.2] hAPP(nat,nat,suc,A)!=hAPP(list(B),nat,size_size(list(B)),C)|hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),$f63(B,A,C)),$f62(B,A,C))=C.
% 12.20/12.19 ** KEPT (pick-wt=27): 373 [] hAPP(nat,nat,suc,A)!=hAPP(list(B),nat,size_size(list(B)),C)|hAPP(list(B),nat,size_size(list(B)),$f62(B,A,C))=A.
% 12.20/12.19 ** KEPT (pick-wt=42): 374 [] hAPP(nat,nat,suc,A)=hAPP(list(B),nat,size_size(list(B)),C)|C!=hAPP(list(B),list(B),hAPP(B,fun(list(B),list(B)),cons(B),D),E)|hAPP(list(B),nat,size_size(list(B)),E)!=A.
% 12.20/12.19 ** KEPT (pick-wt=29): 375 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),$f64(A,B))).
% 12.20/12.19 ** KEPT (pick-wt=29): 376 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),$f64(A,B))=B.
% 12.20/12.19 ** KEPT (pick-wt=55): 377 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less(fun(A,bool)),B),C))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),C)).
% 12.20/12.19 ** KEPT (pick-wt=63): 378 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less(fun(A,bool)),B),C))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less(fun(A,bool)),C),D))|hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less(fun(A,bool)),B),D)).
% 12.20/12.19 ** KEPT (pick-wt=22): 380 [copy,379,flip.2] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A))|hAPP(nat,nat,suc,$f65(A))=A.
% 12.20/12.19
% 12.20/12.19 Search stopped in tp_alloc by max_mem option.
% 12.20/12.19
% 12.20/12.19 ============ end of search ============
% 12.20/12.19
% 12.20/12.19 -------------- statistics -------------
% 12.20/12.19 clauses given 0
% 12.20/12.19 clauses generated 0
% 12.20/12.19 clauses kept 345
% 12.20/12.19 clauses forward subsumed 67
% 12.20/12.19 clauses back subsumed 0
% 12.20/12.19 Kbytes malloced 11718
% 12.20/12.19
% 12.20/12.19 ----------- times (seconds) -----------
% 12.20/12.19 user CPU time 0.16 (0 hr, 0 min, 0 sec)
% 12.20/12.19 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 12.20/12.19 wall-clock time 12 (0 hr, 0 min, 12 sec)
% 12.20/12.19
% 12.20/12.19 Process 31757 finished Wed Jul 27 08:59:57 2022
% 12.20/12.19 Otter interrupted
% 12.20/12.19 PROOF NOT FOUND
%------------------------------------------------------------------------------