%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LCL803_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n023.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 11:31:51 EDT 2023

% Result   : Theorem 48.26s 28.15s
% Output   : Refutation 48.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  176
% Syntax   : Number of formulae    :  296 (  75 unt;  58 typ;   0 def)
%            Number of atoms       : 12331 ( 188 equ;   0 cnn)
%            Maximal formula atoms : 1342 (  51 avg)
%            Number of connectives : 33619 (  98   ~;  32   |;  47   &;33257   @)
%                                         (  13 <=>; 172  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   39 (  13 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :   32 (  32   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   58 (  56 usr;  29 con; 0-5 aty)
%            Number of variables   :  698 (   0   ^; 644   !;  22   ?; 698   :)
%                                         (  32  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(bool_type,type,
    bool: $tType ).

thf(dB_type,type,
    dB: $tType ).

thf(nat_type,type,
    nat: $tType ).

thf(type_type,type,
    type: $tType ).

thf(zero_type,type,
    zero: 
      !>[TA: $tType] : $o ).

thf(combb_type,type,
    combb: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ TB ) @ ( fun @ ( fun @ TA @ TC ) @ ( fun @ TA @ TB ) ) ) ).

thf(combc_type,type,
    combc: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ ( fun @ TB @ TA ) ) @ ( fun @ TB @ ( fun @ TC @ TA ) ) ) ).

thf(combs_type,type,
    combs: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ ( fun @ TB @ TA ) ) @ ( fun @ ( fun @ TC @ TB ) @ ( fun @ TC @ TA ) ) ) ).

thf(zero_zero_type,type,
    zero_zero: 
      !>[TA: $tType] : TA ).

thf(it_type,type,
    it: fun @ dB @ bool ).

thf(beta_type,type,
    beta: fun @ dB @ ( fun @ dB @ bool ) ).

thf(abs_type,type,
    abs: dB > dB ).

thf(app_type,type,
    app: fun @ dB @ ( fun @ dB @ dB ) ).

thf(var_type,type,
    var: nat > dB ).

thf(dB_size_type,type,
    dB_size: dB > nat ).

thf(lift_type,type,
    lift: dB > nat > dB ).

thf(subst_type,type,
    subst: fun @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) ).

thf(step1_type,type,
    step1: 
      !>[TA: $tType] : ( ( fun @ TA @ ( fun @ TA @ bool ) ) > ( list @ TA ) > ( list @ TA ) > $o ) ).

thf(foldl_type,type,
    foldl: 
      !>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TA @ TB ) ) > TB > ( list @ TA ) > TB ) ).

thf(foldr_type,type,
    foldr: 
      !>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TA @ TA ) ) > ( list @ TB ) > TA > TA ) ).

thf(cons_type,type,
    cons: 
      !>[TA: $tType] : ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) ).

thf(list_case_type,type,
    list_case: 
      !>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ ( fun @ ( list @ TA ) @ TB ) ) > ( list @ TA ) > TB ) ).

thf(listset_type,type,
    listset: 
      !>[TA: $tType] : ( ( list @ ( fun @ TA @ bool ) ) > ( fun @ ( list @ TA ) @ bool ) ) ).

thf(listsp_type,type,
    listsp: 
      !>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > $o ) ).

thf(set_Cons_type,type,
    set_Cons: 
      !>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( list @ TA ) @ bool ) > ( fun @ ( list @ TA ) @ bool ) ) ).

thf(size_size_type,type,
    size_size: 
      !>[TA: $tType] : ( TA > nat ) ).

thf(collect_type,type,
    collect: 
      !>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).

thf(shift_type,type,
    shift: 
      !>[TA: $tType] : ( fun @ ( fun @ nat @ TA ) @ ( fun @ nat @ ( fun @ TA @ ( fun @ nat @ TA ) ) ) ) ).

thf(fun1_type,type,
    fun1: fun @ type @ ( fun @ type @ type ) ).

thf(type_case_type,type,
    type_case: 
      !>[TA: $tType] : ( ( fun @ nat @ TA ) > ( fun @ type @ ( fun @ type @ TA ) ) > type > TA ) ).

thf(typing_type,type,
    typing: fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ).

thf(typings_type,type,
    typings: ( fun @ nat @ type ) > ( list @ dB ) > ( fun @ ( list @ type ) @ bool ) ).

thf(aa_type,type,
    aa: 
      !>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).

thf(fAll_type,type,
    fAll: 
      !>[TA: $tType] : ( fun @ ( fun @ TA @ bool ) @ bool ) ).

thf(fEx_type,type,
    fEx: 
      !>[TA: $tType] : ( fun @ ( fun @ TA @ bool ) @ bool ) ).

thf(fFalse_type,type,
    fFalse: bool ).

thf(fTrue_type,type,
    fTrue: bool ).

thf(fconj_type,type,
    fconj: fun @ bool @ ( fun @ bool @ bool ) ).

thf(fequal_type,type,
    fequal: 
      !>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ bool ) ) ).

thf(fimplies_type,type,
    fimplies: fun @ bool @ ( fun @ bool @ bool ) ).

thf(member_type,type,
    member: 
      !>[TA: $tType] : ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) ).

thf(pp_type,type,
    pp: bool > $o ).

thf(t2_type,type,
    t2: type ).

thf(t1_type,type,
    t1: type ).

thf(t_a_type,type,
    t_a: type ).

thf(t_type,type,
    t: type ).

thf(ts_type,type,
    ts: list @ type ).

thf(a_type,type,
    a: dB ).

thf(as_type,type,
    as: list @ dB ).

thf(e_type,type,
    e: fun @ nat @ type ).

thf(ea_type,type,
    ea: fun @ nat @ type ).

thf(i_type,type,
    i: nat ).

thf(ia_type,type,
    ia: nat ).

thf(n_type,type,
    n: nat ).

thf(rs_type,type,
    rs: list @ dB ).

thf(t3_type,type,
    t3: dB ).

thf(u_type,type,
    u: dB ).

thf(ua_type,type,
    ua: dB ).

thf(79,axiom,
    ! [A: nat] :
      ( ( dB_size @ ( var @ A ) )
      = ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_dB_Osize_I1_J) ).

thf(384,plain,
    ! [A: nat] :
      ( ( dB_size @ ( var @ A ) )
      = ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(18,axiom,
    ~ ! [A: list @ type] :
        ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( var @ n ) ) @ a ) ) @ ( foldr @ type @ type @ fun1 @ A @ t1 ) ) )
       => ~ ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) @ as ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43__096_B_Bthesis_O_A_I_B_BTs_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_058_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_124_124_N_Aas_A_058_ATs_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

thf(184,plain,
    ~ ! [A: list @ type] :
        ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( var @ n ) ) @ a ) ) @ ( foldr @ type @ type @ fun1 @ A @ t1 ) ) )
       => ~ ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) @ as ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(19,axiom,
    ! [A: list @ dB,B: type,C: list @ type,D: dB,E: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ E ) @ D ) @ ( foldr @ type @ type @ fun1 @ C @ B ) ) )
     => ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ E @ A ) @ C ) )
       => ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ E ) @ ( foldl @ dB @ dB @ app @ D @ A ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_list__app__typeI) ).

thf(188,plain,
    ! [A: list @ dB,B: type,C: list @ type,D: dB,E: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ E ) @ D ) @ ( foldr @ type @ type @ fun1 @ C @ B ) ) )
     => ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ E @ A ) @ C ) )
       => ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ E ) @ ( foldl @ dB @ dB @ app @ D @ A ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(9,axiom,
    ~ ( pp @ fFalse ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).

thf(150,plain,
    ~ ( pp @ fFalse ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(7,axiom,
    ! [A: dB,B: nat] :
      ( ( var @ B )
     != ( abs @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_dB_Osimps_I6_J) ).

thf(143,plain,
    ! [A: dB,B: nat] :
      ( ( var @ B )
     != ( abs @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(71,axiom,
    pp @ ( aa @ dB @ bool @ it @ u ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_uIT) ).

thf(365,plain,
    pp @ ( aa @ dB @ bool @ it @ u ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(67,axiom,
    ! [A: dB,B: list @ dB,C: list @ dB] :
      ( ( step1 @ dB @ beta @ C @ B )
     => ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ A @ C ) ) @ ( foldl @ dB @ dB @ app @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_apps__preserves__betas) ).

thf(347,plain,
    ! [A: dB,B: list @ dB,C: list @ dB] :
      ( ( step1 @ dB @ beta @ C @ B )
     => ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ A @ C ) ) @ ( foldl @ dB @ dB @ app @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(37,axiom,
    ! [A: dB,B: type,C: nat,D: fun @ nat @ type,E: dB,F: type,G: type] :
      ( ( t
        = ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ G ) @ F ) )
     => ( ( pp @ ( aa @ dB @ bool @ it @ E ) )
       => ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ D ) @ C ) @ G ) ) @ E ) @ B ) )
         => ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
           => ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ A ) @ G ) )
             => ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ E ) @ A ) @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_MI1) ).

thf(249,plain,
    ! [A: dB,B: type,C: nat,D: fun @ nat @ type,E: dB,F: type,G: type] :
      ( ( t
        = ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ G ) @ F ) )
     => ( ( pp @ ( aa @ dB @ bool @ it @ E ) )
       => ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ D ) @ C ) @ G ) ) @ E ) @ B ) )
         => ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
           => ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ A ) @ G ) )
             => ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ E ) @ A ) @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(88,axiom,
    ! [A: nat,B: type,C: dB,D: fun @ nat @ type,E: type,F: dB,G: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ G ) @ F ) @ E ) )
     => ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ C ) @ B ) )
       => ( ( G
            = ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ D ) @ A ) @ B ) )
         => ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ F ) @ C ) @ A ) ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_subst__lemma) ).

thf(408,plain,
    ! [A: nat,B: type,C: dB,D: fun @ nat @ type,E: type,F: dB,G: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ G ) @ F ) @ E ) )
     => ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ C ) @ B ) )
       => ( ( G
            = ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ D ) @ A ) @ B ) )
         => ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ F ) @ C ) @ A ) ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(47,axiom,
    pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) @ ( var @ n ) ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ t2 ) @ ( foldr @ type @ type @ fun1 @ ts @ t1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_varT) ).

thf(276,plain,
    pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) @ ( var @ n ) ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ t2 ) @ ( foldr @ type @ type @ fun1 @ ts @ t1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(77,axiom,
    ( t
    = ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ t2 ) @ ( foldr @ type @ type @ fun1 @ ts @ t1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_T) ).

thf(379,plain,
    ( t
    = ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ t2 ) @ ( foldr @ type @ type @ fun1 @ ts @ t1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(44,axiom,
    pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( var @ n ) ) @ a ) ) @ ( foldr @ type @ type @ fun1 @ ts @ t1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_headT) ).

thf(269,plain,
    pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( var @ n ) ) @ a ) ) @ ( foldr @ type @ type @ fun1 @ ts @ t1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(1,conjecture,
    listsp @ dB @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ bool ) ) @ ( combs @ dB @ bool @ bool ) @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ dB ) @ fconj ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ bool ) @ bool @ dB ) @ ( fAll @ ( fun @ nat @ type ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ bool ) @ bool ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( combb @ ( fun @ type @ bool ) @ bool @ ( fun @ nat @ type ) ) @ ( fAll @ type ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( combb @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ dB @ bool ) @ bool ) @ ( fun @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) ) @ ( combb @ ( fun @ dB @ bool ) @ bool @ type ) @ ( fAll @ dB ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ bool ) @ type ) @ ( aa @ ( fun @ ( fun @ nat @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ nat @ bool ) @ bool @ dB ) @ ( fAll @ nat ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combs @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ dB ) @ ( combs @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ nat @ type ) ) @ ( combc @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ type ) @ ( combb @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) @ dB ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ type ) @ ( combs @ nat @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ bool ) @ ( fun @ nat @ ( fun @ bool @ bool ) ) @ type ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ nat ) @ fimplies ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ type ) ) @ ( combc @ nat @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( combc @ ( fun @ nat @ type ) @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( combc @ nat @ dB @ ( fun @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ nat @ type ) ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ nat @ type ) ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ ( fun @ nat @ type ) ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ nat ) @ typing ) ) @ ( aa @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( combc @ ( fun @ nat @ type ) @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( fun @ nat @ type ) ) @ ( combc @ nat @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) ) ) @ t ) ) ) ) ) ) ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( combs @ dB @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ ( aa @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ dB ) @ ( combb @ bool @ bool @ nat ) ) @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ dB ) @ fimplies ) @ it ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( combc @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( combs @ dB @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ dB ) @ ( combb @ bool @ bool @ nat ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ dB ) @ fimplies ) ) @ ( aa @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) ) @ ( combc @ ( fun @ nat @ type ) @ type @ ( fun @ dB @ bool ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ nat @ type ) ) @ ( combc @ dB @ type @ bool ) ) @ typing ) ) @ t ) ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) ) @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) ) @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( combb @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) @ dB ) @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) ) @ ( combb @ dB @ bool @ nat ) @ it ) ) ) @ subst ) ) ) ) ) ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ ( fun @ type @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ type @ bool ) @ bool @ dB ) @ ( fEx @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) ) ) @ as,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( listsp @ dB @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ bool ) ) @ ( combs @ dB @ bool @ bool ) @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ dB ) @ fconj ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ bool ) @ bool @ dB ) @ ( fAll @ ( fun @ nat @ type ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ bool ) @ bool ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( combb @ ( fun @ type @ bool ) @ bool @ ( fun @ nat @ type ) ) @ ( fAll @ type ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( combb @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ dB @ bool ) @ bool ) @ ( fun @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) ) @ ( combb @ ( fun @ dB @ bool ) @ bool @ type ) @ ( fAll @ dB ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ bool ) @ type ) @ ( aa @ ( fun @ ( fun @ nat @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ nat @ bool ) @ bool @ dB ) @ ( fAll @ nat ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combs @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ dB ) @ ( combs @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ nat @ type ) ) @ ( combc @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ type ) @ ( combb @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) @ dB ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ type ) @ ( combs @ nat @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ bool ) @ ( fun @ nat @ ( fun @ bool @ bool ) ) @ type ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ nat ) @ fimplies ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ type ) ) @ ( combc @ nat @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( combc @ ( fun @ nat @ type ) @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( combc @ nat @ dB @ ( fun @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ nat @ type ) ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ nat @ type ) ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ ( fun @ nat @ type ) ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ nat ) @ typing ) ) @ ( aa @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( combc @ ( fun @ nat @ type ) @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( fun @ nat @ type ) ) @ ( combc @ nat @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) ) ) @ t ) ) ) ) ) ) ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( combs @ dB @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ ( aa @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ dB ) @ ( combb @ bool @ bool @ nat ) ) @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ dB ) @ fimplies ) @ it ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( combc @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( combs @ dB @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ dB ) @ ( combb @ bool @ bool @ nat ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ dB ) @ fimplies ) ) @ ( aa @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) ) @ ( combc @ ( fun @ nat @ type ) @ type @ ( fun @ dB @ bool ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ nat @ type ) ) @ ( combc @ dB @ type @ bool ) ) @ typing ) ) @ t ) ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) ) @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) ) @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( combb @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) @ dB ) @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) ) @ ( combb @ dB @ bool @ nat ) @ it ) ) ) @ subst ) ) ) ) ) ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ ( fun @ type @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ type @ bool ) @ bool @ dB ) @ ( fEx @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) ) ) @ as ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(120,plain,
    ~ ( listsp @ dB @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ bool ) ) @ ( combs @ dB @ bool @ bool ) @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ dB ) @ fconj ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ bool ) @ bool @ dB ) @ ( fAll @ ( fun @ nat @ type ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ bool ) @ bool ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( combb @ ( fun @ type @ bool ) @ bool @ ( fun @ nat @ type ) ) @ ( fAll @ type ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( combb @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ dB @ bool ) @ bool ) @ ( fun @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) ) @ ( combb @ ( fun @ dB @ bool ) @ bool @ type ) @ ( fAll @ dB ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ bool ) @ type ) @ ( aa @ ( fun @ ( fun @ nat @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ nat @ bool ) @ bool @ dB ) @ ( fAll @ nat ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combs @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ dB ) @ ( combs @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ nat @ type ) ) @ ( combc @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ type ) @ ( combb @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) @ dB ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ type ) @ ( combs @ nat @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ bool ) @ ( fun @ nat @ ( fun @ bool @ bool ) ) @ type ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ nat ) @ fimplies ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ type ) ) @ ( combc @ nat @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( combc @ ( fun @ nat @ type ) @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( combc @ nat @ dB @ ( fun @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ nat @ type ) ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ nat @ type ) ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ ( fun @ nat @ type ) ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ nat ) @ typing ) ) @ ( aa @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( combc @ ( fun @ nat @ type ) @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( fun @ nat @ type ) ) @ ( combc @ nat @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) ) ) @ t ) ) ) ) ) ) ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( combs @ dB @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ ( aa @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ dB ) @ ( combb @ bool @ bool @ nat ) ) @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ dB ) @ fimplies ) @ it ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( combc @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( combs @ dB @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ dB ) @ ( combb @ bool @ bool @ nat ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ dB ) @ fimplies ) ) @ ( aa @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) ) @ ( combc @ ( fun @ nat @ type ) @ type @ ( fun @ dB @ bool ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ nat @ type ) ) @ ( combc @ dB @ type @ bool ) ) @ typing ) ) @ t ) ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) ) @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) ) @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( combb @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) @ dB ) @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) ) @ ( combb @ dB @ bool @ nat ) @ it ) ) ) @ subst ) ) ) ) ) ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ ( fun @ type @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ type @ bool ) @ bool @ dB ) @ ( fEx @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) ) ) @ as ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(36,axiom,
    ! [A: dB,B: dB,C: dB] :
      ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
     => ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ A ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_appL) ).

thf(247,plain,
    ! [A: dB,B: dB,C: dB] :
      ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
     => ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ A ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(15,axiom,
    ! [A: list @ type,B: list @ dB,C: dB,D: fun @ nat @ type] :
      ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ C ) @ B ) ) @ A ) )
    <=> ( pp @ ( list_case @ bool @ type @ fFalse @ ( aa @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ type @ ( fun @ ( list @ type ) @ bool ) ) @ ( aa @ ( fun @ type @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ type @ ( fun @ ( list @ type ) @ bool ) ) ) @ ( combc @ type @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) @ ( aa @ ( fun @ type @ ( fun @ bool @ bool ) ) @ ( fun @ type @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) @ ( fun @ ( fun @ type @ ( fun @ bool @ bool ) ) @ ( fun @ type @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) @ type ) @ ( combb @ bool @ bool @ ( list @ type ) ) ) @ ( aa @ ( fun @ type @ bool ) @ ( fun @ type @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ type @ bool ) @ ( fun @ type @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ type ) @ fconj ) @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ C ) ) ) ) @ ( typings @ D @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_typings_Osimps_I2_J) ).

thf(174,plain,
    ! [A: list @ type,B: list @ dB,C: dB,D: fun @ nat @ type] :
      ( ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ C ) @ B ) ) @ A ) )
       => ( pp @ ( list_case @ bool @ type @ fFalse @ ( aa @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ type @ ( fun @ ( list @ type ) @ bool ) ) @ ( aa @ ( fun @ type @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ type @ ( fun @ ( list @ type ) @ bool ) ) ) @ ( combc @ type @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) @ ( aa @ ( fun @ type @ ( fun @ bool @ bool ) ) @ ( fun @ type @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) @ ( fun @ ( fun @ type @ ( fun @ bool @ bool ) ) @ ( fun @ type @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) @ type ) @ ( combb @ bool @ bool @ ( list @ type ) ) ) @ ( aa @ ( fun @ type @ bool ) @ ( fun @ type @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ type @ bool ) @ ( fun @ type @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ type ) @ fconj ) @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ C ) ) ) ) @ ( typings @ D @ B ) ) @ A ) ) )
      & ( ( pp @ ( list_case @ bool @ type @ fFalse @ ( aa @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ type @ ( fun @ ( list @ type ) @ bool ) ) @ ( aa @ ( fun @ type @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ type @ ( fun @ ( list @ type ) @ bool ) ) ) @ ( combc @ type @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) @ ( aa @ ( fun @ type @ ( fun @ bool @ bool ) ) @ ( fun @ type @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) @ ( fun @ ( fun @ type @ ( fun @ bool @ bool ) ) @ ( fun @ type @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ type ) @ bool ) @ ( fun @ ( list @ type ) @ bool ) ) @ type ) @ ( combb @ bool @ bool @ ( list @ type ) ) ) @ ( aa @ ( fun @ type @ bool ) @ ( fun @ type @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ type @ bool ) @ ( fun @ type @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ type ) @ fconj ) @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ C ) ) ) ) @ ( typings @ D @ B ) ) @ A ) )
       => ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ C ) @ B ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(58,axiom,
    ! [A: dB,B: dB,C: dB] :
      ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) ) @ A ) )
     => ( ! [D: dB] :
            ( ( A
              = ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ B ) @ ( zero_zero @ nat ) ) )
           => ( C
             != ( abs @ D ) ) )
       => ( ! [D: dB] :
              ( ( A
                = ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ B ) )
             => ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) ) )
         => ~ ! [D: dB] :
                ( ( A
                  = ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ D ) )
               => ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_beta__cases_I3_J) ).

thf(301,plain,
    ! [A: dB,B: dB,C: dB] :
      ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) ) @ A ) )
     => ( ! [D: dB] :
            ( ( A
              = ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ B ) @ ( zero_zero @ nat ) ) )
           => ( C
             != ( abs @ D ) ) )
       => ( ! [D: dB] :
              ( ( A
                = ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ B ) )
             => ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) ) )
         => ~ ! [D: dB] :
                ( ( A
                  = ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ D ) )
               => ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(10,axiom,
    ! [A: dB,B: dB] :
      ( ( ( abs @ B )
        = ( abs @ A ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_dB_Osimps_I3_J) ).

thf(152,plain,
    ! [A: dB,B: dB] :
      ( ( ( ( abs @ B )
          = ( abs @ A ) )
       => ( B = A ) )
      & ( ( B = A )
       => ( ( abs @ B )
          = ( abs @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(41,axiom,
    ! [A: dB,B: nat] :
      ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( var @ B ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_beta__cases_I1_J) ).

thf(261,plain,
    ! [A: dB,B: nat] :
      ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( var @ B ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(16,axiom,
    ~ ! [A: type] :
        ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) @ ( var @ n ) ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ A ) @ ( foldr @ type @ type @ fun1 @ ts @ t1 ) ) ) )
       => ~ ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) @ a ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42__096_B_Bthesis_O_A_I_B_BT_H_H_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_058_AT_H_H_A_092_060Rightarrow_062_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

thf(179,plain,
    ~ ! [A: type] :
        ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) @ ( var @ n ) ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ A ) @ ( foldr @ type @ type @ fun1 @ ts @ t1 ) ) ) )
       => ~ ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) @ a ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(101,axiom,
    ! [A: dB,B: type,C: nat,D: fun @ nat @ type,E: dB,F: type,G: type] :
      ( ( t
        = ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ G ) @ F ) )
     => ( ( pp @ ( aa @ dB @ bool @ it @ E ) )
       => ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ D ) @ C ) @ F ) ) @ E ) @ B ) )
         => ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
           => ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ A ) @ F ) )
             => ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ E ) @ A ) @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_MI2) ).

thf(443,plain,
    ! [A: dB,B: type,C: nat,D: fun @ nat @ type,E: dB,F: type,G: type] :
      ( ( t
        = ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ G ) @ F ) )
     => ( ( pp @ ( aa @ dB @ bool @ it @ E ) )
       => ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ D ) @ C ) @ F ) ) @ E ) @ B ) )
         => ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
           => ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ A ) @ F ) )
             => ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ E ) @ A ) @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(3,axiom,
    ! [TA: $tType] :
      ( ( zero @ TA )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = A )
        <=> ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_zero__reorient) ).

thf(121,plain,
    ! [TA: $tType] :
      ( ( zero @ TA )
     => ! [A: TA] :
          ( ( ( ( zero_zero @ TA )
              = A )
           => ( A
              = ( zero_zero @ TA ) ) )
          & ( ( A
              = ( zero_zero @ TA ) )
           => ( ( zero_zero @ TA )
              = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(8,axiom,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).

thf(147,plain,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(55,axiom,
    ! [A: type,B: dB,C: dB,D: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) ) @ A ) )
     => ~ ! [E: type] :
            ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ C ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ E ) @ A ) ) )
           => ~ ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ B ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_typing__elims_I2_J) ).

thf(293,plain,
    ! [A: type,B: dB,C: dB,D: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) ) @ A ) )
     => ~ ! [E: type] :
            ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ C ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ E ) @ A ) ) )
           => ~ ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ B ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(104,axiom,
    ! [A: nat,B: nat,C: dB] :
      ( ( pp @ ( aa @ dB @ bool @ it @ C ) )
     => ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ ( var @ B ) ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_subst__Var__IT) ).

thf(453,plain,
    ! [A: nat,B: nat,C: dB] :
      ( ( pp @ ( aa @ dB @ bool @ it @ C ) )
     => ( pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ ( var @ B ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(83,axiom,
    ! [A: type,B: dB,C: type,D: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ D ) @ ( zero_zero @ nat ) ) @ C ) ) @ B ) @ A ) )
     => ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ ( abs @ B ) ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_Abs) ).

thf(396,plain,
    ! [A: type,B: dB,C: type,D: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ D ) @ ( zero_zero @ nat ) ) @ C ) ) @ B ) @ A ) )
     => ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ ( abs @ B ) ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(54,axiom,
    pp @ ( aa @ dB @ bool @ it @ t3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).

thf(292,plain,
    pp @ ( aa @ dB @ bool @ it @ t3 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(32,axiom,
    ! [A: list @ type,B: list @ dB,C: fun @ nat @ type] :
      ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ C @ B ) @ A ) )
     => ( listsp @ dB @ ( aa @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ ( fun @ type @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ type @ bool ) @ bool @ dB ) @ ( fEx @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ C ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_lists__typings) ).

thf(233,plain,
    ! [A: list @ type,B: list @ dB,C: fun @ nat @ type] :
      ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ C @ B ) @ A ) )
     => ( listsp @ dB @ ( aa @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ ( fun @ type @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ type @ bool ) @ bool @ dB ) @ ( fEx @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ C ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(100,axiom,
    ! [A: type,B: nat,C: fun @ nat @ type] :
      ( ( ( aa @ nat @ type @ C @ B )
        = A )
     => ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ C ) @ ( var @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_typing_OVar) ).

thf(439,plain,
    ! [A: type,B: nat,C: fun @ nat @ type] :
      ( ( ( aa @ nat @ type @ C @ B )
        = A )
     => ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ C ) @ ( var @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(45,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: list @ TA] :
      ( ( listsp @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) ) @ A ) @ C )
    <=> ( ( listsp @ TA @ B @ C )
        & ( listsp @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_listsp__conj__eq) ).

thf(270,plain,
    ! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: list @ TA] :
      ( ( ( listsp @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) ) @ A ) @ C )
       => ( ( listsp @ TA @ B @ C )
          & ( listsp @ TA @ A @ C ) ) )
      & ( ( ( listsp @ TA @ B @ C )
          & ( listsp @ TA @ A @ C ) )
       => ( listsp @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(78,axiom,
    ! [A: type,B: type,C: list @ dB,D: nat,E: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ E ) @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) ) @ B ) )
     => ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ E ) @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) ) @ A ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_var__app__type__eq) ).

thf(381,plain,
    ! [A: type,B: type,C: list @ dB,D: nat,E: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ E ) @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) ) @ B ) )
     => ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ E ) @ ( foldl @ dB @ dB @ app @ ( var @ D ) @ C ) ) @ A ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(72,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( B
     != ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_not__Cons__self) ).

thf(366,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( B
     != ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(65,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( B != A )
      | ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).

thf(334,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( B != A )
      | ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(11,axiom,
    pp @ fTrue,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).

thf(160,plain,
    pp @ fTrue,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(94,axiom,
    ! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
      ( ( foldl @ TB @ TA @ D @ C @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
      = ( foldl @ TB @ TA @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ C ) @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_foldl__Cons) ).

thf(424,plain,
    ! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
      ( ( foldl @ TB @ TA @ D @ C @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
      = ( foldl @ TB @ TA @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ C ) @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(21,axiom,
    ! [A: dB,B: nat,C: dB] :
      ( ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( lift @ C @ B ) ) @ A ) @ B )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_subst__lift) ).

thf(192,plain,
    ! [A: dB,B: nat,C: dB] :
      ( ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( lift @ C @ B ) ) @ A ) @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(96,axiom,
    pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ e ) @ u ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ t2 ) @ ( foldr @ type @ type @ fun1 @ ts @ t1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_uT_H) ).

thf(429,plain,
    pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ e ) @ u ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ t2 ) @ ( foldr @ type @ type @ fun1 @ ts @ t1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(40,axiom,
    pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) @ as ) @ ts ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_argsT) ).

thf(260,plain,
    pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) @ as ) @ ts ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(68,axiom,
    ! [A: list @ dB,B: nat,C: list @ dB,D: nat] :
      ( ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
        = ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) )
    <=> ( ( D = B )
        & ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_Var__apps__eq__Var__apps__conv) ).

thf(349,plain,
    ! [A: list @ dB,B: nat,C: list @ dB,D: nat] :
      ( ( ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
          = ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) )
       => ( ( D = B )
          & ( C = A ) ) )
      & ( ( ( D = B )
          & ( C = A ) )
       => ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
          = ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(38,axiom,
    ! [A: dB,B: list @ dB,C: dB] :
      ( ( ( foldl @ dB @ dB @ app @ C @ B )
        = ( foldl @ dB @ dB @ app @ A @ B ) )
    <=> ( C = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_apps__eq__tail__conv) ).

thf(252,plain,
    ! [A: dB,B: list @ dB,C: dB] :
      ( ( ( ( foldl @ dB @ dB @ app @ C @ B )
          = ( foldl @ dB @ dB @ app @ A @ B ) )
       => ( C = A ) )
      & ( ( C = A )
       => ( ( foldl @ dB @ dB @ app @ C @ B )
          = ( foldl @ dB @ dB @ app @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(51,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ B )
      | ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).

thf(285,plain,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ B )
      | ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(112,axiom,
    ! [A: type,B: list @ dB,C: dB,D: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
     => ? [E: list @ type] :
          ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ C ) @ ( foldr @ type @ type @ fun1 @ E @ A ) ) )
          & ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ B ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_list__app__typeD) ).

thf(471,plain,
    ! [A: type,B: list @ dB,C: dB,D: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
     => ? [E: list @ type] :
          ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ C ) @ ( foldr @ type @ type @ fun1 @ E @ A ) ) )
          & ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ B ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(114,axiom,
    pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ea ) @ ua ) @ t ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_Var_I4_J) ).

thf(476,plain,
    pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ea ) @ ua ) @ t ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(4,axiom,
    ! [A: nat,B: nat] :
      ( ( ( var @ B )
        = ( var @ A ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_dB_Osimps_I1_J) ).

thf(128,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( var @ B )
          = ( var @ A ) )
       => ( B = A ) )
      & ( ( B = A )
       => ( ( var @ B )
          = ( var @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(34,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) )
      | ~ ( pp @ B )
      | ( pp @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).

thf(244,plain,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) )
      | ~ ( pp @ B )
      | ( pp @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(84,axiom,
    ! [A: nat,B: dB,C: dB,D: dB] :
      ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ D ) @ C ) )
     => ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ B ) @ A ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_subst__preserves__beta) ).

thf(398,plain,
    ! [A: nat,B: dB,C: dB,D: dB] :
      ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ D ) @ C ) )
     => ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ B ) @ A ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(57,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
      ( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TB @ TC ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combb @ TB @ TC @ TA ) @ C ) @ B ) @ A )
      = ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).

thf(298,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
      ( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TB @ TC ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combb @ TB @ TC @ TA ) @ C ) @ B ) @ A )
      = ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(89,axiom,
    pp @ ( aa @ dB @ bool @ it @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ u ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ a ) @ u ) @ i ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19__096IT_A_Iu_A_092_060degree_062_Aa_091u_Pi_093_J_096) ).

thf(412,plain,
    pp @ ( aa @ dB @ bool @ it @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ u ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ a ) @ u ) @ i ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(97,axiom,
    ! [A: dB,B: dB,C: dB] :
      ( ( abs @ C )
     != ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_dB_Osimps_I9_J) ).

thf(430,plain,
    ! [A: dB,B: dB,C: dB] :
      ( ( abs @ C )
     != ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(42,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: TA] :
      ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
    <=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).

thf(264,plain,
    ! [TA: $tType,A: fun @ TA @ bool,B: TA] :
      ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
       => ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
      & ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
       => ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(12,axiom,
    ~ ( pp @ fFalse ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

thf(161,plain,
    ~ ( pp @ fFalse ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(49,axiom,
    ! [A: list @ dB,B: dB,C: list @ dB,D: nat] :
      ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
     != ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Var__apps__neq__Abs__apps) ).

thf(279,plain,
    ! [A: list @ dB,B: dB,C: list @ dB,D: nat] :
      ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
     != ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(56,axiom,
    ! [A: dB] :
      ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
     => ( pp @ ( aa @ dB @ bool @ it @ ( abs @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_Lambda) ).

thf(296,plain,
    ! [A: dB] :
      ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
     => ( pp @ ( aa @ dB @ bool @ it @ ( abs @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(75,axiom,
    ! [A: type,B: dB,C: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ C ) @ ( abs @ B ) ) @ A ) )
     => ~ ! [D: type,E: type] :
            ~ ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ C ) @ ( zero_zero @ nat ) ) @ D ) ) @ B ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_abs__typeE) ).

thf(375,plain,
    ! [A: type,B: dB,C: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ C ) @ ( abs @ B ) ) @ A ) )
     => ~ ! [D: type,E: type] :
            ~ ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ C ) @ ( zero_zero @ nat ) ) @ D ) ) @ B ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(86,axiom,
    ! [A: type,B: list @ dB,C: nat,D: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) ) @ A ) )
     => ~ ! [E: list @ type] :
            ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ ( var @ C ) ) @ ( foldr @ type @ type @ fun1 @ E @ A ) ) )
           => ~ ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ B ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_var__app__typesE) ).

thf(402,plain,
    ! [A: type,B: list @ dB,C: nat,D: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) ) @ A ) )
     => ~ ! [E: list @ type] :
            ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ ( var @ C ) ) @ ( foldr @ type @ type @ fun1 @ E @ A ) ) )
           => ~ ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ B ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(26,axiom,
    ! [A: nat,B: dB,C: dB] :
      ( ( lift @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
      = ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( lift @ C @ A ) ) @ ( lift @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_lift_Osimps_I2_J) ).

thf(204,plain,
    ! [A: nat,B: dB,C: dB] :
      ( ( lift @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
      = ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( lift @ C @ A ) ) @ ( lift @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(39,axiom,
    listsp @ dB @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ bool ) @ bool @ dB ) @ ( fAll @ ( fun @ nat @ type ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ bool ) @ bool ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( combb @ ( fun @ type @ bool ) @ bool @ ( fun @ nat @ type ) ) @ ( fAll @ type ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( combb @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ dB @ bool ) @ bool ) @ ( fun @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) ) @ ( combb @ ( fun @ dB @ bool ) @ bool @ type ) @ ( fAll @ dB ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ bool ) @ type ) @ ( aa @ ( fun @ ( fun @ nat @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ nat @ bool ) @ bool @ dB ) @ ( fAll @ nat ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combs @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ dB ) @ ( combs @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ nat @ type ) ) @ ( combc @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ type ) @ ( combb @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) @ dB ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ type ) @ ( combs @ nat @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ bool ) @ ( fun @ nat @ ( fun @ bool @ bool ) ) @ type ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ nat ) @ fimplies ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ type ) ) @ ( combc @ nat @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( combc @ ( fun @ nat @ type ) @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( combc @ nat @ dB @ ( fun @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ nat @ type ) ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ nat @ type ) ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ ( fun @ nat @ type ) ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ nat ) @ typing ) ) @ ( aa @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( combc @ ( fun @ nat @ type ) @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( fun @ nat @ type ) ) @ ( combc @ nat @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) ) ) @ t ) ) ) ) ) ) ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( combs @ dB @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ ( aa @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ dB ) @ ( combb @ bool @ bool @ nat ) ) @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ dB ) @ fimplies ) @ it ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( combc @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( combs @ dB @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ dB ) @ ( combb @ bool @ bool @ nat ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ dB ) @ fimplies ) ) @ ( aa @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) ) @ ( combc @ ( fun @ nat @ type ) @ type @ ( fun @ dB @ bool ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ nat @ type ) ) @ ( combc @ dB @ type @ bool ) ) @ typing ) ) @ t ) ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) ) @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) ) @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( combb @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) @ dB ) @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) ) @ ( combb @ dB @ bool @ nat ) @ it ) ) ) @ subst ) ) ) ) ) ) ) ) @ as,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__096listsp_A_I_Ft_O_AALL_Ae_AT_H_Au_Ai_O_Ae_060i_058T_062_A_092_060turnstile_062_At_A_058_AT_H_A_N_N_062_AIT_Au_A_N_N_062_Ae_A_092_060turnstile_062_Au_A_058_AT_A_N_N_062_AIT_A_It_091u_Pi_093_J_J_Aas_096) ).

thf(259,plain,
    listsp @ dB @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ bool ) @ bool @ dB ) @ ( fAll @ ( fun @ nat @ type ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ bool ) @ bool ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( combb @ ( fun @ type @ bool ) @ bool @ ( fun @ nat @ type ) ) @ ( fAll @ type ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( combb @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ dB @ bool ) @ bool ) @ ( fun @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) ) @ ( combb @ ( fun @ dB @ bool ) @ bool @ type ) @ ( fAll @ dB ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ bool ) @ type ) @ ( aa @ ( fun @ ( fun @ nat @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ nat @ bool ) @ bool @ dB ) @ ( fAll @ nat ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combs @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ dB ) @ ( combs @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ nat @ type ) ) @ ( combc @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ type ) @ ( combb @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) @ dB ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ type ) @ ( combs @ nat @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ bool ) @ ( fun @ nat @ ( fun @ bool @ bool ) ) @ type ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ nat ) @ fimplies ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ type ) ) @ ( combc @ nat @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( combc @ ( fun @ nat @ type ) @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( combc @ nat @ dB @ ( fun @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ nat @ type ) ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ nat @ type ) ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ ( fun @ nat @ type ) ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ nat ) @ typing ) ) @ ( aa @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( combc @ ( fun @ nat @ type ) @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( fun @ nat @ type ) ) @ ( combc @ nat @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) ) ) @ t ) ) ) ) ) ) ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( combs @ dB @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ ( aa @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ dB ) @ ( combb @ bool @ bool @ nat ) ) @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ dB ) @ fimplies ) @ it ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( combc @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( combs @ dB @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ dB ) @ ( combb @ bool @ bool @ nat ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ dB ) @ fimplies ) ) @ ( aa @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) ) @ ( combc @ ( fun @ nat @ type ) @ type @ ( fun @ dB @ bool ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ nat @ type ) ) @ ( combc @ dB @ type @ bool ) ) @ typing ) ) @ t ) ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) ) @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) ) @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( combb @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) @ dB ) @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) ) @ ( combb @ dB @ bool @ nat ) @ it ) ) ) @ subst ) ) ) ) ) ) ) ) @ as,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(90,axiom,
    ! [A: nat,B: dB,C: dB] :
      ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
     => ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( lift @ C @ A ) ) @ ( lift @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_lift__preserves__beta) ).

thf(413,plain,
    ! [A: nat,B: dB,C: dB] :
      ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
     => ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( lift @ C @ A ) ) @ ( lift @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(81,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( aa @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ TB ) @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ TA @ ( fun @ TC @ TB ) ) @ ( combc @ TC @ TA @ TB ) @ C ) @ B ) @ A )
      = ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).

thf(391,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( aa @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ TB ) @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ TA @ ( fun @ TC @ TB ) ) @ ( combc @ TC @ TA @ TB ) @ C ) @ B ) @ A )
      = ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(59,axiom,
    ! [TA: $tType,A: TA,B: fun @ TA @ bool] :
      ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( fAll @ TA ) @ B ) )
      | ( pp @ ( aa @ TA @ bool @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fAll_1_1_U) ).

thf(313,plain,
    ! [TA: $tType,A: TA,B: fun @ TA @ bool] :
      ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( fAll @ TA ) @ B ) )
      | ( pp @ ( aa @ TA @ bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(116,axiom,
    ! [A: type,B: nat,C: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ C ) @ ( var @ B ) ) @ A ) )
     => ( ( aa @ nat @ type @ C @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_typing__elims_I1_J) ).

thf(498,plain,
    ! [A: type,B: nat,C: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ C ) @ ( var @ B ) ) @ A ) )
     => ( ( aa @ nat @ type @ C @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(109,axiom,
    ! [TA: $tType,A: list @ ( fun @ TA @ bool ),B: fun @ TA @ bool] :
      ( ( listset @ TA @ ( aa @ ( list @ ( fun @ TA @ bool ) ) @ ( list @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( list @ ( fun @ TA @ bool ) ) @ ( list @ ( fun @ TA @ bool ) ) ) @ ( cons @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
      = ( set_Cons @ TA @ B @ ( listset @ TA @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_listset_Osimps_I2_J) ).

thf(466,plain,
    ! [TA: $tType,A: list @ ( fun @ TA @ bool ),B: fun @ TA @ bool] :
      ( ( listset @ TA @ ( aa @ ( list @ ( fun @ TA @ bool ) ) @ ( list @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( list @ ( fun @ TA @ bool ) ) @ ( list @ ( fun @ TA @ bool ) ) ) @ ( cons @ ( fun @ TA @ bool ) ) @ B ) @ A ) )
      = ( set_Cons @ TA @ B @ ( listset @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(46,axiom,
    ! [A: type,B: nat,C: type,D: dB,E: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ E ) @ D ) @ C ) )
     => ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ E ) @ B ) @ A ) ) @ ( lift @ D @ B ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_lift__type) ).

thf(274,plain,
    ! [A: type,B: nat,C: type,D: dB,E: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ E ) @ D ) @ C ) )
     => ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ E ) @ B ) @ A ) ) @ ( lift @ D @ B ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(92,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
      | ( pp @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

thf(419,plain,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
      | ( pp @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(70,axiom,
    ! [A: type,B: list @ dB,C: dB,D: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
     => ~ ! [E: list @ type] :
            ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ C ) @ ( foldr @ type @ type @ fun1 @ E @ A ) ) )
           => ~ ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ B ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_list__app__typeE) ).

thf(362,plain,
    ! [A: type,B: list @ dB,C: dB,D: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
     => ~ ! [E: list @ type] :
            ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ C ) @ ( foldr @ type @ type @ fun1 @ E @ A ) ) )
           => ~ ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ D @ B ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(61,axiom,
    listsp @ dB @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ bool ) ) @ ( combs @ dB @ bool @ bool ) @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ dB ) @ fconj ) @ it ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ bool ) @ bool @ dB ) @ ( fAll @ ( fun @ nat @ type ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ bool ) @ bool ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( combb @ ( fun @ type @ bool ) @ bool @ ( fun @ nat @ type ) ) @ ( fAll @ type ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( combb @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ dB @ bool ) @ bool ) @ ( fun @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) ) @ ( combb @ ( fun @ dB @ bool ) @ bool @ type ) @ ( fAll @ dB ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ 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fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ dB ) @ ( combb @ bool @ bool @ nat ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ dB ) @ fimplies ) ) @ ( aa @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) ) @ ( combc @ ( fun @ nat @ type ) @ type @ ( fun @ dB @ bool ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ nat @ type ) ) @ ( combc @ dB @ type @ bool ) ) @ typing ) ) @ t ) ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) ) @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) ) @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( combb @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) @ dB ) @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) ) @ ( combb @ dB @ bool @ nat ) @ it ) ) ) @ subst ) ) ) ) ) ) ) ) ) @ rs,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Var_Ohyps) ).

thf(318,plain,
    listsp @ dB @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ bool ) ) @ ( combs @ dB @ bool @ bool ) @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ dB ) @ fconj ) @ it ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ bool ) @ bool @ dB ) @ ( fAll @ ( fun @ nat @ type ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ bool ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ bool ) @ bool ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ bool ) ) @ ( combb @ ( fun @ type @ bool ) @ bool @ ( fun @ nat @ type ) ) @ ( fAll @ type ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ bool ) ) ) @ ( combb @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ dB @ bool ) @ bool ) @ ( fun @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ type @ bool ) ) @ ( combb @ ( fun @ dB @ bool ) @ bool @ type ) @ ( fAll @ dB ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ bool ) @ type ) @ ( aa @ ( fun @ ( fun @ nat @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ nat @ bool ) @ bool @ dB ) @ ( fAll @ nat ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combs @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ dB ) @ ( combs @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ nat @ type ) ) @ ( combc @ type @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ type ) @ ( combb @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) @ dB ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ type ) @ ( combs @ nat @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ bool ) @ ( fun @ nat @ ( fun @ bool @ bool ) ) @ type ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ nat ) @ fimplies ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ type ) ) @ ( combc @ nat @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( combc @ ( fun @ nat @ type ) @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ dB @ ( fun @ nat @ ( fun @ type @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( combc @ nat @ dB @ ( fun @ type @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ nat @ type ) ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ nat @ type ) ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ ( fun @ nat @ type ) ) @ ( fun @ nat @ ( fun @ dB @ ( fun @ type @ bool ) ) ) ) @ ( combb @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ nat ) @ typing ) ) @ ( aa @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( combc @ ( fun @ nat @ type ) @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) ) ) @ ( combb @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( fun @ type @ ( fun @ nat @ ( fun @ nat @ type ) ) ) @ ( fun @ nat @ type ) ) @ ( combc @ nat @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) ) ) @ t ) ) ) ) ) ) ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( combs @ dB @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ ( aa @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ dB ) @ ( combb @ bool @ bool @ nat ) ) @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ dB ) @ fimplies ) @ it ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( combc @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( combs @ dB @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ dB @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) ) @ dB ) @ ( combb @ bool @ bool @ nat ) ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ dB @ bool ) @ ( fun @ dB @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ dB ) @ fimplies ) ) @ ( aa @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ type @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ bool ) ) ) @ ( combc @ ( fun @ nat @ type ) @ type @ ( fun @ dB @ bool ) ) @ ( aa @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) ) @ ( fun @ ( fun @ nat @ type ) @ ( fun @ type @ ( fun @ dB @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ type @ ( fun @ dB @ bool ) ) @ ( fun @ nat @ type ) ) @ ( combc @ dB @ type @ bool ) ) @ typing ) ) @ t ) ) ) ) ) ) @ ( aa @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) ) @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( fun @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) ) @ ( fun @ dB @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) ) @ ( combb @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) @ dB ) @ ( aa @ ( fun @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ ( fun @ dB @ ( fun @ nat @ bool ) ) ) @ ( combb @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) @ dB ) @ ( aa @ ( fun @ dB @ bool ) @ ( fun @ ( fun @ nat @ dB ) @ ( fun @ nat @ bool ) ) @ ( combb @ dB @ bool @ nat ) @ it ) ) ) @ subst ) ) ) ) ) ) ) ) ) @ rs,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(98,axiom,
    ! [A: nat,B: dB,C: dB,D: dB] :
      ( ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) ) @ B ) @ A )
      = ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ B ) @ A ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_subst__App) ).

thf(434,plain,
    ! [A: nat,B: dB,C: dB,D: dB] :
      ( ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) ) @ B ) @ A )
      = ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ B ) @ A ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(115,axiom,
    ! [A: dB] :
      ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
    <=> ( ? [B: list @ dB,C: nat] :
            ( ( A
              = ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) )
            & ( listsp @ dB @ it @ B ) )
        | ? [B: dB] :
            ( ( A
              = ( abs @ B ) )
            & ( pp @ ( aa @ dB @ bool @ it @ B ) ) )
        | ? [B: dB,C: dB,D: list @ dB] :
            ( ( A
              = ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ C ) @ D ) )
            & ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ B ) @ C ) @ ( zero_zero @ nat ) ) @ D ) ) )
            & ( pp @ ( aa @ dB @ bool @ it @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_IT_Osimps) ).

thf(477,plain,
    ! [A: dB] :
      ( ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
       => ( ? [B: list @ dB,C: nat] :
              ( ( A
                = ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) )
              & ( listsp @ dB @ it @ B ) )
          | ? [B: dB] :
              ( ( A
                = ( abs @ B ) )
              & ( pp @ ( aa @ dB @ bool @ it @ B ) ) )
          | ? [B: dB,C: dB,D: list @ dB] :
              ( ( A
                = ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ C ) @ D ) )
              & ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ B ) @ C ) @ ( zero_zero @ nat ) ) @ D ) ) )
              & ( pp @ ( aa @ dB @ bool @ it @ C ) ) ) ) )
      & ( ( ? [B: list @ dB,C: nat] :
              ( ( A
                = ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) )
              & ( listsp @ dB @ it @ B ) )
          | ? [B: dB] :
              ( ( A
                = ( abs @ B ) )
              & ( pp @ ( aa @ dB @ bool @ it @ B ) ) )
          | ? [B: dB,C: dB,D: list @ dB] :
              ( ( A
                = ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ C ) @ D ) )
              & ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ B ) @ C ) @ ( zero_zero @ nat ) ) @ D ) ) )
              & ( pp @ ( aa @ dB @ bool @ it @ C ) ) ) )
       => ( pp @ ( aa @ dB @ bool @ it @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(80,axiom,
    ! [A: type,B: list @ type,C: type,D: list @ dB,E: list @ dB,F: nat,G: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ G ) @ ( foldl @ dB @ dB @ app @ ( foldl @ dB @ dB @ app @ ( var @ F ) @ E ) @ D ) ) @ C ) )
     => ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ G @ E ) @ B ) )
       => ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ G ) @ ( foldl @ dB @ dB @ app @ ( var @ F ) @ E ) ) @ A ) )
         => ? [H: list @ type] :
              ( ( A
                = ( foldr @ type @ type @ fun1 @ H @ C ) )
              & ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ G @ D ) @ H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_var__app__types) ).

thf(387,plain,
    ! [A: type,B: list @ type,C: type,D: list @ dB,E: list @ dB,F: nat,G: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ G ) @ ( foldl @ dB @ dB @ app @ ( foldl @ dB @ dB @ app @ ( var @ F ) @ E ) @ D ) ) @ C ) )
     => ( ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ G @ E ) @ B ) )
       => ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ G ) @ ( foldl @ dB @ dB @ app @ ( var @ F ) @ E ) ) @ A ) )
         => ? [H: list @ type] :
              ( ( A
                = ( foldr @ type @ type @ fun1 @ H @ C ) )
              & ( pp @ ( aa @ ( list @ type ) @ bool @ ( typings @ G @ D ) @ H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(63,axiom,
    ! [A: list @ dB,B: dB,C: list @ dB,D: dB] :
      ( ( ( foldl @ dB @ dB @ app @ ( abs @ D ) @ C )
        = ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) )
    <=> ( ( D = B )
        & ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_Abs__apps__eq__Abs__apps__conv) ).

thf(323,plain,
    ! [A: list @ dB,B: dB,C: list @ dB,D: dB] :
      ( ( ( ( foldl @ dB @ dB @ app @ ( abs @ D ) @ C )
          = ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) )
       => ( ( D = B )
          & ( C = A ) ) )
      & ( ( ( D = B )
          & ( C = A ) )
       => ( ( foldl @ dB @ dB @ app @ ( abs @ D ) @ C )
          = ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(23,axiom,
    pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) @ a ) @ t2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_argT) ).

thf(198,plain,
    pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) @ a ) @ t2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(107,axiom,
    ( rs
    = ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ a ) @ as ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Cons) ).

thf(462,plain,
    ( rs
    = ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ a ) @ as ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(105,axiom,
    ! [A: list @ dB,B: nat,C: dB,D: dB] :
      ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ D ) ) @ C )
     != ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Abs__App__neq__Var__apps) ).

thf(455,plain,
    ! [A: list @ dB,B: nat,C: dB,D: dB] :
      ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ D ) ) @ C )
     != ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(28,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
      | ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).

thf(223,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
      | ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(82,axiom,
    ! [A: dB,B: dB] :
      ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ A ) )
     => ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( abs @ B ) ) @ ( abs @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_abs) ).

thf(394,plain,
    ! [A: dB,B: dB] :
      ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ A ) )
     => ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( abs @ B ) ) @ ( abs @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(29,axiom,
    zero @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).

thf(226,plain,
    zero @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(43,axiom,
    ! [A: dB,B: type,C: type,D: dB,E: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ E ) @ D ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ C ) @ B ) ) )
     => ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ E ) @ A ) @ C ) )
       => ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ E ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ A ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_App) ).

thf(267,plain,
    ! [A: dB,B: type,C: type,D: dB,E: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ E ) @ D ) @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ C ) @ B ) ) )
     => ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ E ) @ A ) @ C ) )
       => ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ E ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ A ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(119,axiom,
    ! [A: nat] : ( pp @ ( aa @ dB @ bool @ it @ ( var @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_Var__IT) ).

thf(505,plain,
    ! [A: nat] : ( pp @ ( aa @ dB @ bool @ it @ ( var @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(24,axiom,
    pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) @ ( foldl @ dB @ dB @ app @ ( var @ n ) @ rs ) ) @ t1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_nT) ).

thf(199,plain,
    pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) @ ( foldl @ dB @ dB @ app @ ( var @ n ) @ rs ) ) @ t1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(118,axiom,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A )
     != A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_not__Cons__self2) ).

thf(502,plain,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(66,axiom,
    ! [A: dB,B: dB,C: dB,D: dB] :
      ( ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
        = ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
    <=> ( ( D = B )
        & ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_dB_Osimps_I2_J) ).

thf(338,plain,
    ! [A: dB,B: dB,C: dB,D: dB] :
      ( ( ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
          = ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
       => ( ( D = B )
          & ( C = A ) ) )
      & ( ( ( D = B )
          & ( C = A ) )
       => ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
          = ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(111,axiom,
    pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( var @ n ) ) @ a ) @ as ) ) @ t1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41__096e_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_092_060degree_062_092_060degree_062_Aas_A_058_AT_H_096) ).

thf(470,plain,
    pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( var @ n ) ) @ a ) @ as ) ) @ t1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(31,axiom,
    ! [A: bool,B: bool] :
      ( ( pp @ B )
      | ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).

thf(231,plain,
    ! [A: bool,B: bool] :
      ( ( pp @ B )
      | ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(103,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
      ( ! [C: TA] :
          ( ( aa @ TA @ TB @ B @ C )
          = ( aa @ TA @ TB @ A @ C ) )
     => ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).

thf(450,plain,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
      ( ! [C: TA] :
          ( ( aa @ TA @ TB @ B @ C )
          = ( aa @ TA @ TB @ A @ C ) )
     => ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(62,axiom,
    ! [TA: $tType,A: TA,B: fun @ nat @ TA,C: nat,D: nat] :
      ( ( D = C )
     => ( ( aa @ nat @ TA @ ( aa @ TA @ ( fun @ nat @ TA ) @ ( aa @ nat @ ( fun @ TA @ ( fun @ nat @ TA ) ) @ ( aa @ ( fun @ nat @ TA ) @ ( fun @ nat @ ( fun @ TA @ ( fun @ nat @ TA ) ) ) @ ( shift @ TA ) @ B ) @ D ) @ A ) @ C )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_shift__eq) ).

thf(319,plain,
    ! [TA: $tType,A: TA,B: fun @ nat @ TA,C: nat,D: nat] :
      ( ( D = C )
     => ( ( aa @ nat @ TA @ ( aa @ TA @ ( fun @ nat @ TA ) @ ( aa @ nat @ ( fun @ TA @ ( fun @ nat @ TA ) ) @ ( aa @ ( fun @ nat @ TA ) @ ( fun @ nat @ ( fun @ TA @ ( fun @ nat @ TA ) ) ) @ ( shift @ TA ) @ B ) @ D ) @ A ) @ C )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(14,axiom,
    ! [A: nat] :
      ( ( size_size @ dB @ ( var @ A ) )
      = ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_dB_Osize_I4_J) ).

thf(171,plain,
    ! [A: nat] :
      ( ( size_size @ dB @ ( var @ A ) )
      = ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(6,axiom,
    ! [A: nat,B: dB] :
      ( ( abs @ B )
     != ( var @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_dB_Osimps_I7_J) ).

thf(139,plain,
    ! [A: nat,B: dB] :
      ( ( abs @ B )
     != ( var @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(27,axiom,
    ! [A: dB,B: list @ dB,C: dB] :
      ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
     => ( ! [D: dB] :
            ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) )
           => ( A
             != ( foldl @ dB @ dB @ app @ D @ B ) ) )
       => ( ! [D: list @ dB] :
              ( ( step1 @ dB @ beta @ B @ D )
             => ( A
               != ( foldl @ dB @ dB @ app @ C @ D ) ) )
         => ~ ! [D: dB] :
                ( ( C
                  = ( abs @ D ) )
               => ! [E: dB,F: list @ dB] :
                    ( ( B
                      = ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ E ) @ F ) )
                   => ( A
                     != ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ E ) @ ( zero_zero @ nat ) ) @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_apps__betasE) ).

thf(207,plain,
    ! [A: dB,B: list @ dB,C: dB] :
      ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
     => ( ! [D: dB] :
            ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) )
           => ( A
             != ( foldl @ dB @ dB @ app @ D @ B ) ) )
       => ( ! [D: list @ dB] :
              ( ( step1 @ dB @ beta @ B @ D )
             => ( A
               != ( foldl @ dB @ dB @ app @ C @ D ) ) )
         => ~ ! [D: dB] :
                ( ( C
                  = ( abs @ D ) )
               => ! [E: dB,F: list @ dB] :
                    ( ( B
                      = ( aa @ ( list @ dB ) @ ( list @ dB ) @ ( aa @ dB @ ( fun @ ( list @ dB ) @ ( list @ dB ) ) @ ( cons @ dB ) @ E ) @ F ) )
                   => ( A
                     != ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ D ) @ E ) @ ( zero_zero @ nat ) ) @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(52,axiom,
    ! [TA: $tType,A: fun @ ( list @ TA ) @ bool,B: fun @ TA @ bool] :
      ( ( set_Cons @ TA @ B @ A )
      = ( collect @ ( list @ TA ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( list @ TA ) @ bool ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ ( list @ TA ) ) @ ( fEx @ TA ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ bool ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ bool ) @ ( list @ TA ) ) @ ( aa @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ bool ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( combb @ ( fun @ ( list @ TA ) @ bool ) @ bool @ TA ) @ ( fEx @ ( list @ TA ) ) ) ) @ ( aa @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( combc @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( list @ TA ) ) @ ( combs @ TA @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( list @ TA ) ) @ ( aa @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) @ TA ) @ ( combs @ ( list @ TA ) @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( list @ TA ) ) @ ( aa @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) @ TA ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ ( list @ TA ) ) @ fconj ) ) ) @ ( aa @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( combc @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( list @ TA ) ) @ ( combb @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) @ TA ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( list @ TA ) ) @ ( combb @ ( list @ TA ) @ bool @ ( list @ TA ) ) ) @ ( fequal @ ( list @ TA ) ) ) ) ) @ ( cons @ TA ) ) ) ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( combc @ TA @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) @ TA ) @ ( combb @ bool @ bool @ ( list @ TA ) ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) ) @ B ) ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( combc @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ bool ) @ ( member @ ( list @ TA ) ) ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_set__Cons__def) ).

thf(287,plain,
    ! [TA: $tType,A: fun @ ( list @ TA ) @ bool,B: fun @ TA @ bool] :
      ( ( set_Cons @ TA @ B @ A )
      = ( collect @ ( list @ TA ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( list @ TA ) @ bool ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ ( list @ TA ) ) @ ( fEx @ TA ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ bool ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ bool ) @ ( list @ TA ) ) @ ( aa @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ bool ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( combb @ ( fun @ ( list @ TA ) @ bool ) @ bool @ TA ) @ ( fEx @ ( list @ TA ) ) ) ) @ ( aa @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( combc @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( list @ TA ) ) @ ( combs @ TA @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( list @ TA ) ) @ ( aa @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) @ TA ) @ ( combs @ ( list @ TA ) @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( list @ TA ) ) @ ( aa @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) @ TA ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ ( list @ TA ) ) @ fconj ) ) ) @ ( aa @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( combc @ ( list @ TA ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( list @ TA ) ) @ ( combb @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) @ TA ) ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( list @ TA ) ) @ ( combb @ ( list @ TA ) @ bool @ ( list @ TA ) ) ) @ ( fequal @ ( list @ TA ) ) ) ) ) @ ( cons @ TA ) ) ) ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ TA @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( combc @ TA @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) ) ) @ ( combb @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) @ TA ) @ ( combb @ bool @ bool @ ( list @ TA ) ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) ) @ B ) ) ) ) @ ( aa @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) @ ( aa @ ( fun @ ( list @ TA ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( list @ TA ) @ bool ) @ ( fun @ ( list @ TA ) @ bool ) ) @ ( combc @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ bool ) @ bool ) @ ( member @ ( list @ TA ) ) ) @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(53,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ B )
      | ~ ( pp @ A )
      | ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

thf(290,plain,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ B )
      | ~ ( pp @ A )
      | ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(76,axiom,
    listsp @ dB @ ( aa @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ ( fun @ type @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ type @ bool ) @ bool @ dB ) @ ( fEx @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) ) @ as,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__096listsp_A_I_Ft_O_AEX_AT_H_O_Ae_060i_058T_062_A_092_060turnstile_062_At_A_058_AT_H_J_Aas_096) ).

thf(378,plain,
    listsp @ dB @ ( aa @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) @ ( aa @ ( fun @ ( fun @ type @ bool ) @ bool ) @ ( fun @ ( fun @ dB @ ( fun @ type @ bool ) ) @ ( fun @ dB @ bool ) ) @ ( combb @ ( fun @ type @ bool ) @ bool @ dB ) @ ( fEx @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ e ) @ i ) @ t ) ) ) @ as,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(33,axiom,
    ! [A: type,B: type,C: type,D: type] :
      ( ( ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ D ) @ C )
        = ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ B ) @ A ) )
    <=> ( ( D = B )
        & ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_type_Osimps_I2_J) ).

thf(235,plain,
    ! [A: type,B: type,C: type,D: type] :
      ( ( ( ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ D ) @ C )
          = ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ B ) @ A ) )
       => ( ( D = B )
          & ( C = A ) ) )
      & ( ( ( D = B )
          & ( C = A ) )
       => ( ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ D ) @ C )
          = ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(35,axiom,
    pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( lift @ u @ ( zero_zero @ nat ) ) ) @ ( var @ ( zero_zero @ nat ) ) ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ a ) @ u ) @ i ) ) @ ( zero_zero @ nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096) ).

thf(246,plain,
    pp @ ( aa @ dB @ bool @ it @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( lift @ u @ ( zero_zero @ nat ) ) ) @ ( var @ ( zero_zero @ nat ) ) ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ a ) @ u ) @ i ) ) @ ( zero_zero @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(102,axiom,
    ! [A: dB,B: nat] :
      ( ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( var @ B ) ) @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_subst__eq) ).

thf(447,plain,
    ! [A: dB,B: nat] :
      ( ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ ( var @ B ) ) @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(60,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
      ( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combs @ TA @ TB @ TC ) @ C ) @ B ) @ A )
      = ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).

thf(315,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
      ( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combs @ TA @ TB @ TC ) @ C ) @ B ) @ A )
      = ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(87,axiom,
    ! [TA: $tType,A: type,B: type,C: fun @ type @ ( fun @ type @ TA ),D: fun @ nat @ TA] :
      ( ( type_case @ TA @ D @ C @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ B ) @ A ) )
      = ( aa @ type @ TA @ ( aa @ type @ ( fun @ type @ TA ) @ C @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_type_Osimps_I6_J) ).

thf(405,plain,
    ! [TA: $tType,A: type,B: type,C: fun @ type @ ( fun @ type @ TA ),D: fun @ nat @ TA] :
      ( ( type_case @ TA @ D @ C @ ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ B ) @ A ) )
      = ( aa @ type @ TA @ ( aa @ type @ ( fun @ type @ TA ) @ C @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(20,axiom,
    ! [A: nat,B: list @ dB] :
      ( ( listsp @ dB @ it @ B )
     => ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( var @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_IT_OVar) ).

thf(190,plain,
    ! [A: nat,B: list @ dB] :
      ( ( listsp @ dB @ it @ B )
     => ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( var @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(17,axiom,
    pp @ ( aa @ dB @ bool @ it @ ua ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_Var_I3_J) ).

thf(183,plain,
    pp @ ( aa @ dB @ bool @ it @ ua ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(93,axiom,
    ! [A: nat,B: dB] :
      ( ( pp @ ( aa @ dB @ bool @ it @ B ) )
     => ( pp @ ( aa @ dB @ bool @ it @ ( lift @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_lift__IT) ).

thf(422,plain,
    ! [A: nat,B: dB] :
      ( ( pp @ ( aa @ dB @ bool @ it @ B ) )
     => ( pp @ ( aa @ dB @ bool @ it @ ( lift @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(74,axiom,
    n = i,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_True) ).

thf(373,plain,
    n = i,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(5,axiom,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( collect @ TA @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Collect__def) ).

thf(136,plain,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( collect @ TA @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(69,axiom,
    ! [A: dB,B: dB] :
      ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( abs @ B ) ) @ A ) )
     => ~ ! [C: dB] :
            ( ( A
              = ( abs @ C ) )
           => ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_beta__cases_I2_J) ).

thf(358,plain,
    ! [A: dB,B: dB] :
      ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( abs @ B ) ) @ A ) )
     => ~ ! [C: dB] :
            ( ( A
              = ( abs @ C ) )
           => ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(22,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: list @ TB,C: TB,D: fun @ TB @ ( fun @ TA @ TA )] :
      ( ( foldr @ TB @ TA @ D @ ( aa @ ( list @ TB ) @ ( list @ TB ) @ ( aa @ TB @ ( fun @ ( list @ TB ) @ ( list @ TB ) ) @ ( cons @ TB ) @ C ) @ B ) @ A )
      = ( aa @ TA @ TA @ ( aa @ TB @ ( fun @ TA @ TA ) @ D @ C ) @ ( foldr @ TB @ TA @ D @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_foldr_Osimps_I2_J) ).

thf(195,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: list @ TB,C: TB,D: fun @ TB @ ( fun @ TA @ TA )] :
      ( ( foldr @ TB @ TA @ D @ ( aa @ ( list @ TB ) @ ( list @ TB ) @ ( aa @ TB @ ( fun @ ( list @ TB ) @ ( list @ TB ) ) @ ( cons @ TB ) @ C ) @ B ) @ A )
      = ( aa @ TA @ TA @ ( aa @ TB @ ( fun @ TA @ TA ) @ D @ C ) @ ( foldr @ TB @ TA @ D @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(99,axiom,
    ! [TA: $tType,A: TA,B: fun @ TA @ bool] :
      ( ~ ( pp @ ( aa @ TA @ bool @ B @ A ) )
      | ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( fEx @ TA ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fEx_1_1_U) ).

thf(437,plain,
    ! [TA: $tType,A: TA,B: fun @ TA @ bool] :
      ( ~ ( pp @ ( aa @ TA @ bool @ B @ A ) )
      | ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( fEx @ TA ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(113,axiom,
    ! [A: list @ dB,B: dB,C: dB] :
      ( ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ B ) @ ( zero_zero @ nat ) ) @ A ) ) )
     => ( ( pp @ ( aa @ dB @ bool @ it @ B ) )
       => ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ C ) ) @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_Beta) ).

thf(474,plain,
    ! [A: list @ dB,B: dB,C: dB] :
      ( ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ C ) @ B ) @ ( zero_zero @ nat ) ) @ A ) ) )
     => ( ( pp @ ( aa @ dB @ bool @ it @ B ) )
       => ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ C ) ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(85,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
      | ( pp @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

thf(400,plain,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
      | ( pp @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(50,axiom,
    ! [A: dB,B: dB,C: dB] :
      ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
     => ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ C ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_appR) ).

thf(283,plain,
    ! [A: dB,B: dB,C: dB] :
      ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
     => ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ C ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(91,axiom,
    ! [A: type,B: dB,C: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ C ) @ ( abs @ B ) ) @ A ) )
     => ~ ! [D: type,E: type] :
            ( ( A
              = ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ D ) @ E ) )
           => ~ ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ C ) @ ( zero_zero @ nat ) ) @ D ) ) @ B ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_typing__elims_I3_J) ).

thf(415,plain,
    ! [A: type,B: dB,C: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ C ) @ ( abs @ B ) ) @ A ) )
     => ~ ! [D: type,E: type] :
            ( ( A
              = ( aa @ type @ type @ ( aa @ type @ ( fun @ type @ type ) @ fun1 @ D ) @ E ) )
           => ~ ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ C ) @ ( zero_zero @ nat ) ) @ D ) ) @ B ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(108,axiom,
    ! [A: dB,B: dB] : ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ A ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ B ) @ A ) @ ( zero_zero @ nat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_beta) ).

thf(464,plain,
    ! [A: dB,B: dB] : ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ A ) ) @ ( aa @ nat @ dB @ ( aa @ dB @ ( fun @ nat @ dB ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ nat @ dB ) ) @ subst @ B ) @ A ) @ ( zero_zero @ nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(64,axiom,
    ! [A: list @ dB,B: dB,C: dB] :
      ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
     => ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ C @ A ) ) @ ( foldl @ dB @ dB @ app @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_apps__preserves__beta) ).

thf(332,plain,
    ! [A: list @ dB,B: dB,C: dB] :
      ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
     => ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ C @ A ) ) @ ( foldl @ dB @ dB @ app @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(95,axiom,
    ! [A: nat,B: dB] :
      ( ( pp @ ( aa @ dB @ bool @ it @ B ) )
     => ( pp @ ( aa @ dB @ bool @ it @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ ( var @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_app__Var__IT) ).

thf(427,plain,
    ! [A: nat,B: dB] :
      ( ( pp @ ( aa @ dB @ bool @ it @ B ) )
     => ( pp @ ( aa @ dB @ bool @ it @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ ( var @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(106,axiom,
    ! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ TB ),D: TB] :
      ( ( list_case @ TB @ TA @ D @ C @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
      = ( aa @ ( list @ TA ) @ TB @ ( aa @ TA @ ( fun @ ( list @ TA ) @ TB ) @ C @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_list_Osimps_I5_J) ).

thf(459,plain,
    ! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ TB ),D: TB] :
      ( ( list_case @ TB @ TA @ D @ C @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
      = ( aa @ ( list @ TA ) @ TB @ ( aa @ TA @ ( fun @ ( list @ TA ) @ TB ) @ C @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(48,axiom,
    ! [A: dB,B: type,C: dB,D: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ C ) @ B ) )
     => ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ A ) )
       => ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_subject__reduction) ).

thf(277,plain,
    ! [A: dB,B: type,C: dB,D: fun @ nat @ type] :
      ( ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ C ) @ B ) )
     => ( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ A ) )
       => ( pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ D ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(117,axiom,
    pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ ea ) @ ia ) @ t ) ) @ ( foldl @ dB @ dB @ app @ ( var @ n ) @ rs ) ) @ t_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_Var_I2_J) ).

thf(501,plain,
    pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ ( aa @ type @ ( fun @ nat @ type ) @ ( aa @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ nat @ ( fun @ type @ ( fun @ nat @ type ) ) ) @ ( shift @ type ) @ ea ) @ ia ) @ t ) ) @ ( foldl @ dB @ dB @ app @ ( var @ n ) @ rs ) ) @ t_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(73,axiom,
    ! [A: nat,B: dB,C: dB] :
      ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
     != ( var @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_dB_Osimps_I5_J) ).

thf(369,plain,
    ! [A: nat,B: dB,C: dB] :
      ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
     != ( var @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(13,axiom,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
      ( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ D ) @ C )
        = ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
    <=> ( ( D = B )
        & ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_list_Oinject) ).

thf(163,plain,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
      ( ( ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ D ) @ C )
          = ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) )
       => ( ( D = B )
          & ( C = A ) ) )
      & ( ( ( D = B )
          & ( C = A ) )
       => ( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ D ) @ C )
          = ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( cons @ TA ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(25,axiom,
    ! [A: dB,B: dB,C: dB] :
      ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
     != ( abs @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_dB_Osimps_I8_J) ).

thf(200,plain,
    ! [A: dB,B: dB,C: dB] :
      ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
     != ( abs @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(30,axiom,
    ! [A: dB,B: dB,C: nat] :
      ( ( var @ C )
     != ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_dB_Osimps_I4_J) ).

thf(227,plain,
    ! [A: dB,B: dB,C: nat] :
      ( ( var @ C )
     != ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(110,axiom,
    pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ e ) @ u ) @ t ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_uT) ).

thf(469,plain,
    pp @ ( aa @ type @ bool @ ( aa @ dB @ ( fun @ type @ bool ) @ ( aa @ ( fun @ nat @ type ) @ ( fun @ dB @ ( fun @ type @ bool ) ) @ typing @ e ) @ u ) @ t ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(507,plain,
    $false,
    inference(e,[status(thm)],[384,184,188,150,143,365,347,249,408,276,379,269,120,247,174,301,152,261,179,443,121,147,293,453,396,292,233,439,270,381,366,334,160,424,192,429,260,349,252,285,471,476,128,244,398,298,412,430,264,161,279,296,375,402,204,259,413,391,313,498,466,274,419,362,318,434,477,387,323,198,462,455,223,394,226,267,505,199,502,338,470,231,450,319,171,139,207,287,290,378,235,246,447,315,405,190,183,422,373,136,358,195,437,474,400,283,415,464,332,427,459,277,501,369,163,200,227,469]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : LCL803_5 : TPTP v8.1.2. Released v6.0.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n023.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu May 18 16:11:30 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.86/0.80  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.80/1.03  % [INFO] 	 Parsing done (227ms). 
% 1.80/1.04  % [INFO] 	 Running in sequential loop mode. 
% 2.34/1.24  % [INFO] 	 eprover registered as external prover. 
% 2.34/1.25  % [INFO] 	 cvc4 registered as external prover. 
% 2.34/1.25  % [INFO] 	 Scanning for conjecture ... 
% 3.40/1.50  % [INFO] 	 Found a conjecture and 117 axioms. Running axiom selection ... 
% 3.86/1.63  % [INFO] 	 Axiom selection finished. Selected 117 axioms (removed 0 axioms). 
% 4.59/1.80  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 4.59/1.82  % [INFO] 	 Type checking passed. 
% 4.59/1.82  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 5.68/2.10  % [INFO] 	 [Domain constraints] Detected constraint on bool 
% 5.68/2.10  % [INFO] 	 [Domain constraints] dom(bool) ⊆ {fTrue,fFalse} 
% 48.26/28.15  % External prover 'e' found a proof!
% 48.26/28.15  % [INFO] 	 Killing All external provers ... 
% 48.26/28.15  % Time passed: 27617ms (effective reasoning time: 27105ms)
% 48.26/28.15  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 48.26/28.15  % Axioms used in derivation (117): fact_98_apps__preserves__betas, fact_75_mem__def, fact_94_beta__cases_I3_J, fact_78_Var__apps__neq__Abs__apps, help_fimplies_2_1_U, fact_49_var__app__type__eq, fact_8_Var_Ohyps, help_COMBS_1_1_U, fact_88_abs, help_fconj_3_1_U, fact_83_IT_Osimps, fact_65_Beta, fact_14_subst__lemma, fact_82_listset_Osimps_I2_J, fact_85_appR, fact_18_lift__type, fact_79_Abs__App__neq__Var__apps, fact_71_dB_Osimps_I7_J, fact_73_dB_Osimps_I9_J, fact_16_lists__typings, fact_2_uIT, fact_50_dB_Osimps_I5_J, fact_93_apps__preserves__beta, fact_70_Abs, fact_15_shift__eq, fact_5_Var_I4_J, fact_53_subst__lift, fact_0__096IT_At_096, fact_55_var__app__types, help_fFalse_1_1_T, fact_74_ext, fact_21_type_Osimps_I2_J, fact_19__096IT_A_Iu_A_092_060degree_062_Aa_091u_Pi_093_J_096, fact_37_dB_Osimps_I1_J, fact_84_beta, fact_64_dB_Osize_I1_J, fact_48_list__app__typeI, fact_17_subst__Var__IT, fact_41__096e_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_092_060degree_062_092_060degree_062_Aas_A_058_AT_H_096, fact_58_list__app__typeE, help_COMBB_1_1_U, fact_3_True, fact_10_argsT, fact_62_zero__reorient, fact_63_list_Osimps_I5_J, fact_44_not__Cons__self, fact_25_Cons, help_fconj_2_1_U, help_fAll_1_1_U, fact_89_lift__preserves__beta, fact_47_foldr_Osimps_I2_J, fact_76_Collect__def, fact_38_subst__App, fact_20_lift__IT, fact_35_list_Oinject, fact_57_Var__apps__eq__Var__apps__conv, fact_6__096listsp_A_I_Ft_O_AALL_Ae_AT_H_Au_Ai_O_Ae_060i_058T_062_A_092_060turnstile_062_At_A_058_AT_H_A_N_N_062_AIT_Au_A_N_N_062_Ae_A_092_060turnstile_062_Au_A_058_AT_A_N_N_062_AIT_A_It_091u_Pi_093_J_J_Aas_096, fact_1_Var_I3_J, fact_29_varT, fact_13_listsp__conj__eq, fact_28_headT, fact_67_dB_Osimps_I3_J, fact_26_app__Var__IT, help_fequal_1_1_T, fact_11_MI1, arity_Nat_Onat___Groups_Ozero, fact_92_beta__cases_I2_J, fact_12_MI2, fact_81_abs__typeE, fact_80_typing__elims_I3_J, fact_60_list__app__typeD, fact_72_dB_Osimps_I6_J, fact_45_not__Cons__self2, help_COMBC_1_1_U, fact_24_App, fact_42__096_B_Bthesis_O_A_I_B_BT_H_H_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_058_AT_H_H_A_092_060Rightarrow_062_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_66_set__Cons__def, fact_77_dB_Osimps_I8_J, help_fequal_2_1_T, fact_56_var__app__typesE, fact_90_subst__preserves__beta, fact_36_dB_Osimps_I2_J, fact_23_typing_OVar, fact_32_Var_I2_J, help_fconj_1_1_U, fact_27_Var__IT, fact_54_IT_OVar, fact_30__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096, fact_69_Abs__apps__eq__Abs__apps__conv, fact_7_uT, help_fFalse_1_1_U, fact_86_appL, fact_96_apps__betasE, fact_22_typing__elims_I1_J, fact_46_foldl__Cons, fact_34_lift_Osimps_I2_J, help_pp_1_1_U, fact_33_nT, fact_51_dB_Osimps_I4_J, fact_59_apps__eq__tail__conv, fact_61_typings_Osimps_I2_J, fact_87_beta__cases_I1_J, fact_43__096_B_Bthesis_O_A_I_B_BTs_O_A_091_124_Ae_060i_058T_062_A_092_060turnstile_062_AVar_An_A_092_060degree_062_Aa_A_058_ATs_A_061_062_062_AT_H_059_Ae_060i_058T_062_A_124_124_N_Aas_A_058_ATs_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, help_fimplies_1_1_U, fact_95_dB_Osize_I4_J, help_fimplies_3_1_U, fact_4__096listsp_A_I_Ft_O_AEX_AT_H_O_Ae_060i_058T_062_A_092_060turnstile_062_At_A_058_AT_H_J_Aas_096, help_pp_2_1_U, fact_68_Lambda, fact_39_T, fact_40_uT_H, fact_31_typing__elims_I2_J, help_fEx_1_1_U, fact_91_subject__reduction, fact_97_type_Osimps_I6_J, fact_52_subst__eq, fact_9_argT
% 48.26/28.15  % No. of inferences in proof: 238
% 48.26/28.15  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 27617 ms resp. 27105 ms w/o parsing
% 48.86/28.32  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 48.86/28.32  % [INFO] 	 Killing All external provers ... 
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