TSTP Solution File: LCL806_5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL806_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n002.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 : Sun May  5 07:53:32 EDT 2024

% Result   : Theorem 1.31s 0.60s
% Output   : Refutation 1.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :  400
% Syntax   : Number of formulae    :  980 ( 296 unt;  90 typ;   0 def)
%            Number of atoms       : 2133 ( 553 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 1979 ( 736   ~; 725   |; 179   &)
%                                         ( 212 <=>; 127  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :   28 (   2 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :   86 (  39   >;  47   *;   0   +;   0  <<)
%            Number of predicates  :  189 ( 187 usr; 182 prp; 0-3 aty)
%            Number of functors    :   80 (  80 usr;  35 con; 0-6 aty)
%            Number of variables   : 2056 (1913   !; 101   ?;2056   :)
%                                         (  42  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    bool: $tType ).

tff(type_def_6,type,
    dB: $tType ).

tff(type_def_7,type,
    list: $tType > $tType ).

tff(type_def_8,type,
    nat: $tType ).

tff(type_def_9,type,
    type: $tType ).

tff(type_def_10,type,
    fun: ( $tType * $tType ) > $tType ).

tff(func_def_0,type,
    combb: 
      !>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))) ).

tff(func_def_1,type,
    combc: 
      !>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2))) ).

tff(func_def_2,type,
    combi: 
      !>[X0: $tType] : fun(X0,X0) ).

tff(func_def_3,type,
    combs: 
      !>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))) ).

tff(func_def_4,type,
    zero_zero: 
      !>[X0: $tType] : X0 ).

tff(func_def_5,type,
    it: fun(dB,bool) ).

tff(func_def_6,type,
    abs: dB > dB ).

tff(func_def_7,type,
    app: fun(dB,fun(dB,dB)) ).

tff(func_def_8,type,
    var: nat > dB ).

tff(func_def_9,type,
    dB_size: dB > nat ).

tff(func_def_10,type,
    lift: fun(dB,fun(nat,dB)) ).

tff(func_def_11,type,
    subst: fun(dB,fun(dB,fun(nat,dB))) ).

tff(func_def_12,type,
    foldl: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).

tff(func_def_13,type,
    foldr: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * list(X0) * X1 ) > X1 ) ).

tff(func_def_14,type,
    cons: 
      !>[X0: $tType] : fun(X0,fun(list(X0),list(X0))) ).

tff(func_def_15,type,
    list_case: 
      !>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).

tff(func_def_16,type,
    listset: 
      !>[X0: $tType] : ( list(fun(X0,bool)) > fun(list(X0),bool) ) ).

tff(func_def_17,type,
    map: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).

tff(func_def_18,type,
    set_Cons: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(list(X0),bool) ) > fun(list(X0),bool) ) ).

tff(func_def_19,type,
    collect: 
      !>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).

tff(func_def_20,type,
    shift: 
      !>[X0: $tType] : fun(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0)))) ).

tff(func_def_21,type,
    fun1: fun(type,fun(type,type)) ).

tff(func_def_22,type,
    typing: fun(fun(nat,type),fun(dB,fun(type,bool))) ).

tff(func_def_23,type,
    typings: ( fun(nat,type) * list(dB) ) > fun(list(type),bool) ).

tff(func_def_24,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_25,type,
    fAll: 
      !>[X0: $tType] : fun(fun(X0,bool),bool) ).

tff(func_def_26,type,
    fEx: 
      !>[X0: $tType] : fun(fun(X0,bool),bool) ).

tff(func_def_27,type,
    fFalse: bool ).

tff(func_def_28,type,
    fTrue: bool ).

tff(func_def_29,type,
    fconj: fun(bool,fun(bool,bool)) ).

tff(func_def_30,type,
    fequal: 
      !>[X0: $tType] : fun(X0,fun(X0,bool)) ).

tff(func_def_31,type,
    fimplies: fun(bool,fun(bool,bool)) ).

tff(func_def_32,type,
    member: 
      !>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).

tff(func_def_33,type,
    t2: type ).

tff(func_def_34,type,
    t1: type ).

tff(func_def_35,type,
    t_a: type ).

tff(func_def_36,type,
    t: type ).

tff(func_def_37,type,
    ts: list(type) ).

tff(func_def_38,type,
    a: dB ).

tff(func_def_39,type,
    as: list(dB) ).

tff(func_def_40,type,
    b: dB ).

tff(func_def_41,type,
    bs: list(dB) ).

tff(func_def_42,type,
    e: fun(nat,type) ).

tff(func_def_43,type,
    ea: fun(nat,type) ).

tff(func_def_44,type,
    i: nat ).

tff(func_def_45,type,
    ia: nat ).

tff(func_def_46,type,
    n: nat ).

tff(func_def_47,type,
    rs: list(dB) ).

tff(func_def_48,type,
    t3: dB ).

tff(func_def_49,type,
    u: dB ).

tff(func_def_50,type,
    ua: dB ).

tff(func_def_51,type,
    sK2: fun(nat,type) ).

tff(func_def_52,type,
    sK3: type ).

tff(func_def_53,type,
    sK4: dB ).

tff(func_def_54,type,
    sK5: nat ).

tff(func_def_55,type,
    sK6: type ).

tff(func_def_56,type,
    sK7: type ).

tff(func_def_57,type,
    sK8: list(type) ).

tff(func_def_58,type,
    sK9: dB > dB ).

tff(func_def_59,type,
    sK10: dB > list(dB) ).

tff(func_def_60,type,
    sK11: dB > nat ).

tff(func_def_61,type,
    sK12: dB > dB ).

tff(func_def_62,type,
    sK13: dB > dB ).

tff(func_def_63,type,
    sK14: dB > list(dB) ).

tff(func_def_64,type,
    sK15: ( dB * fun(nat,type) ) > type ).

tff(func_def_65,type,
    sK16: ( dB * fun(nat,type) ) > type ).

tff(func_def_66,type,
    sK17: ( type * dB * fun(nat,type) ) > type ).

tff(func_def_67,type,
    sK18: ( type * dB * fun(nat,type) ) > type ).

tff(func_def_68,type,
    sK19: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).

tff(func_def_69,type,
    sK20: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).

tff(func_def_70,type,
    sK21: ( type * list(dB) * nat * fun(nat,type) ) > list(type) ).

tff(func_def_71,type,
    sK22: ( type * dB * dB * fun(nat,type) ) > type ).

tff(func_def_72,type,
    sK23: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

tff(func_def_73,type,
    sK24: 
      !>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > X0 ) ).

tff(func_def_74,type,
    sK25: 
      !>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > list(X0) ) ).

tff(func_def_75,type,
    sK26: 
      !>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > X1 ) ).

tff(func_def_76,type,
    sK27: 
      !>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > list(X1) ) ).

tff(func_def_77,type,
    sK28: ( type * type * list(dB) * fun(nat,type) ) > list(type) ).

tff(pred_def_1,type,
    zero: 
      !>[X0: $tType] : $o ).

tff(pred_def_2,type,
    beta: ( dB * dB ) > $o ).

tff(pred_def_3,type,
    listsp: 
      !>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).

tff(pred_def_4,type,
    pp: bool > $o ).

tff(pred_def_5,type,
    sP0: dB > $o ).

tff(pred_def_6,type,
    sP1: dB > $o ).

tff(f2575,plain,
    $false,
    inference(avatar_sat_refutation,[],[f529,f534,f539,f544,f548,f552,f557,f562,f567,f572,f577,f581,f585,f598,f602,f607,f611,f615,f619,f624,f628,f644,f648,f652,f659,f671,f676,f681,f685,f693,f697,f701,f705,f709,f713,f717,f724,f730,f734,f738,f758,f762,f766,f770,f774,f778,f807,f811,f815,f822,f826,f831,f835,f839,f846,f850,f858,f863,f868,f872,f876,f880,f897,f901,f905,f909,f921,f925,f936,f940,f944,f948,f960,f967,f973,f977,f988,f992,f996,f1008,f1012,f1029,f1034,f1038,f1042,f1046,f1058,f1062,f1066,f1078,f1082,f1086,f1090,f1094,f1098,f1179,f1183,f1187,f1195,f1201,f1206,f1210,f1215,f1354,f1359,f1364,f1374,f1389,f1393,f1397,f1421,f1426,f1431,f1449,f1453,f1457,f1461,f1465,f1505,f1516,f1523,f1533,f1537,f1545,f1550,f1556,f1561,f1579,f1583,f1591,f1595,f1612,f1622,f1626,f1631,f1635,f1661,f1675,f1686,f1698,f1703,f1726,f1730,f1741,f1752,f1769,f1797,f1811,f1815,f1825,f1838,f1848,f1852,f1873,f1880,f1885,f1892,f1897,f1906,f1911,f1915,f1919,f1923,f1982,f1987,f1993,f2015,f2020,f2469,f2498,f2502,f2520,f2528,f2539,f2544,f2548,f2573,f2574]) ).

tff(f2574,plain,
    ( ~ spl29_4
    | ~ spl29_7
    | spl29_8
    | ~ spl29_20
    | ~ spl29_163
    | ~ spl29_180 ),
    inference(avatar_split_clause,[],[f2569,f2546,f1913,f621,f559,f554,f541]) ).

tff(f541,plain,
    ( spl29_4
  <=> pp(fTrue) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_4])]) ).

tff(f554,plain,
    ( spl29_7
  <=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4),t)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_7])]) ).

tff(f559,plain,
    ( spl29_8
  <=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),sK4),sK5))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_8])]) ).

tff(f621,plain,
    ( spl29_20
  <=> ( fTrue = aa(dB,bool,it,sK4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_20])]) ).

tff(f1913,plain,
    ( spl29_163
  <=> ! [X0: bool] :
        ( ~ pp(X0)
        | ( fTrue = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_163])]) ).

tff(f2546,plain,
    ( spl29_180
  <=> ! [X0: dB] :
        ( ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),X0),t))
        | ~ pp(aa(dB,bool,it,X0))
        | pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X0),sK5))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_180])]) ).

tff(f2569,plain,
    ( ~ pp(fTrue)
    | ~ spl29_7
    | spl29_8
    | ~ spl29_20
    | ~ spl29_163
    | ~ spl29_180 ),
    inference(duplicate_literal_removal,[],[f2568]) ).

tff(f2568,plain,
    ( ~ pp(fTrue)
    | ~ pp(fTrue)
    | ~ spl29_7
    | spl29_8
    | ~ spl29_20
    | ~ spl29_163
    | ~ spl29_180 ),
    inference(forward_demodulation,[],[f2567,f1960]) ).

tff(f1960,plain,
    ( ( fTrue = aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4),t) )
    | ~ spl29_7
    | ~ spl29_163 ),
    inference(resolution,[],[f1914,f556]) ).

tff(f556,plain,
    ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4),t))
    | ~ spl29_7 ),
    inference(avatar_component_clause,[],[f554]) ).

tff(f1914,plain,
    ( ! [X0: bool] :
        ( ~ pp(X0)
        | ( fTrue = X0 ) )
    | ~ spl29_163 ),
    inference(avatar_component_clause,[],[f1913]) ).

tff(f2567,plain,
    ( ~ pp(fTrue)
    | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4),t))
    | spl29_8
    | ~ spl29_20
    | ~ spl29_180 ),
    inference(forward_demodulation,[],[f2556,f623]) ).

tff(f623,plain,
    ( ( fTrue = aa(dB,bool,it,sK4) )
    | ~ spl29_20 ),
    inference(avatar_component_clause,[],[f621]) ).

tff(f2556,plain,
    ( ~ pp(aa(dB,bool,it,sK4))
    | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4),t))
    | spl29_8
    | ~ spl29_180 ),
    inference(resolution,[],[f2547,f561]) ).

tff(f561,plain,
    ( ~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),sK4),sK5)))
    | spl29_8 ),
    inference(avatar_component_clause,[],[f559]) ).

tff(f2547,plain,
    ( ! [X0: dB] :
        ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X0),sK5)))
        | ~ pp(aa(dB,bool,it,X0))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),X0),t)) )
    | ~ spl29_180 ),
    inference(avatar_component_clause,[],[f2546]) ).

tff(f2573,plain,
    ( spl29_181
    | ~ spl29_24
    | ~ spl29_41 ),
    inference(avatar_split_clause,[],[f779,f756,f650,f2571]) ).

tff(f2571,plain,
    ( spl29_181
  <=> ! [X0: dB] :
        ( sP0(X0)
        | listsp(dB,it,sK10(X0))
        | ~ sP1(X0)
        | sP1(abs(sK9(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_181])]) ).

tff(f650,plain,
    ( spl29_24
  <=> ! [X1: dB] :
        ( sP1(abs(X1))
        | ~ pp(aa(dB,bool,it,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_24])]) ).

tff(f756,plain,
    ( spl29_41
  <=> ! [X0: dB] :
        ( sP0(X0)
        | pp(aa(dB,bool,it,sK9(X0)))
        | listsp(dB,it,sK10(X0))
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_41])]) ).

tff(f779,plain,
    ( ! [X0: dB] :
        ( sP0(X0)
        | listsp(dB,it,sK10(X0))
        | ~ sP1(X0)
        | sP1(abs(sK9(X0))) )
    | ~ spl29_24
    | ~ spl29_41 ),
    inference(resolution,[],[f757,f651]) ).

tff(f651,plain,
    ( ! [X1: dB] :
        ( ~ pp(aa(dB,bool,it,X1))
        | sP1(abs(X1)) )
    | ~ spl29_24 ),
    inference(avatar_component_clause,[],[f650]) ).

tff(f757,plain,
    ( ! [X0: dB] :
        ( pp(aa(dB,bool,it,sK9(X0)))
        | sP0(X0)
        | listsp(dB,it,sK10(X0))
        | ~ sP1(X0) )
    | ~ spl29_41 ),
    inference(avatar_component_clause,[],[f756]) ).

tff(f2548,plain,
    ( spl29_180
    | ~ spl29_27
    | ~ spl29_144 ),
    inference(avatar_split_clause,[],[f1745,f1739,f673,f2546]) ).

tff(f673,plain,
    ( spl29_27
  <=> 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),sK2),sK5),t)),b),sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_27])]) ).

tff(f1739,plain,
    ( spl29_144
  <=> ! [X4: nat,X3: dB,X2: type,X1: fun(nat,type)] :
        ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X3),X4)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
        | ~ pp(aa(dB,bool,it,X3))
        | ~ 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),X1),X4),t)),b),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_144])]) ).

tff(f1745,plain,
    ( ! [X0: dB] :
        ( ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),X0),t))
        | ~ pp(aa(dB,bool,it,X0))
        | pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X0),sK5))) )
    | ~ spl29_27
    | ~ spl29_144 ),
    inference(resolution,[],[f1740,f675]) ).

tff(f675,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),sK2),sK5),t)),b),sK3))
    | ~ spl29_27 ),
    inference(avatar_component_clause,[],[f673]) ).

tff(f1740,plain,
    ( ! [X2: type,X3: dB,X1: fun(nat,type),X4: nat] :
        ( ~ 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),X1),X4),t)),b),X2))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
        | ~ pp(aa(dB,bool,it,X3))
        | pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X3),X4))) )
    | ~ spl29_144 ),
    inference(avatar_component_clause,[],[f1739]) ).

tff(f2544,plain,
    ( spl29_179
    | ~ spl29_27
    | ~ spl29_38 ),
    inference(avatar_split_clause,[],[f751,f728,f673,f2541]) ).

tff(f2541,plain,
    ( spl29_179
  <=> pp(aa(fun(type,bool),bool,fEx(type),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),sK2),sK5),t)),b))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_179])]) ).

tff(f728,plain,
    ( spl29_38
  <=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
        ( pp(aa(fun(X0,bool),bool,fEx(X0),X2))
        | ~ pp(aa(X0,bool,X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_38])]) ).

tff(f751,plain,
    ( pp(aa(fun(type,bool),bool,fEx(type),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),sK2),sK5),t)),b)))
    | ~ spl29_27
    | ~ spl29_38 ),
    inference(resolution,[],[f729,f675]) ).

tff(f729,plain,
    ( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
        ( ~ pp(aa(X0,bool,X2,X1))
        | pp(aa(fun(X0,bool),bool,fEx(X0),X2)) )
    | ~ spl29_38 ),
    inference(avatar_component_clause,[],[f728]) ).

tff(f2539,plain,
    ( spl29_178
    | ~ spl29_16
    | ~ spl29_41 ),
    inference(avatar_split_clause,[],[f780,f756,f605,f2537]) ).

tff(f2537,plain,
    ( spl29_178
  <=> ! [X0: dB] :
        ( sP0(X0)
        | listsp(dB,it,sK10(X0))
        | ~ sP1(X0)
        | sP1(sK9(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_178])]) ).

tff(f605,plain,
    ( spl29_16
  <=> ! [X0: dB] :
        ( sP1(X0)
        | ~ pp(aa(dB,bool,it,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_16])]) ).

tff(f780,plain,
    ( ! [X0: dB] :
        ( sP0(X0)
        | listsp(dB,it,sK10(X0))
        | ~ sP1(X0)
        | sP1(sK9(X0)) )
    | ~ spl29_16
    | ~ spl29_41 ),
    inference(resolution,[],[f757,f606]) ).

tff(f606,plain,
    ( ! [X0: dB] :
        ( ~ pp(aa(dB,bool,it,X0))
        | sP1(X0) )
    | ~ spl29_16 ),
    inference(avatar_component_clause,[],[f605]) ).

tff(f2528,plain,
    ( spl29_176
    | spl29_177
    | ~ spl29_18
    | ~ spl29_38 ),
    inference(avatar_split_clause,[],[f752,f728,f613,f2526,f2522]) ).

tff(f2522,plain,
    ( spl29_176
  <=> pp(aa(fun(bool,bool),bool,fEx(bool),combi(bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_176])]) ).

tff(f2526,plain,
    ( spl29_177
  <=> ! [X0: bool] : ~ pp(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_177])]) ).

tff(f613,plain,
    ( spl29_18
  <=> ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_18])]) ).

tff(f752,plain,
    ( ! [X0: bool] :
        ( ~ pp(X0)
        | pp(aa(fun(bool,bool),bool,fEx(bool),combi(bool))) )
    | ~ spl29_18
    | ~ spl29_38 ),
    inference(superposition,[],[f729,f614]) ).

tff(f614,plain,
    ( ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 )
    | ~ spl29_18 ),
    inference(avatar_component_clause,[],[f613]) ).

tff(f2520,plain,
    ( spl29_175
    | ~ spl29_1
    | ~ spl29_172 ),
    inference(avatar_split_clause,[],[f2483,f2467,f526,f2517]) ).

tff(f2517,plain,
    ( spl29_175
  <=> sP1(abs(abs(sK4))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_175])]) ).

tff(f526,plain,
    ( spl29_1
  <=> pp(aa(dB,bool,it,sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_1])]) ).

tff(f2467,plain,
    ( spl29_172
  <=> ! [X0: dB] :
        ( ~ pp(aa(dB,bool,it,X0))
        | sP1(abs(abs(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_172])]) ).

tff(f2483,plain,
    ( sP1(abs(abs(sK4)))
    | ~ spl29_1
    | ~ spl29_172 ),
    inference(resolution,[],[f2468,f528]) ).

tff(f528,plain,
    ( pp(aa(dB,bool,it,sK4))
    | ~ spl29_1 ),
    inference(avatar_component_clause,[],[f526]) ).

tff(f2468,plain,
    ( ! [X0: dB] :
        ( ~ pp(aa(dB,bool,it,X0))
        | sP1(abs(abs(X0))) )
    | ~ spl29_172 ),
    inference(avatar_component_clause,[],[f2467]) ).

tff(f2502,plain,
    ( spl29_174
    | ~ spl29_50
    | ~ spl29_81 ),
    inference(avatar_split_clause,[],[f1022,f1010,f819,f2500]) ).

tff(f2500,plain,
    ( spl29_174
  <=> ! [X0: list(dB)] : ( rs = list_case(list(dB),dB,X0,cons(dB),rs) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_174])]) ).

tff(f819,plain,
    ( spl29_50
  <=> ( rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_50])]) ).

tff(f1010,plain,
    ( spl29_81
  <=> ! [X1: $tType,X0: $tType,X5: X0,X4: fun(X1,fun(list(X1),X0)),X3: X1,X2: list(X1)] : ( list_case(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_81])]) ).

tff(f1022,plain,
    ( ! [X0: list(dB)] : ( rs = list_case(list(dB),dB,X0,cons(dB),rs) )
    | ~ spl29_50
    | ~ spl29_81 ),
    inference(superposition,[],[f1011,f821]) ).

tff(f821,plain,
    ( ( rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as) )
    | ~ spl29_50 ),
    inference(avatar_component_clause,[],[f819]) ).

tff(f1011,plain,
    ( ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( list_case(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) )
    | ~ spl29_81 ),
    inference(avatar_component_clause,[],[f1010]) ).

tff(f2498,plain,
    ( spl29_173
    | ~ spl29_13
    | ~ spl29_18 ),
    inference(avatar_split_clause,[],[f638,f613,f583,f2496]) ).

tff(f2496,plain,
    ( spl29_173
  <=> ! [X0: bool] :
        ( ( fFalse = X0 )
        | ( fTrue = aa(bool,bool,combi(bool),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_173])]) ).

tff(f583,plain,
    ( spl29_13
  <=> ! [X0: bool] :
        ( ( fFalse = X0 )
        | ( fTrue = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_13])]) ).

tff(f638,plain,
    ( ! [X0: bool] :
        ( ( fFalse = X0 )
        | ( fTrue = aa(bool,bool,combi(bool),X0) ) )
    | ~ spl29_13
    | ~ spl29_18 ),
    inference(superposition,[],[f614,f584]) ).

tff(f584,plain,
    ( ! [X0: bool] :
        ( ( fFalse = X0 )
        | ( fTrue = X0 ) )
    | ~ spl29_13 ),
    inference(avatar_component_clause,[],[f583]) ).

tff(f2469,plain,
    ( spl29_172
    | ~ spl29_24
    | ~ spl29_28 ),
    inference(avatar_split_clause,[],[f686,f679,f650,f2467]) ).

tff(f679,plain,
    ( spl29_28
  <=> ! [X0: dB] :
        ( pp(aa(dB,bool,it,abs(X0)))
        | ~ pp(aa(dB,bool,it,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_28])]) ).

tff(f686,plain,
    ( ! [X0: dB] :
        ( ~ pp(aa(dB,bool,it,X0))
        | sP1(abs(abs(X0))) )
    | ~ spl29_24
    | ~ spl29_28 ),
    inference(resolution,[],[f680,f651]) ).

tff(f680,plain,
    ( ! [X0: dB] :
        ( pp(aa(dB,bool,it,abs(X0)))
        | ~ pp(aa(dB,bool,it,X0)) )
    | ~ spl29_28 ),
    inference(avatar_component_clause,[],[f679]) ).

tff(f2020,plain,
    ( spl29_171
    | ~ spl29_14
    | ~ spl29_38 ),
    inference(avatar_split_clause,[],[f744,f728,f596,f2017]) ).

tff(f2017,plain,
    ( spl29_171
  <=> pp(aa(fun(dB,bool),bool,fEx(dB),it)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_171])]) ).

tff(f596,plain,
    ( spl29_14
  <=> ! [X0: nat] : pp(aa(dB,bool,it,var(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_14])]) ).

tff(f744,plain,
    ( pp(aa(fun(dB,bool),bool,fEx(dB),it))
    | ~ spl29_14
    | ~ spl29_38 ),
    inference(resolution,[],[f729,f597]) ).

tff(f597,plain,
    ( ! [X0: nat] : pp(aa(dB,bool,it,var(X0)))
    | ~ spl29_14 ),
    inference(avatar_component_clause,[],[f596]) ).

tff(f2015,plain,
    ( spl29_170
    | ~ spl29_13 ),
    inference(avatar_split_clause,[],[f586,f583,f2013]) ).

tff(f2013,plain,
    ( spl29_170
  <=> ! [X0: bool,X1: bool] :
        ( ( X0 = X1 )
        | ( fTrue = X1 )
        | ( fTrue = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_170])]) ).

tff(f586,plain,
    ( ! [X0: bool,X1: bool] :
        ( ( X0 = X1 )
        | ( fTrue = X1 )
        | ( fTrue = X0 ) )
    | ~ spl29_13 ),
    inference(superposition,[],[f584,f584]) ).

tff(f1993,plain,
    ( spl29_169
    | ~ spl29_7
    | ~ spl29_38 ),
    inference(avatar_split_clause,[],[f750,f728,f554,f1990]) ).

tff(f1990,plain,
    ( spl29_169
  <=> pp(aa(fun(type,bool),bool,fEx(type),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_169])]) ).

tff(f750,plain,
    ( pp(aa(fun(type,bool),bool,fEx(type),aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4)))
    | ~ spl29_7
    | ~ spl29_38 ),
    inference(resolution,[],[f729,f556]) ).

tff(f1987,plain,
    ( spl29_168
    | ~ spl29_22
    | ~ spl29_24 ),
    inference(avatar_split_clause,[],[f666,f650,f642,f1985]) ).

tff(f1985,plain,
    ( spl29_168
  <=> ! [X0: dB] :
        ( sP1(abs(sK13(X0)))
        | ~ sP0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_168])]) ).

tff(f642,plain,
    ( spl29_22
  <=> ! [X0: dB] :
        ( pp(aa(dB,bool,it,sK13(X0)))
        | ~ sP0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_22])]) ).

tff(f666,plain,
    ( ! [X0: dB] :
        ( sP1(abs(sK13(X0)))
        | ~ sP0(X0) )
    | ~ spl29_22
    | ~ spl29_24 ),
    inference(resolution,[],[f651,f643]) ).

tff(f643,plain,
    ( ! [X0: dB] :
        ( pp(aa(dB,bool,it,sK13(X0)))
        | ~ sP0(X0) )
    | ~ spl29_22 ),
    inference(avatar_component_clause,[],[f642]) ).

tff(f1982,plain,
    ( spl29_166
    | ~ spl29_167
    | ~ spl29_13 ),
    inference(avatar_split_clause,[],[f594,f583,f1979,f1976]) ).

tff(f1976,plain,
    ( spl29_166
  <=> ! [X0: bool] : ( fTrue = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_166])]) ).

tff(f1979,plain,
    ( spl29_167
  <=> ( fFalse = fTrue ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_167])]) ).

tff(f594,plain,
    ( ! [X0: bool] :
        ( ( fFalse != fTrue )
        | ( fTrue = X0 ) )
    | ~ spl29_13 ),
    inference(equality_factoring,[],[f584]) ).

tff(f1923,plain,
    ( spl29_165
    | ~ spl29_17
    | ~ spl29_24 ),
    inference(avatar_split_clause,[],[f660,f650,f609,f1921]) ).

tff(f1921,plain,
    ( spl29_165
  <=> ! [X0: dB] :
        ( sP1(abs(X0))
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_165])]) ).

tff(f609,plain,
    ( spl29_17
  <=> ! [X0: dB] :
        ( pp(aa(dB,bool,it,X0))
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_17])]) ).

tff(f660,plain,
    ( ! [X0: dB] :
        ( sP1(abs(X0))
        | ~ sP1(X0) )
    | ~ spl29_17
    | ~ spl29_24 ),
    inference(resolution,[],[f651,f610]) ).

tff(f610,plain,
    ( ! [X0: dB] :
        ( pp(aa(dB,bool,it,X0))
        | ~ sP1(X0) )
    | ~ spl29_17 ),
    inference(avatar_component_clause,[],[f609]) ).

tff(f1919,plain,
    ( spl29_164
    | ~ spl29_16
    | ~ spl29_22 ),
    inference(avatar_split_clause,[],[f653,f642,f605,f1917]) ).

tff(f1917,plain,
    ( spl29_164
  <=> ! [X0: dB] :
        ( ~ sP0(X0)
        | sP1(sK13(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_164])]) ).

tff(f653,plain,
    ( ! [X0: dB] :
        ( ~ sP0(X0)
        | sP1(sK13(X0)) )
    | ~ spl29_16
    | ~ spl29_22 ),
    inference(resolution,[],[f643,f606]) ).

tff(f1915,plain,
    ( spl29_163
    | spl29_2
    | ~ spl29_13 ),
    inference(avatar_split_clause,[],[f587,f583,f531,f1913]) ).

tff(f531,plain,
    ( spl29_2
  <=> pp(fFalse) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_2])]) ).

tff(f587,plain,
    ( ! [X0: bool] :
        ( ~ pp(X0)
        | ( fTrue = X0 ) )
    | spl29_2
    | ~ spl29_13 ),
    inference(superposition,[],[f533,f584]) ).

tff(f533,plain,
    ( ~ pp(fFalse)
    | spl29_2 ),
    inference(avatar_component_clause,[],[f531]) ).

tff(f1911,plain,
    ( ~ spl29_162
    | spl29_8
    | ~ spl29_17 ),
    inference(avatar_split_clause,[],[f635,f609,f559,f1908]) ).

tff(f1908,plain,
    ( spl29_162
  <=> sP1(aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),sK4),sK5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_162])]) ).

tff(f635,plain,
    ( ~ sP1(aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),sK4),sK5))
    | spl29_8
    | ~ spl29_17 ),
    inference(resolution,[],[f610,f561]) ).

tff(f1906,plain,
    ( spl29_161
    | ~ spl29_122
    | ~ spl29_158 ),
    inference(avatar_split_clause,[],[f1887,f1882,f1531,f1903]) ).

tff(f1903,plain,
    ( spl29_161
  <=> listsp(dB,it,rs) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_161])]) ).

tff(f1531,plain,
    ( spl29_122
  <=> ! [X0: $tType,X3: list(X0),X2: fun(X0,bool),X1: fun(X0,bool)] :
        ( listsp(X0,X2,X3)
        | ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_122])]) ).

tff(f1882,plain,
    ( spl29_158
  <=> 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,typ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),
    introduced(avatar_definition,[new_symbols(naming,[spl29_158])]) ).

tff(f1887,plain,
    ( listsp(dB,it,rs)
    | ~ spl29_122
    | ~ spl29_158 ),
    inference(resolution,[],[f1884,f1532]) ).

tff(f1532,plain,
    ( ! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
        ( ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
        | listsp(X0,X2,X3) )
    | ~ spl29_122 ),
    inference(avatar_component_clause,[],[f1531]) ).

tff(f1884,plain,
    ( 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    | ~ spl29_158 ),
    inference(avatar_component_clause,[],[f1882]) ).

tff(f1897,plain,
    spl29_160,
    inference(avatar_split_clause,[],[f352,f1894]) ).

tff(f1894,plain,
    ( spl29_160
  <=> 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),
    introduced(avatar_definition,[new_symbols(naming,[spl29_160])]) ).

tff(f352,plain,
    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    inference(cnf_transformation,[],[f41]) ).

tff(f41,axiom,
    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    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40__096listsp_A_I_Ft_O_A_IALL_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_A_G_A_IEX_AT_H_O_Ae_060i_058T_062_A_092_060turnstile_062_At_A_058_AT_H_J_J_Aas_096) ).

tff(f1892,plain,
    spl29_159,
    inference(avatar_split_clause,[],[f351,f1889]) ).

tff(f1889,plain,
    ( spl29_159
  <=> 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),
    introduced(avatar_definition,[new_symbols(naming,[spl29_159])]) ).

tff(f351,plain,
    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    inference(cnf_transformation,[],[f30]) ).

tff(f30,axiom,
    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    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_Cons_I2_J) ).

tff(f1885,plain,
    spl29_158,
    inference(avatar_split_clause,[],[f350,f1882]) ).

tff(f350,plain,
    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    inference(cnf_transformation,[],[f45]) ).

tff(f45,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(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(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    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Var_Ohyps) ).

tff(f1880,plain,
    spl29_157,
    inference(avatar_split_clause,[],[f349,f1877]) ).

tff(f1877,plain,
    ( spl29_157
  <=> 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),
    introduced(avatar_definition,[new_symbols(naming,[spl29_157])]) ).

tff(f349,plain,
    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    inference(cnf_transformation,[],[f40]) ).

tff(f40,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(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    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39__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) ).

tff(f1873,plain,
    spl29_156,
    inference(avatar_split_clause,[],[f494,f1871]) ).

tff(f1871,plain,
    ( spl29_156
  <=> ! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),aa(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),aa(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0))))),cons(X0)))))),aa(fun(list(X0),bool),fun(X0,fun(list(X0),bool)),aa(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(list(X0),bool),fun(X0,fun(list(X0),bool))),combc(X0,fun(list(X0),bool),fun(list(X0),bool)),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)))),aa(fun(list(X0),bool),fun(list(X0),bool),aa(fun(list(X0),fun(fun(list(X0),bool),bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),combc(list(X0),fun(list(X0),bool),bool),member(list(X0))),listset(X0,X1))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_156])]) ).

tff(f494,plain,
    ! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),aa(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),aa(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0))))),cons(X0)))))),aa(fun(list(X0),bool),fun(X0,fun(list(X0),bool)),aa(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(list(X0),bool),fun(X0,fun(list(X0),bool))),combc(X0,fun(list(X0),bool),fun(list(X0),bool)),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)))),aa(fun(list(X0),bool),fun(list(X0),bool),aa(fun(list(X0),fun(fun(list(X0),bool),bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),combc(list(X0),fun(list(X0),bool),bool),member(list(X0))),listset(X0,X1))))))) ),
    inference(definition_unfolding,[],[f405,f408]) ).

tff(f408,plain,
    ! [X0: $tType,X2: fun(X0,bool),X1: fun(list(X0),bool)] : ( set_Cons(X0,X2,X1) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),aa(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),aa(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0))))),cons(X0)))))),aa(fun(list(X0),bool),fun(X0,fun(list(X0),bool)),aa(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(list(X0),bool),fun(X0,fun(list(X0),bool))),combc(X0,fun(list(X0),bool),fun(list(X0),bool)),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)))),aa(fun(list(X0),bool),fun(list(X0),bool),aa(fun(list(X0),fun(fun(list(X0),bool),bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),combc(list(X0),fun(list(X0),bool),bool),member(list(X0))),X1)))))) ),
    inference(cnf_transformation,[],[f160]) ).

tff(f160,plain,
    ! [X0: $tType,X1: fun(list(X0),bool),X2: fun(X0,bool)] : ( set_Cons(X0,X2,X1) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),aa(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),aa(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0))))),cons(X0)))))),aa(fun(list(X0),bool),fun(X0,fun(list(X0),bool)),aa(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(list(X0),bool),fun(X0,fun(list(X0),bool))),combc(X0,fun(list(X0),bool),fun(list(X0),bool)),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)))),aa(fun(list(X0),bool),fun(list(X0),bool),aa(fun(list(X0),fun(fun(list(X0),bool),bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),combc(list(X0),fun(list(X0),bool),bool),member(list(X0))),X1)))))) ),
    inference(rectify,[],[f97]) ).

tff(f97,axiom,
    ! [X0: $tType,X87: fun(list(X0),bool),X49: fun(X0,bool)] : ( set_Cons(X0,X49,X87) = collect(list(X0),aa(fun(list(X0),fun(X0,bool)),fun(list(X0),bool),aa(fun(fun(X0,bool),bool),fun(fun(list(X0),fun(X0,bool)),fun(list(X0),bool)),combb(fun(X0,bool),bool,list(X0)),fEx(X0)),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool)),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,bool))),combb(fun(X0,fun(list(X0),bool)),fun(X0,bool),list(X0)),aa(fun(fun(list(X0),bool),bool),fun(fun(X0,fun(list(X0),bool)),fun(X0,bool)),combb(fun(list(X0),bool),bool,X0),fEx(list(X0)))),aa(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),bool)),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),aa(fun(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(list(X0),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))))),combb(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),bool))),list(X0)),combs(X0,fun(list(X0),bool),fun(list(X0),bool))),aa(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),aa(fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),fun(list(X0),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))))),combb(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),list(X0)),aa(fun(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(list(X0),fun(bool,bool))),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(list(X0),fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combs(list(X0),bool,bool))),aa(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool)))),aa(fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),fun(fun(list(X0),fun(X0,fun(list(X0),bool))),fun(list(X0),fun(X0,fun(list(X0),fun(bool,bool))))),combb(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool))),list(X0)),aa(fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),fun(fun(X0,fun(list(X0),bool)),fun(X0,fun(list(X0),fun(bool,bool)))),combb(fun(list(X0),bool),fun(list(X0),fun(bool,bool)),X0),aa(fun(bool,fun(bool,bool)),fun(fun(list(X0),bool),fun(list(X0),fun(bool,bool))),combb(bool,fun(bool,bool),list(X0)),fconj))),aa(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(X0,fun(list(X0),list(X0))),fun(list(X0),fun(X0,fun(list(X0),bool)))),combc(list(X0),fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),aa(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),aa(fun(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool)))),fun(fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(list(X0),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))))),combb(fun(fun(list(X0),list(X0)),fun(list(X0),bool)),fun(fun(X0,fun(list(X0),list(X0))),fun(X0,fun(list(X0),bool))),list(X0)),combb(fun(list(X0),list(X0)),fun(list(X0),bool),X0)),aa(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),aa(fun(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool))),fun(fun(list(X0),fun(list(X0),bool)),fun(list(X0),fun(fun(list(X0),list(X0)),fun(list(X0),bool)))),combb(fun(list(X0),bool),fun(fun(list(X0),list(X0)),fun(list(X0),bool)),list(X0)),combb(list(X0),bool,list(X0))),fequal(list(X0))))),cons(X0)))))),aa(fun(list(X0),bool),fun(X0,fun(list(X0),bool)),aa(fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(list(X0),bool),fun(X0,fun(list(X0),bool))),combc(X0,fun(list(X0),bool),fun(list(X0),bool)),aa(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool))),aa(fun(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool))),fun(fun(X0,fun(bool,bool)),fun(X0,fun(fun(list(X0),bool),fun(list(X0),bool)))),combb(fun(bool,bool),fun(fun(list(X0),bool),fun(list(X0),bool)),X0),combb(bool,bool,list(X0))),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X49)))),aa(fun(list(X0),bool),fun(list(X0),bool),aa(fun(list(X0),fun(fun(list(X0),bool),bool)),fun(fun(list(X0),bool),fun(list(X0),bool)),combc(list(X0),fun(list(X0),bool),bool),member(list(X0))),X87)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_set__Cons__def) ).

tff(f405,plain,
    ! [X0: $tType,X2: fun(X0,bool),X1: list(fun(X0,bool))] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = set_Cons(X0,X2,listset(X0,X1)) ),
    inference(cnf_transformation,[],[f157]) ).

tff(f157,plain,
    ! [X0: $tType,X1: list(fun(X0,bool)),X2: fun(X0,bool)] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X2),X1)) = set_Cons(X0,X2,listset(X0,X1)) ),
    inference(rectify,[],[f98]) ).

tff(f98,axiom,
    ! [X0: $tType,X88: list(fun(X0,bool)),X49: fun(X0,bool)] : ( listset(X0,aa(list(fun(X0,bool)),list(fun(X0,bool)),aa(fun(X0,bool),fun(list(fun(X0,bool)),list(fun(X0,bool))),cons(fun(X0,bool)),X49),X88)) = set_Cons(X0,X49,listset(X0,X88)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_listset_Osimps_I2_J) ).

tff(f1852,plain,
    spl29_155,
    inference(avatar_split_clause,[],[f452,f1850]) ).

tff(f1850,plain,
    ( spl29_155
  <=> ! [X0: list(type),X3: fun(nat,type),X2: dB,X1: list(dB)] :
        ( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
        | ~ 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,X3),X2)))),typings(X3,X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_155])]) ).

tff(f452,plain,
    ! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
      ( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
      | ~ 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,X3),X2)))),typings(X3,X1)),X0)) ),
    inference(cnf_transformation,[],[f306]) ).

tff(f306,plain,
    ! [X0: list(type),X1: list(dB),X2: dB,X3: fun(nat,type)] :
      ( ( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
        | ~ 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,X3),X2)))),typings(X3,X1)),X0)) )
      & ( 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,X3),X2)))),typings(X3,X1)),X0))
        | ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0)) ) ),
    inference(nnf_transformation,[],[f188]) ).

tff(f188,plain,
    ! [X0: list(type),X1: list(dB),X2: dB,X3: fun(nat,type)] :
      ( pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0))
    <=> 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,X3),X2)))),typings(X3,X1)),X0)) ),
    inference(rectify,[],[f74]) ).

tff(f74,axiom,
    ! [X44: list(type),X45: list(dB),X15: dB,X14: fun(nat,type)] :
      ( pp(aa(list(type),bool,typings(X14,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X15),X45)),X44))
    <=> 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,X14),X15)))),typings(X14,X45)),X44)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_typings_Osimps_I2_J) ).

tff(f1848,plain,
    spl29_154,
    inference(avatar_split_clause,[],[f451,f1846]) ).

tff(f1846,plain,
    ( spl29_154
  <=> ! [X0: list(type),X3: fun(nat,type),X2: dB,X1: list(dB)] :
        ( 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,X3),X2)))),typings(X3,X1)),X0))
        | ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_154])]) ).

tff(f451,plain,
    ! [X2: dB,X3: fun(nat,type),X0: list(type),X1: list(dB)] :
      ( 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,X3),X2)))),typings(X3,X1)),X0))
      | ~ pp(aa(list(type),bool,typings(X3,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),X2),X1)),X0)) ),
    inference(cnf_transformation,[],[f306]) ).

tff(f1838,plain,
    ( spl29_151
    | spl29_152
    | spl29_153
    | ~ spl29_25
    | ~ spl29_55 ),
    inference(avatar_split_clause,[],[f852,f844,f656,f1835,f1831,f1827]) ).

tff(f1827,plain,
    ( spl29_151
  <=> sP0(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_151])]) ).

tff(f1831,plain,
    ( spl29_152
  <=> ( sK4 = foldl(dB,dB,app,var(sK11(sK4)),sK10(sK4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_152])]) ).

tff(f1835,plain,
    ( spl29_153
  <=> ( sK4 = abs(sK9(sK4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_153])]) ).

tff(f656,plain,
    ( spl29_25
  <=> sP1(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_25])]) ).

tff(f844,plain,
    ( spl29_55
  <=> ! [X0: dB] :
        ( sP0(X0)
        | ( abs(sK9(X0)) = X0 )
        | ( foldl(dB,dB,app,var(sK11(X0)),sK10(X0)) = X0 )
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_55])]) ).

tff(f852,plain,
    ( ( sK4 = abs(sK9(sK4)) )
    | ( sK4 = foldl(dB,dB,app,var(sK11(sK4)),sK10(sK4)) )
    | sP0(sK4)
    | ~ spl29_25
    | ~ spl29_55 ),
    inference(resolution,[],[f845,f658]) ).

tff(f658,plain,
    ( sP1(sK4)
    | ~ spl29_25 ),
    inference(avatar_component_clause,[],[f656]) ).

tff(f845,plain,
    ( ! [X0: dB] :
        ( ~ sP1(X0)
        | ( abs(sK9(X0)) = X0 )
        | ( foldl(dB,dB,app,var(sK11(X0)),sK10(X0)) = X0 )
        | sP0(X0) )
    | ~ spl29_55 ),
    inference(avatar_component_clause,[],[f844]) ).

tff(f1825,plain,
    spl29_150,
    inference(avatar_split_clause,[],[f472,f1823]) ).

tff(f1823,plain,
    ( spl29_150
  <=> ! [X3: type,X4: dB,X0: list(type),X5: fun(nat,type),X2: nat,X1: list(dB)] :
        ( pp(aa(list(type),bool,typings(X5,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X4)),X2),X1)),X0))
        | ~ 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),X5),X2),X3),X1),X0))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X5),X4),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_150])]) ).

tff(f472,plain,
    ! [X2: nat,X3: type,X0: list(type),X1: list(dB),X4: dB,X5: fun(nat,type)] :
      ( pp(aa(list(type),bool,typings(X5,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X4)),X2),X1)),X0))
      | ~ 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),X5),X2),X3),X1),X0))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X5),X4),X3)) ),
    inference(cnf_transformation,[],[f248]) ).

tff(f248,plain,
    ! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun(nat,type)] :
      ( pp(aa(list(type),bool,typings(X5,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X4)),X2),X1)),X0))
      | ~ 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),X5),X2),X3),X1),X0))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X5),X4),X3)) ),
    inference(flattening,[],[f247]) ).

tff(f247,plain,
    ! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun(nat,type)] :
      ( pp(aa(list(type),bool,typings(X5,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X4)),X2),X1)),X0))
      | ~ 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),X5),X2),X3),X1),X0))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X5),X4),X3)) ),
    inference(ennf_transformation,[],[f204]) ).

tff(f204,plain,
    ! [X0: list(type),X1: list(dB),X2: nat,X3: type,X4: dB,X5: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X5),X4),X3))
     => ( 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),X5),X2),X3),X1),X0))
       => pp(aa(list(type),bool,typings(X5,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X4)),X2),X1)),X0)) ) ),
    inference(rectify,[],[f39]) ).

tff(f39,axiom,
    ! [X44: list(type),X45: list(dB),X13: nat,X12: type,X11: dB,X14: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X11),X12))
     => ( 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),X14),X13),X12),X45),X44))
       => pp(aa(list(type),bool,typings(X14,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X11)),X13),X45)),X44)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_substs__lemma) ).

tff(f1815,plain,
    spl29_149,
    inference(avatar_split_clause,[],[f483,f1813]) ).

tff(f1813,plain,
    ( spl29_149
  <=> ! [X5: type,X3: fun(nat,type),X4: dB,X0: dB,X6: type,X2: nat,X1: type] :
        ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X6))
        | ~ pp(aa(dB,bool,it,X0))
        | ~ 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),X3),X2),X6)),X4),X1))
        | ~ pp(aa(dB,bool,it,X4))
        | ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_149])]) ).

tff(f483,plain,
    ! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
      ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X6))
      | ~ pp(aa(dB,bool,it,X0))
      | ~ 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),X3),X2),X6)),X4),X1))
      | ~ pp(aa(dB,bool,it,X4))
      | ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
    inference(cnf_transformation,[],[f252]) ).

tff(f252,plain,
    ! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
      ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X6))
      | ~ pp(aa(dB,bool,it,X0))
      | ~ 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),X3),X2),X6)),X4),X1))
      | ~ pp(aa(dB,bool,it,X4))
      | ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
    inference(flattening,[],[f251]) ).

tff(f251,plain,
    ! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
      ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X6))
      | ~ pp(aa(dB,bool,it,X0))
      | ~ 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),X3),X2),X6)),X4),X1))
      | ~ pp(aa(dB,bool,it,X4))
      | ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
    inference(ennf_transformation,[],[f209]) ).

tff(f209,plain,
    ! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
      ( ( t = aa(type,type,aa(type,fun(type,type),fun1,X6),X5) )
     => ( pp(aa(dB,bool,it,X4))
       => ( 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),X3),X2),X6)),X4),X1))
         => ( pp(aa(dB,bool,it,X0))
           => ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X6))
             => pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2))) ) ) ) ) ),
    inference(rectify,[],[f8]) ).

tff(f8,axiom,
    ! [X11: dB,X12: type,X13: nat,X14: fun(nat,type),X15: dB,X16: type,X17: type] :
      ( ( t = aa(type,type,aa(type,fun(type,type),fun1,X17),X16) )
     => ( pp(aa(dB,bool,it,X15))
       => ( 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),X14),X13),X17)),X15),X12))
         => ( pp(aa(dB,bool,it,X11))
           => ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X11),X17))
             => pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X15),X11),X13))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_MI1) ).

tff(f1811,plain,
    spl29_148,
    inference(avatar_split_clause,[],[f482,f1809]) ).

tff(f1809,plain,
    ( spl29_148
  <=> ! [X3: fun(nat,type),X4: dB,X0: dB,X6: type,X5: type,X2: nat,X1: type] :
        ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X5))
        | ~ pp(aa(dB,bool,it,X0))
        | ~ 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),X3),X2),X5)),X4),X1))
        | ~ pp(aa(dB,bool,it,X4))
        | ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_148])]) ).

tff(f482,plain,
    ! [X2: nat,X3: fun(nat,type),X0: dB,X1: type,X6: type,X4: dB,X5: type] :
      ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X5))
      | ~ pp(aa(dB,bool,it,X0))
      | ~ 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),X3),X2),X5)),X4),X1))
      | ~ pp(aa(dB,bool,it,X4))
      | ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
    inference(cnf_transformation,[],[f250]) ).

tff(f250,plain,
    ! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
      ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X5))
      | ~ pp(aa(dB,bool,it,X0))
      | ~ 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),X3),X2),X5)),X4),X1))
      | ~ pp(aa(dB,bool,it,X4))
      | ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
    inference(flattening,[],[f249]) ).

tff(f249,plain,
    ! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
      ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X5))
      | ~ pp(aa(dB,bool,it,X0))
      | ~ 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),X3),X2),X5)),X4),X1))
      | ~ pp(aa(dB,bool,it,X4))
      | ( t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5) ) ),
    inference(ennf_transformation,[],[f208]) ).

tff(f208,plain,
    ! [X0: dB,X1: type,X2: nat,X3: fun(nat,type),X4: dB,X5: type,X6: type] :
      ( ( t = aa(type,type,aa(type,fun(type,type),fun1,X6),X5) )
     => ( pp(aa(dB,bool,it,X4))
       => ( 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),X3),X2),X5)),X4),X1))
         => ( pp(aa(dB,bool,it,X0))
           => ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X0),X5))
             => pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X4),X0),X2))) ) ) ) ) ),
    inference(rectify,[],[f9]) ).

tff(f9,axiom,
    ! [X11: dB,X12: type,X13: nat,X14: fun(nat,type),X15: dB,X16: type,X17: type] :
      ( ( t = aa(type,type,aa(type,fun(type,type),fun1,X17),X16) )
     => ( pp(aa(dB,bool,it,X15))
       => ( 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),X14),X13),X16)),X15),X12))
         => ( pp(aa(dB,bool,it,X11))
           => ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X11),X16))
             => pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X15),X11),X13))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_MI2) ).

tff(f1797,plain,
    spl29_147,
    inference(avatar_split_clause,[],[f481,f1795]) ).

tff(f1795,plain,
    ( spl29_147
  <=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X0,X4: fun(X2,X1),X6: fun(X0,fun(X1,X0)),X3: list(X2)] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,aa(fun(X2,X1),fun(X0,fun(X2,X0)),aa(fun(X0,fun(fun(X2,X1),fun(X2,X0))),fun(fun(X2,X1),fun(X0,fun(X2,X0))),combc(X0,fun(X2,X1),fun(X2,X0)),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X6)),X4),X5,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_147])]) ).

tff(f481,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: list(X2),X6: fun(X0,fun(X1,X0)),X4: fun(X2,X1),X5: X0] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,aa(fun(X2,X1),fun(X0,fun(X2,X0)),aa(fun(X0,fun(fun(X2,X1),fun(X2,X0))),fun(fun(X2,X1),fun(X0,fun(X2,X0))),combc(X0,fun(X2,X1),fun(X2,X0)),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X6)),X4),X5,X3) ),
    inference(cnf_transformation,[],[f207]) ).

tff(f207,plain,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: list(X2),X4: fun(X2,X1),X5: X0,X6: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X6,X5,map(X2,X1,X4,X3)) = foldl(X0,X2,aa(fun(X2,X1),fun(X0,fun(X2,X0)),aa(fun(X0,fun(fun(X2,X1),fun(X2,X0))),fun(fun(X2,X1),fun(X0,fun(X2,X0))),combc(X0,fun(X2,X1),fun(X2,X0)),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X6)),X4),X5,X3) ),
    inference(rectify,[],[f56]) ).

tff(f56,axiom,
    ! [X0: $tType,X1: $tType,X2: $tType,X51: list(X2),X52: fun(X2,X1),X53: X0,X54: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X54,X53,map(X2,X1,X52,X51)) = foldl(X0,X2,aa(fun(X2,X1),fun(X0,fun(X2,X0)),aa(fun(X0,fun(fun(X2,X1),fun(X2,X0))),fun(fun(X2,X1),fun(X0,fun(X2,X0))),combc(X0,fun(X2,X1),fun(X2,X0)),aa(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0))),aa(fun(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0))),fun(fun(X0,fun(X1,X0)),fun(X0,fun(fun(X2,X1),fun(X2,X0)))),combb(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),X0),combb(X1,X0,X2)),X54)),X52),X53,X51) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_foldl__map) ).

tff(f1769,plain,
    spl29_146,
    inference(avatar_split_clause,[],[f522,f1767]) ).

tff(f1767,plain,
    ( spl29_146
  <=> ! [X3: fun(nat,type),X4: type,X0: nat,X5: dB,X2: dB,X1: type] :
        ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
        | ~ 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),X3),X0),X1)),X5),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_146])]) ).

tff(f522,plain,
    ! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X4: type,X5: dB] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
      | ~ 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),X3),X0),X1)),X5),X4)) ),
    inference(equality_resolution,[],[f484]) ).

tff(f484,plain,
    ! [X2: dB,X3: fun(nat,type),X0: nat,X1: type,X6: fun(nat,type),X4: type,X5: dB] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
      | ( 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),X3),X0),X1) != X6 )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),X5),X4)) ),
    inference(cnf_transformation,[],[f254]) ).

tff(f254,plain,
    ! [X0: nat,X1: type,X2: dB,X3: fun(nat,type),X4: type,X5: dB,X6: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
      | ( 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),X3),X0),X1) != X6 )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),X5),X4)) ),
    inference(flattening,[],[f253]) ).

tff(f253,plain,
    ! [X0: nat,X1: type,X2: dB,X3: fun(nat,type),X4: type,X5: dB,X6: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4))
      | ( 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),X3),X0),X1) != X6 )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),X5),X4)) ),
    inference(ennf_transformation,[],[f210]) ).

tff(f210,plain,
    ! [X0: nat,X1: type,X2: dB,X3: fun(nat,type),X4: type,X5: dB,X6: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),X5),X4))
     => ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),X1))
       => ( ( 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),X3),X0),X1) = X6 )
         => pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X5),X2),X0)),X4)) ) ) ),
    inference(rectify,[],[f10]) ).

tff(f10,axiom,
    ! [X13: nat,X18: type,X11: dB,X19: fun(nat,type),X12: type,X15: dB,X14: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X15),X12))
     => ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X19),X11),X18))
       => ( ( 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),X19),X13),X18) = X14 )
         => pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X19),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X15),X11),X13)),X12)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_subst__lemma) ).

tff(f1752,plain,
    spl29_145,
    inference(avatar_split_clause,[],[f428,f1750]) ).

tff(f1750,plain,
    ( spl29_145
  <=> ! [X0: nat,X3: dB,X2: list(dB),X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X1)),X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_145])]) ).

tff(f428,plain,
    ! [X2: list(dB),X3: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X1)),X0),X2)) ),
    inference(cnf_transformation,[],[f177]) ).

tff(f177,plain,
    ! [X0: nat,X1: dB,X2: list(dB),X3: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X3,X2)),X1),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X1)),X0),X2)) ),
    inference(rectify,[],[f61]) ).

tff(f61,axiom,
    ! [X13: nat,X11: dB,X45: list(dB),X15: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,X15,X45)),X11),X13) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X15),X11),X13),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),X11)),X13),X45)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_subst__map) ).

tff(f1741,plain,
    spl29_144,
    inference(avatar_split_clause,[],[f353,f1739]) ).

tff(f353,plain,
    ! [X2: type,X3: dB,X1: fun(nat,type),X4: nat] :
      ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X3),X4)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
      | ~ pp(aa(dB,bool,it,X3))
      | ~ 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),X1),X4),t)),b),X2)) ),
    inference(cnf_transformation,[],[f263]) ).

tff(f263,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)),b),sK6))
    & ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
        ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X3),X4)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
        | ~ pp(aa(dB,bool,it,X3))
        | ~ 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),X1),X4),t)),b),X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f215,f262]) ).

tff(f262,plain,
    ( ? [X0: 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)),b),X0))
   => 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)),b),sK6)) ),
    introduced(choice_axiom,[]) ).

tff(f215,plain,
    ( ? [X0: 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)),b),X0))
    & ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
        ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X3),X4)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
        | ~ pp(aa(dB,bool,it,X3))
        | ~ 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),X1),X4),t)),b),X2)) ) ),
    inference(flattening,[],[f214]) ).

tff(f214,plain,
    ( ? [X0: 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)),b),X0))
    & ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
        ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X3),X4)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
        | ~ pp(aa(dB,bool,it,X3))
        | ~ 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),X1),X4),t)),b),X2)) ) ),
    inference(ennf_transformation,[],[f122]) ).

tff(f122,plain,
    ( ? [X0: 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)),b),X0))
    & ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
        ( 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),X1),X4),t)),b),X2))
       => ( pp(aa(dB,bool,it,X3))
         => ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
           => pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X3),X4))) ) ) ) ),
    inference(rectify,[],[f6]) ).

tff(f6,axiom,
    ( ? [X8: 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)),b),X8))
    & ! [X4: fun(nat,type),X5: type,X6: dB,X7: nat] :
        ( 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),X4),X7),t)),b),X5))
       => ( pp(aa(dB,bool,it,X6))
         => ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X6),t))
           => pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X6),X7))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Cons_I1_J) ).

tff(f1730,plain,
    spl29_143,
    inference(avatar_split_clause,[],[f462,f1728]) ).

tff(f1728,plain,
    ( spl29_143
  <=> ! [X2: type,X4: fun(nat,type),X0: dB,X3: dB,X1: type] :
        ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X0),X2))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_143])]) ).

tff(f462,plain,
    ! [X2: type,X3: dB,X0: dB,X1: type,X4: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X0),X2))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ),
    inference(cnf_transformation,[],[f246]) ).

tff(f246,plain,
    ! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X0),X2))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ),
    inference(flattening,[],[f245]) ).

tff(f245,plain,
    ! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X0),X2))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1))) ),
    inference(ennf_transformation,[],[f196]) ).

tff(f196,plain,
    ! [X0: dB,X1: type,X2: type,X3: dB,X4: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),aa(type,type,aa(type,fun(type,type),fun1,X2),X1)))
     => ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X0),X2))
       => pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X0)),X1)) ) ),
    inference(rectify,[],[f27]) ).

tff(f27,axiom,
    ! [X15: dB,X18: type,X12: type,X38: dB,X37: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X37),X38),aa(type,type,aa(type,fun(type,type),fun1,X12),X18)))
     => ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X37),X15),X12))
       => pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X37),aa(dB,dB,aa(dB,fun(dB,dB),app,X38),X15)),X18)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_App) ).

tff(f1726,plain,
    spl29_142,
    inference(avatar_split_clause,[],[f348,f1723]) ).

tff(f1723,plain,
    ( spl29_142
  <=> listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),u)),i),bs))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_142])]) ).

tff(f348,plain,
    listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),u)),i),bs))),
    inference(cnf_transformation,[],[f22]) ).

tff(f22,axiom,
    listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),u)),i),bs))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Cons_I3_J) ).

tff(f1703,plain,
    spl29_141,
    inference(avatar_split_clause,[],[f486,f1701]) ).

tff(f1701,plain,
    ( spl29_141
  <=> ! [X5: nat,X3: list(dB),X4: list(dB),X0: type,X6: fun(nat,type),X2: type,X1: list(type)] :
        ( pp(aa(list(type),bool,typings(X6,X3),sK28(X0,X2,X3,X6)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,var(X5),X4)),X0))
        | ~ pp(aa(list(type),bool,typings(X6,X4),X1))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_141])]) ).

tff(f486,plain,
    ! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
      ( pp(aa(list(type),bool,typings(X6,X3),sK28(X0,X2,X3,X6)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,var(X5),X4)),X0))
      | ~ pp(aa(list(type),bool,typings(X6,X4),X1))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
    inference(cnf_transformation,[],[f320]) ).

tff(f320,plain,
    ! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
      ( ( pp(aa(list(type),bool,typings(X6,X3),sK28(X0,X2,X3,X6)))
        & ( foldr(type,type,fun1,sK28(X0,X2,X3,X6),X2) = X0 ) )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,var(X5),X4)),X0))
      | ~ pp(aa(list(type),bool,typings(X6,X4),X1))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f256,f319]) ).

tff(f319,plain,
    ! [X0: type,X2: type,X3: list(dB),X6: fun(nat,type)] :
      ( ? [X7: list(type)] :
          ( pp(aa(list(type),bool,typings(X6,X3),X7))
          & ( foldr(type,type,fun1,X7,X2) = X0 ) )
     => ( pp(aa(list(type),bool,typings(X6,X3),sK28(X0,X2,X3,X6)))
        & ( foldr(type,type,fun1,sK28(X0,X2,X3,X6),X2) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f256,plain,
    ! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
      ( ? [X7: list(type)] :
          ( pp(aa(list(type),bool,typings(X6,X3),X7))
          & ( foldr(type,type,fun1,X7,X2) = X0 ) )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,var(X5),X4)),X0))
      | ~ pp(aa(list(type),bool,typings(X6,X4),X1))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
    inference(flattening,[],[f255]) ).

tff(f255,plain,
    ! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
      ( ? [X7: list(type)] :
          ( pp(aa(list(type),bool,typings(X6,X3),X7))
          & ( foldr(type,type,fun1,X7,X2) = X0 ) )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,var(X5),X4)),X0))
      | ~ pp(aa(list(type),bool,typings(X6,X4),X1))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
    inference(ennf_transformation,[],[f211]) ).

tff(f211,plain,
    ! [X0: type,X1: list(type),X2: type,X3: list(dB),X4: list(dB),X5: nat,X6: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2))
     => ( pp(aa(list(type),bool,typings(X6,X4),X1))
       => ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,var(X5),X4)),X0))
         => ? [X7: list(type)] :
              ( pp(aa(list(type),bool,typings(X6,X3),X7))
              & ( foldr(type,type,fun1,X7,X2) = X0 ) ) ) ) ),
    inference(rectify,[],[f71]) ).

tff(f71,axiom,
    ! [X18: type,X44: list(type),X12: type,X65: list(dB),X45: list(dB),X13: nat,X14: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),foldl(dB,dB,app,foldl(dB,dB,app,var(X13),X45),X65)),X12))
     => ( pp(aa(list(type),bool,typings(X14,X45),X44))
       => ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),foldl(dB,dB,app,var(X13),X45)),X18))
         => ? [X66: list(type)] :
              ( pp(aa(list(type),bool,typings(X14,X65),X66))
              & ( foldr(type,type,fun1,X66,X12) = X18 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_var__app__types) ).

tff(f1698,plain,
    spl29_140,
    inference(avatar_split_clause,[],[f437,f1696]) ).

tff(f1696,plain,
    ( spl29_140
  <=> ! [X0: type,X3: fun(nat,type),X2: type,X1: dB] :
        ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0)))
        | ~ 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),X3),zero_zero(nat)),X2)),X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_140])]) ).

tff(f437,plain,
    ! [X2: type,X3: fun(nat,type),X0: type,X1: dB] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0)))
      | ~ 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),X3),zero_zero(nat)),X2)),X1),X0)) ),
    inference(cnf_transformation,[],[f236]) ).

tff(f236,plain,
    ! [X0: type,X1: dB,X2: type,X3: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0)))
      | ~ 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),X3),zero_zero(nat)),X2)),X1),X0)) ),
    inference(ennf_transformation,[],[f182]) ).

tff(f182,plain,
    ! [X0: type,X1: dB,X2: type,X3: 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),X3),zero_zero(nat)),X2)),X1),X0))
     => pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),abs(X1)),aa(type,type,aa(type,fun(type,type),fun1,X2),X0))) ),
    inference(rectify,[],[f87]) ).

tff(f87,axiom,
    ! [X18: type,X15: dB,X12: type,X37: 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),X37),zero_zero(nat)),X12)),X15),X18))
     => pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X37),abs(X15)),aa(type,type,aa(type,fun(type,type),fun1,X12),X18))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Abs) ).

tff(f1686,plain,
    spl29_139,
    inference(avatar_split_clause,[],[f485,f1684]) ).

tff(f1684,plain,
    ( spl29_139
  <=> ! [X5: nat,X3: list(dB),X4: list(dB),X0: type,X6: fun(nat,type),X2: type,X1: list(type)] :
        ( ( foldr(type,type,fun1,sK28(X0,X2,X3,X6),X2) = X0 )
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,var(X5),X4)),X0))
        | ~ pp(aa(list(type),bool,typings(X6,X4),X1))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_139])]) ).

tff(f485,plain,
    ! [X2: type,X3: list(dB),X0: type,X1: list(type),X6: fun(nat,type),X4: list(dB),X5: nat] :
      ( ( foldr(type,type,fun1,sK28(X0,X2,X3,X6),X2) = X0 )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,var(X5),X4)),X0))
      | ~ pp(aa(list(type),bool,typings(X6,X4),X1))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X6),foldl(dB,dB,app,foldl(dB,dB,app,var(X5),X4),X3)),X2)) ),
    inference(cnf_transformation,[],[f320]) ).

tff(f1675,plain,
    spl29_138,
    inference(avatar_split_clause,[],[f459,f1673]) ).

tff(f1673,plain,
    ( spl29_138
  <=> ! [X4: fun(nat,type),X0: type,X3: dB,X2: type,X1: nat] :
        ( 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),X4),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_138])]) ).

tff(f459,plain,
    ! [X2: type,X3: dB,X0: type,X1: nat,X4: 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),X4),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),X2)) ),
    inference(cnf_transformation,[],[f240]) ).

tff(f240,plain,
    ! [X0: type,X1: nat,X2: type,X3: dB,X4: 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),X4),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),X2)) ),
    inference(ennf_transformation,[],[f193]) ).

tff(f193,plain,
    ! [X0: type,X1: nat,X2: type,X3: dB,X4: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),X2))
     => 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),X4),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X3),X1)),X2)) ),
    inference(rectify,[],[f11]) ).

tff(f11,axiom,
    ! [X18: type,X13: nat,X12: type,X15: dB,X14: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X15),X12))
     => 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),X14),X13),X18)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X15),X13)),X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_lift__type) ).

tff(f1661,plain,
    spl29_137,
    inference(avatar_split_clause,[],[f418,f1659]) ).

tff(f1659,plain,
    ( spl29_137
  <=> ! [X2: fun(nat,type),X0: type,X1: dB] :
        ( 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),X2),zero_zero(nat)),sK17(X0,X1,X2))),X1),sK18(X0,X1,X2)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_137])]) ).

tff(f418,plain,
    ! [X2: fun(nat,type),X0: type,X1: dB] :
      ( 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),X2),zero_zero(nat)),sK17(X0,X1,X2))),X1),sK18(X0,X1,X2)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
    inference(cnf_transformation,[],[f285]) ).

tff(f285,plain,
    ! [X0: type,X1: dB,X2: 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),X2),zero_zero(nat)),sK17(X0,X1,X2))),X1),sK18(X0,X1,X2)))
        & ( aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2)),sK18(X0,X1,X2)) = X0 ) )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18])],[f228,f284]) ).

tff(f284,plain,
    ! [X0: type,X1: dB,X2: fun(nat,type)] :
      ( ? [X3: type,X4: 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),X2),zero_zero(nat)),X3)),X1),X4))
          & ( aa(type,type,aa(type,fun(type,type),fun1,X3),X4) = X0 ) )
     => ( 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),X2),zero_zero(nat)),sK17(X0,X1,X2))),X1),sK18(X0,X1,X2)))
        & ( aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2)),sK18(X0,X1,X2)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f228,plain,
    ! [X0: type,X1: dB,X2: fun(nat,type)] :
      ( ? [X3: type,X4: 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),X2),zero_zero(nat)),X3)),X1),X4))
          & ( aa(type,type,aa(type,fun(type,type),fun1,X3),X4) = X0 ) )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
    inference(ennf_transformation,[],[f169]) ).

tff(f169,plain,
    ! [X0: type,X1: dB,X2: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0))
     => ~ ! [X3: type,X4: type] :
            ( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X4) = X0 )
           => ~ 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),X2),zero_zero(nat)),X3)),X1),X4)) ) ),
    inference(rectify,[],[f94]) ).

tff(f94,axiom,
    ! [X12: type,X15: dB,X14: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),abs(X15)),X12))
     => ~ ! [X43: type,X80: type] :
            ( ( aa(type,type,aa(type,fun(type,type),fun1,X43),X80) = X12 )
           => ~ 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),X14),zero_zero(nat)),X43)),X15),X80)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_typing__elims_I3_J) ).

tff(f1635,plain,
    spl29_136,
    inference(avatar_split_clause,[],[f427,f1633]) ).

tff(f1633,plain,
    ( spl29_136
  <=> ! [X0: nat,X3: dB,X2: dB,X1: 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,X3),X2)),X1),X0) = 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,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_136])]) ).

tff(f427,plain,
    ! [X2: dB,X3: dB,X0: nat,X1: 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,X3),X2)),X1),X0) = 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,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) ),
    inference(cnf_transformation,[],[f176]) ).

tff(f176,plain,
    ! [X0: nat,X1: dB,X2: dB,X3: 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,X3),X2)),X1),X0) = 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,X3),X1),X0)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),X1),X0)) ),
    inference(rectify,[],[f23]) ).

tff(f23,axiom,
    ! [X24: nat,X23: dB,X35: dB,X10: 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,X10),X35)),X23),X24) = 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,X10),X23),X24)),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X35),X23),X24)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_subst__App) ).

tff(f1631,plain,
    ( ~ spl29_135
    | ~ spl29_50
    | ~ spl29_51 ),
    inference(avatar_split_clause,[],[f840,f824,f819,f1628]) ).

tff(f1628,plain,
    ( spl29_135
  <=> ( as = rs ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_135])]) ).

tff(f824,plain,
    ( spl29_51
  <=> ! [X0: $tType,X2: X0,X1: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_51])]) ).

tff(f840,plain,
    ( ( as != rs )
    | ~ spl29_50
    | ~ spl29_51 ),
    inference(superposition,[],[f825,f821]) ).

tff(f825,plain,
    ( ! [X0: $tType,X2: X0,X1: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != X1 )
    | ~ spl29_51 ),
    inference(avatar_component_clause,[],[f824]) ).

tff(f1626,plain,
    spl29_134,
    inference(avatar_split_clause,[],[f416,f1624]) ).

tff(f1624,plain,
    ( spl29_134
  <=> ! [X2: fun(nat,type),X0: type,X1: dB] :
        ( 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),X2),zero_zero(nat)),sK15(X1,X2))),X1),sK16(X1,X2)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_134])]) ).

tff(f416,plain,
    ! [X2: fun(nat,type),X0: type,X1: dB] :
      ( 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),X2),zero_zero(nat)),sK15(X1,X2))),X1),sK16(X1,X2)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
    inference(cnf_transformation,[],[f283]) ).

tff(f283,plain,
    ! [X0: type,X1: dB,X2: 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),X2),zero_zero(nat)),sK15(X1,X2))),X1),sK16(X1,X2)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f227,f282]) ).

tff(f282,plain,
    ! [X1: dB,X2: fun(nat,type)] :
      ( ? [X3: type,X4: 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),X2),zero_zero(nat)),X3)),X1),X4))
     => 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),X2),zero_zero(nat)),sK15(X1,X2))),X1),sK16(X1,X2))) ),
    introduced(choice_axiom,[]) ).

tff(f227,plain,
    ! [X0: type,X1: dB,X2: fun(nat,type)] :
      ( ? [X3: type,X4: 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),X2),zero_zero(nat)),X3)),X1),X4))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
    inference(ennf_transformation,[],[f168]) ).

tff(f168,plain,
    ! [X0: type,X1: dB,X2: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0))
     => ~ ! [X3: type,X4: 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),X2),zero_zero(nat)),X3)),X1),X4)) ),
    inference(rectify,[],[f95]) ).

tff(f95,axiom,
    ! [X12: type,X15: dB,X14: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),abs(X15)),X12))
     => ~ ! [X80: type,X81: 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),X14),zero_zero(nat)),X80)),X15),X81)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_abs__typeE) ).

tff(f1622,plain,
    spl29_133,
    inference(avatar_split_clause,[],[f347,f1619]) ).

tff(f1619,plain,
    ( spl29_133
  <=> 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) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_133])]) ).

tff(f347,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(cnf_transformation,[],[f29]) ).

tff(f29,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/sandbox/benchmark/theBenchmark.p',fact_28__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) ).

tff(f1612,plain,
    spl29_132,
    inference(avatar_split_clause,[],[f458,f1610]) ).

tff(f1610,plain,
    ( spl29_132
  <=> ! [X4: fun(nat,type),X0: type,X3: list(dB),X2: list(type),X1: nat] :
        ( 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),X4),X1),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X1),X3)),X2))
        | ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_132])]) ).

tff(f458,plain,
    ! [X2: list(type),X3: list(dB),X0: type,X1: nat,X4: fun(nat,type)] :
      ( 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),X4),X1),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X1),X3)),X2))
      | ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ),
    inference(cnf_transformation,[],[f239]) ).

tff(f239,plain,
    ! [X0: type,X1: nat,X2: list(type),X3: list(dB),X4: fun(nat,type)] :
      ( 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),X4),X1),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X1),X3)),X2))
      | ~ pp(aa(list(type),bool,typings(X4,X3),X2)) ),
    inference(ennf_transformation,[],[f192]) ).

tff(f192,plain,
    ! [X0: type,X1: nat,X2: list(type),X3: list(dB),X4: fun(nat,type)] :
      ( pp(aa(list(type),bool,typings(X4,X3),X2))
     => 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),X4),X1),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X1),X3)),X2)) ),
    inference(rectify,[],[f42]) ).

tff(f42,axiom,
    ! [X18: type,X13: nat,X44: list(type),X45: list(dB),X14: fun(nat,type)] :
      ( pp(aa(list(type),bool,typings(X14,X45),X44))
     => 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),X14),X13),X18),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X13),X45)),X44)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_lift__types) ).

tff(f1595,plain,
    spl29_131,
    inference(avatar_split_clause,[],[f455,f1593]) ).

tff(f1593,plain,
    ( spl29_131
  <=> ! [X0: $tType,X3: list(X0),X2: fun(X0,bool),X1: fun(X0,bool)] :
        ( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
        | ~ listsp(X0,X1,X3)
        | ~ listsp(X0,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_131])]) ).

tff(f455,plain,
    ! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
      ( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
      | ~ listsp(X0,X1,X3)
      | ~ listsp(X0,X2,X3) ),
    inference(cnf_transformation,[],[f308]) ).

tff(f308,plain,
    ! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
      ( ( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
        | ~ listsp(X0,X1,X3)
        | ~ listsp(X0,X2,X3) )
      & ( ( listsp(X0,X1,X3)
          & listsp(X0,X2,X3) )
        | ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
    inference(flattening,[],[f307]) ).

tff(f307,plain,
    ! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
      ( ( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
        | ~ listsp(X0,X1,X3)
        | ~ listsp(X0,X2,X3) )
      & ( ( listsp(X0,X1,X3)
          & listsp(X0,X2,X3) )
        | ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
    inference(nnf_transformation,[],[f189]) ).

tff(f189,plain,
    ! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: list(X0)] :
      ( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3)
    <=> ( listsp(X0,X1,X3)
        & listsp(X0,X2,X3) ) ),
    inference(rectify,[],[f52]) ).

tff(f52,axiom,
    ! [X0: $tType,X48: fun(X0,bool),X49: fun(X0,bool),X50: list(X0)] :
      ( listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X49)),X48),X50)
    <=> ( listsp(X0,X48,X50)
        & listsp(X0,X49,X50) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_listsp__conj__eq) ).

tff(f1591,plain,
    spl29_130,
    inference(avatar_split_clause,[],[f435,f1589]) ).

tff(f1589,plain,
    ( spl29_130
  <=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
        ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK22(X0,X1,X2,X3)),X0)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_130])]) ).

tff(f435,plain,
    ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK22(X0,X1,X2,X3)),X0)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
    inference(cnf_transformation,[],[f295]) ).

tff(f295,plain,
    ! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
      ( ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),sK22(X0,X1,X2,X3)))
        & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK22(X0,X1,X2,X3)),X0))) )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f235,f294]) ).

tff(f294,plain,
    ! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
      ( ? [X4: type] :
          ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),X4))
          & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),aa(type,type,aa(type,fun(type,type),fun1,X4),X0))) )
     => ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),sK22(X0,X1,X2,X3)))
        & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),aa(type,type,aa(type,fun(type,type),fun1,sK22(X0,X1,X2,X3)),X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f235,plain,
    ! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
      ( ? [X4: type] :
          ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),X4))
          & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),aa(type,type,aa(type,fun(type,type),fun1,X4),X0))) )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
    inference(ennf_transformation,[],[f181]) ).

tff(f181,plain,
    ! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))
     => ~ ! [X4: type] :
            ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),aa(type,type,aa(type,fun(type,type),fun1,X4),X0)))
           => ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),X4)) ) ),
    inference(rectify,[],[f38]) ).

tff(f38,axiom,
    ! [X12: type,X11: dB,X15: dB,X14: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),aa(dB,dB,aa(dB,fun(dB,dB),app,X15),X11)),X12))
     => ~ ! [X43: type] :
            ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X15),aa(type,type,aa(type,fun(type,type),fun1,X43),X12)))
           => ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X11),X43)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_typing__elims_I2_J) ).

tff(f1583,plain,
    ( spl29_129
    | ~ spl29_14
    | ~ spl29_24 ),
    inference(avatar_split_clause,[],[f661,f650,f596,f1581]) ).

tff(f1581,plain,
    ( spl29_129
  <=> ! [X0: nat] : sP1(abs(var(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_129])]) ).

tff(f661,plain,
    ( ! [X0: nat] : sP1(abs(var(X0)))
    | ~ spl29_14
    | ~ spl29_24 ),
    inference(resolution,[],[f651,f597]) ).

tff(f1579,plain,
    spl29_128,
    inference(avatar_split_clause,[],[f346,f1576]) ).

tff(f1576,plain,
    ( spl29_128
  <=> 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,aa(nat,dB,aa(dB,fun(nat,dB),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)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_128])]) ).

tff(f346,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,aa(nat,dB,aa(dB,fun(nat,dB),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(cnf_transformation,[],[f28]) ).

tff(f28,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,aa(nat,dB,aa(dB,fun(nat,dB),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/sandbox/benchmark/theBenchmark.p',fact_27__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096) ).

tff(f1561,plain,
    spl29_127,
    inference(avatar_split_clause,[],[f493,f1558]) ).

tff(f1558,plain,
    ( spl29_127
  <=> 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(i)),a)),foldr(type,type,fun1,sK8,t1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_127])]) ).

tff(f493,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(i)),a)),foldr(type,type,fun1,sK8,t1))),
    inference(definition_unfolding,[],[f357,f329]) ).

tff(f329,plain,
    n = i,
    inference(cnf_transformation,[],[f4]) ).

tff(f4,axiom,
    n = i,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_True) ).

tff(f357,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,sK8,t1))),
    inference(cnf_transformation,[],[f267]) ).

tff(f267,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),sK8))
    & 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,sK8,t1))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f217,f266]) ).

tff(f266,plain,
    ( ? [X0: list(type)] :
        ( 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),X0))
        & 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,X0,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),sK8))
      & 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,sK8,t1))) ) ),
    introduced(choice_axiom,[]) ).

tff(f217,plain,
    ? [X0: list(type)] :
      ( 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),X0))
      & 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,X0,t1))) ),
    inference(ennf_transformation,[],[f124]) ).

tff(f124,plain,
    ~ ! [X0: 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,X0,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),X0)) ),
    inference(rectify,[],[f43]) ).

tff(f43,axiom,
    ~ ! [X46: 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,X46,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),X46)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42__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) ).

tff(f1556,plain,
    spl29_126,
    inference(avatar_split_clause,[],[f492,f1553]) ).

tff(f1553,plain,
    ( spl29_126
  <=> 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(i)),aa(type,type,aa(type,fun(type,type),fun1,sK7),foldr(type,type,fun1,ts,t1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_126])]) ).

tff(f492,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(i)),aa(type,type,aa(type,fun(type,type),fun1,sK7),foldr(type,type,fun1,ts,t1)))),
    inference(definition_unfolding,[],[f355,f329]) ).

tff(f355,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,sK7),foldr(type,type,fun1,ts,t1)))),
    inference(cnf_transformation,[],[f265]) ).

tff(f265,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),sK7))
    & 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,sK7),foldr(type,type,fun1,ts,t1)))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f216,f264]) ).

tff(f264,plain,
    ( ? [X0: 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)),a),X0))
        & 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,X0),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),sK7))
      & 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,sK7),foldr(type,type,fun1,ts,t1)))) ) ),
    introduced(choice_axiom,[]) ).

tff(f216,plain,
    ? [X0: 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)),a),X0))
      & 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,X0),foldr(type,type,fun1,ts,t1)))) ),
    inference(ennf_transformation,[],[f123]) ).

tff(f123,plain,
    ~ ! [X0: 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,X0),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),X0)) ),
    inference(rectify,[],[f47]) ).

tff(f47,axiom,
    ~ ! [X47: 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,X47),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),X47)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46__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) ).

tff(f1550,plain,
    spl29_125,
    inference(avatar_split_clause,[],[f491,f1547]) ).

tff(f1547,plain,
    ( spl29_125
  <=> 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(i)),a),as)),t1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_125])]) ).

tff(f491,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(i)),a),as)),t1)),
    inference(definition_unfolding,[],[f345,f329]) ).

tff(f345,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(cnf_transformation,[],[f50]) ).

tff(f50,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/sandbox/benchmark/theBenchmark.p',fact_49__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) ).

tff(f1545,plain,
    spl29_124,
    inference(avatar_split_clause,[],[f490,f1542]) ).

tff(f1542,plain,
    ( spl29_124
  <=> 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(i)),a)),foldr(type,type,fun1,ts,t1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_124])]) ).

tff(f490,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(i)),a)),foldr(type,type,fun1,ts,t1))),
    inference(definition_unfolding,[],[f344,f329]) ).

tff(f344,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(cnf_transformation,[],[f36]) ).

tff(f36,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/sandbox/benchmark/theBenchmark.p',fact_35_headT) ).

tff(f1537,plain,
    spl29_123,
    inference(avatar_split_clause,[],[f454,f1535]) ).

tff(f1535,plain,
    ( spl29_123
  <=> ! [X0: $tType,X3: list(X0),X2: fun(X0,bool),X1: fun(X0,bool)] :
        ( listsp(X0,X1,X3)
        | ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_123])]) ).

tff(f454,plain,
    ! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
      ( listsp(X0,X1,X3)
      | ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ),
    inference(cnf_transformation,[],[f308]) ).

tff(f1533,plain,
    spl29_122,
    inference(avatar_split_clause,[],[f453,f1531]) ).

tff(f453,plain,
    ! [X0: $tType,X2: fun(X0,bool),X3: list(X0),X1: fun(X0,bool)] :
      ( listsp(X0,X2,X3)
      | ~ listsp(X0,aa(fun(X0,bool),fun(X0,bool),aa(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),aa(fun(X0,bool),fun(X0,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1),X3) ),
    inference(cnf_transformation,[],[f308]) ).

tff(f1523,plain,
    spl29_121,
    inference(avatar_split_clause,[],[f460,f1521]) ).

tff(f1521,plain,
    ( spl29_121
  <=> ! [X2: list(type),X4: fun(nat,type),X0: list(dB),X3: dB,X1: type] :
        ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,X3,X0)),X1))
        | ~ pp(aa(list(type),bool,typings(X4,X0),X2))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),foldr(type,type,fun1,X2,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_121])]) ).

tff(f460,plain,
    ! [X2: list(type),X3: dB,X0: list(dB),X1: type,X4: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,X3,X0)),X1))
      | ~ pp(aa(list(type),bool,typings(X4,X0),X2))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),foldr(type,type,fun1,X2,X1))) ),
    inference(cnf_transformation,[],[f242]) ).

tff(f242,plain,
    ! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,X3,X0)),X1))
      | ~ pp(aa(list(type),bool,typings(X4,X0),X2))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),foldr(type,type,fun1,X2,X1))) ),
    inference(flattening,[],[f241]) ).

tff(f241,plain,
    ! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,X3,X0)),X1))
      | ~ pp(aa(list(type),bool,typings(X4,X0),X2))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),foldr(type,type,fun1,X2,X1))) ),
    inference(ennf_transformation,[],[f194]) ).

tff(f194,plain,
    ! [X0: list(dB),X1: type,X2: list(type),X3: dB,X4: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X3),foldr(type,type,fun1,X2,X1)))
     => ( pp(aa(list(type),bool,typings(X4,X0),X2))
       => pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,X3,X0)),X1)) ) ),
    inference(rectify,[],[f58]) ).

tff(f58,axiom,
    ! [X45: list(dB),X12: type,X44: list(type),X15: dB,X14: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X15),foldr(type,type,fun1,X44,X12)))
     => ( pp(aa(list(type),bool,typings(X14,X45),X44))
       => pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),foldl(dB,dB,app,X15,X45)),X12)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_list__app__typeI) ).

tff(f1516,plain,
    spl29_120,
    inference(avatar_split_clause,[],[f433,f1514]) ).

tff(f1514,plain,
    ( spl29_120
  <=> ! [X0: type,X3: fun(nat,type),X2: nat,X1: list(dB)] :
        ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,sK21(X0,X1,X2,X3),X0)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_120])]) ).

tff(f433,plain,
    ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,sK21(X0,X1,X2,X3),X0)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
    inference(cnf_transformation,[],[f293]) ).

tff(f293,plain,
    ! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
      ( ( pp(aa(list(type),bool,typings(X3,X1),sK21(X0,X1,X2,X3)))
        & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,sK21(X0,X1,X2,X3),X0))) )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f234,f292]) ).

tff(f292,plain,
    ! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
      ( ? [X4: list(type)] :
          ( pp(aa(list(type),bool,typings(X3,X1),X4))
          & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,X4,X0))) )
     => ( pp(aa(list(type),bool,typings(X3,X1),sK21(X0,X1,X2,X3)))
        & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,sK21(X0,X1,X2,X3),X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f234,plain,
    ! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
      ( ? [X4: list(type)] :
          ( pp(aa(list(type),bool,typings(X3,X1),X4))
          & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,X4,X0))) )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
    inference(ennf_transformation,[],[f180]) ).

tff(f180,plain,
    ! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0))
     => ~ ! [X4: list(type)] :
            ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,X4,X0)))
           => ~ pp(aa(list(type),bool,typings(X3,X1),X4)) ) ),
    inference(rectify,[],[f62]) ).

tff(f62,axiom,
    ! [X12: type,X45: list(dB),X13: nat,X14: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),foldl(dB,dB,app,var(X13),X45)),X12))
     => ~ ! [X46: list(type)] :
            ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),var(X13)),foldr(type,type,fun1,X46,X12)))
           => ~ pp(aa(list(type),bool,typings(X14,X45),X46)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_var__app__typesE) ).

tff(f1505,plain,
    spl29_119,
    inference(avatar_split_clause,[],[f461,f1503]) ).

tff(f1503,plain,
    ( spl29_119
  <=> ! [X4: fun(nat,type),X0: type,X3: nat,X2: list(dB),X1: type] :
        ( ( X0 = X1 )
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X0))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_119])]) ).

tff(f461,plain,
    ! [X2: list(dB),X3: nat,X0: type,X1: type,X4: fun(nat,type)] :
      ( ( X0 = X1 )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X0))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
    inference(cnf_transformation,[],[f244]) ).

tff(f244,plain,
    ! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun(nat,type)] :
      ( ( X0 = X1 )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X0))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
    inference(flattening,[],[f243]) ).

tff(f243,plain,
    ! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun(nat,type)] :
      ( ( X0 = X1 )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X0))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X1)) ),
    inference(ennf_transformation,[],[f195]) ).

tff(f195,plain,
    ! [X0: type,X1: type,X2: list(dB),X3: nat,X4: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X1))
     => ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,var(X3),X2)),X0))
       => ( X0 = X1 ) ) ),
    inference(rectify,[],[f57]) ).

tff(f57,axiom,
    ! [X18: type,X12: type,X45: list(dB),X13: nat,X14: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),foldl(dB,dB,app,var(X13),X45)),X12))
     => ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),foldl(dB,dB,app,var(X13),X45)),X18))
       => ( X12 = X18 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_var__app__type__eq) ).

tff(f1465,plain,
    spl29_118,
    inference(avatar_split_clause,[],[f436,f1463]) ).

tff(f1463,plain,
    ( spl29_118
  <=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: dB] :
        ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),sK22(X0,X1,X2,X3)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_118])]) ).

tff(f436,plain,
    ! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X1),sK22(X0,X1,X2,X3)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)) ),
    inference(cnf_transformation,[],[f295]) ).

tff(f1461,plain,
    spl29_117,
    inference(avatar_split_clause,[],[f431,f1459]) ).

tff(f1459,plain,
    ( spl29_117
  <=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
        ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK20(X0,X1,X2,X3),X0)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_117])]) ).

tff(f431,plain,
    ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK20(X0,X1,X2,X3),X0)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
    inference(cnf_transformation,[],[f291]) ).

tff(f291,plain,
    ! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
      ( ( pp(aa(list(type),bool,typings(X3,X1),sK20(X0,X1,X2,X3)))
        & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK20(X0,X1,X2,X3),X0))) )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f233,f290]) ).

tff(f290,plain,
    ! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
      ( ? [X4: list(type)] :
          ( pp(aa(list(type),bool,typings(X3,X1),X4))
          & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0))) )
     => ( pp(aa(list(type),bool,typings(X3,X1),sK20(X0,X1,X2,X3)))
        & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK20(X0,X1,X2,X3),X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f233,plain,
    ! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
      ( ? [X4: list(type)] :
          ( pp(aa(list(type),bool,typings(X3,X1),X4))
          & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0))) )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
    inference(ennf_transformation,[],[f179]) ).

tff(f179,plain,
    ! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0))
     => ? [X4: list(type)] :
          ( pp(aa(list(type),bool,typings(X3,X1),X4))
          & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0))) ) ),
    inference(rectify,[],[f73]) ).

tff(f73,axiom,
    ! [X12: type,X45: list(dB),X15: dB,X14: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),foldl(dB,dB,app,X15,X45)),X12))
     => ? [X46: list(type)] :
          ( pp(aa(list(type),bool,typings(X14,X45),X46))
          & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X15),foldr(type,type,fun1,X46,X12))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_list__app__typeD) ).

tff(f1457,plain,
    spl29_116,
    inference(avatar_split_clause,[],[f429,f1455]) ).

tff(f1455,plain,
    ( spl29_116
  <=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
        ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK19(X0,X1,X2,X3),X0)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_116])]) ).

tff(f429,plain,
    ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK19(X0,X1,X2,X3),X0)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
    inference(cnf_transformation,[],[f289]) ).

tff(f289,plain,
    ! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
      ( ( pp(aa(list(type),bool,typings(X3,X1),sK19(X0,X1,X2,X3)))
        & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK19(X0,X1,X2,X3),X0))) )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f232,f288]) ).

tff(f288,plain,
    ! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
      ( ? [X4: list(type)] :
          ( pp(aa(list(type),bool,typings(X3,X1),X4))
          & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0))) )
     => ( pp(aa(list(type),bool,typings(X3,X1),sK19(X0,X1,X2,X3)))
        & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK19(X0,X1,X2,X3),X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f232,plain,
    ! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
      ( ? [X4: list(type)] :
          ( pp(aa(list(type),bool,typings(X3,X1),X4))
          & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0))) )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
    inference(ennf_transformation,[],[f178]) ).

tff(f178,plain,
    ! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0))
     => ~ ! [X4: list(type)] :
            ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0)))
           => ~ pp(aa(list(type),bool,typings(X3,X1),X4)) ) ),
    inference(rectify,[],[f72]) ).

tff(f72,axiom,
    ! [X12: type,X45: list(dB),X15: dB,X14: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),foldl(dB,dB,app,X15,X45)),X12))
     => ~ ! [X46: list(type)] :
            ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),X15),foldr(type,type,fun1,X46,X12)))
           => ~ pp(aa(list(type),bool,typings(X14,X45),X46)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_list__app__typeE) ).

tff(f1453,plain,
    spl29_115,
    inference(avatar_split_clause,[],[f420,f1451]) ).

tff(f1451,plain,
    ( spl29_115
  <=> ! [X2: dB,X0: list(dB),X1: dB] :
        ( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
        | ~ pp(aa(dB,bool,it,X1))
        | ~ 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,X2),X1),zero_zero(nat)),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_115])]) ).

tff(f420,plain,
    ! [X2: dB,X0: list(dB),X1: dB] :
      ( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
      | ~ pp(aa(dB,bool,it,X1))
      | ~ 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,X2),X1),zero_zero(nat)),X0))) ),
    inference(cnf_transformation,[],[f231]) ).

tff(f231,plain,
    ! [X0: list(dB),X1: dB,X2: dB] :
      ( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
      | ~ pp(aa(dB,bool,it,X1))
      | ~ 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,X2),X1),zero_zero(nat)),X0))) ),
    inference(flattening,[],[f230]) ).

tff(f230,plain,
    ! [X0: list(dB),X1: dB,X2: dB] :
      ( pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)))
      | ~ pp(aa(dB,bool,it,X1))
      | ~ 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,X2),X1),zero_zero(nat)),X0))) ),
    inference(ennf_transformation,[],[f171]) ).

tff(f171,plain,
    ! [X0: list(dB),X1: dB,X2: 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,X2),X1),zero_zero(nat)),X0)))
     => ( pp(aa(dB,bool,it,X1))
       => pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0))) ) ),
    inference(rectify,[],[f83]) ).

tff(f83,axiom,
    ! [X61: list(dB),X38: dB,X60: 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,X60),X38),zero_zero(nat)),X61)))
     => ( pp(aa(dB,bool,it,X38))
       => pp(aa(dB,bool,it,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X60)),X38),X61))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Beta) ).

tff(f1449,plain,
    spl29_114,
    inference(avatar_split_clause,[],[f407,f1447]) ).

tff(f1447,plain,
    ( spl29_114
  <=> ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_114])]) ).

tff(f407,plain,
    ! [X2: dB,X0: nat,X1: list(dB)] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X0),X1)) ),
    inference(cnf_transformation,[],[f159]) ).

tff(f159,plain,
    ! [X0: nat,X1: list(dB),X2: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X0),X1)) ),
    inference(rectify,[],[f60]) ).

tff(f60,axiom,
    ! [X13: nat,X45: list(dB),X15: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,foldl(dB,dB,app,X15,X45)),X13) = foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X15),X13),map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),X13),X45)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_lift__map) ).

tff(f1431,plain,
    spl29_113,
    inference(avatar_split_clause,[],[f488,f1428]) ).

tff(f1428,plain,
    ( spl29_113
  <=> 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(i),rs)),t1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_113])]) ).

tff(f488,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(i),rs)),t1)),
    inference(definition_unfolding,[],[f342,f329]) ).

tff(f342,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(cnf_transformation,[],[f51]) ).

tff(f51,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/sandbox/benchmark/theBenchmark.p',fact_50_nT) ).

tff(f1426,plain,
    spl29_112,
    inference(avatar_split_clause,[],[f487,f1423]) ).

tff(f1423,plain,
    ( spl29_112
  <=> 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(i),rs)),t_a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_112])]) ).

tff(f487,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(i),rs)),t_a)),
    inference(definition_unfolding,[],[f341,f329]) ).

tff(f341,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(cnf_transformation,[],[f54]) ).

tff(f54,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/sandbox/benchmark/theBenchmark.p',fact_53_Var_I2_J) ).

tff(f1421,plain,
    spl29_111,
    inference(avatar_split_clause,[],[f415,f1419]) ).

tff(f1419,plain,
    ( spl29_111
  <=> ! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
        ( 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,X2)),X1)
        | ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_111])]) ).

tff(f415,plain,
    ! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
      ( 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,X2)),X1)
      | ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ),
    inference(cnf_transformation,[],[f226]) ).

tff(f226,plain,
    ! [X0: list(type),X1: list(dB),X2: fun(nat,type)] :
      ( 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,X2)),X1)
      | ~ pp(aa(list(type),bool,typings(X2,X1),X0)) ),
    inference(ennf_transformation,[],[f167]) ).

tff(f167,plain,
    ! [X0: list(type),X1: list(dB),X2: fun(nat,type)] :
      ( pp(aa(list(type),bool,typings(X2,X1),X0))
     => 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,X2)),X1) ),
    inference(rectify,[],[f49]) ).

tff(f49,axiom,
    ! [X44: list(type),X45: list(dB),X14: fun(nat,type)] :
      ( pp(aa(list(type),bool,typings(X14,X45),X44))
     => 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,X14)),X45) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_lists__typings) ).

tff(f1397,plain,
    spl29_110,
    inference(avatar_split_clause,[],[f499,f1395]) ).

tff(f1395,plain,
    ( spl29_110
  <=> ! [X2: dB,X1: dB,X3: list(dB)] :
        ( sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3))
        | ~ pp(aa(dB,bool,it,X2))
        | ~ 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,X1),X2),zero_zero(nat)),X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_110])]) ).

tff(f499,plain,
    ! [X2: dB,X3: list(dB),X1: dB] :
      ( sP0(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3))
      | ~ pp(aa(dB,bool,it,X2))
      | ~ 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,X1),X2),zero_zero(nat)),X3))) ),
    inference(equality_resolution,[],[f376]) ).

tff(f376,plain,
    ! [X2: dB,X3: list(dB),X0: dB,X1: dB] :
      ( sP0(X0)
      | ~ pp(aa(dB,bool,it,X2))
      | ~ 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,X1),X2),zero_zero(nat)),X3)))
      | ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ),
    inference(cnf_transformation,[],[f278]) ).

tff(f278,plain,
    ! [X0: dB] :
      ( ( sP0(X0)
        | ! [X1: dB,X2: dB,X3: list(dB)] :
            ( ~ pp(aa(dB,bool,it,X2))
            | ~ 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,X1),X2),zero_zero(nat)),X3)))
            | ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
      & ( ( pp(aa(dB,bool,it,sK13(X0)))
          & 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,sK12(X0)),sK13(X0)),zero_zero(nat)),sK14(X0))))
          & ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK12(X0))),sK13(X0)),sK14(X0)) = X0 ) )
        | ~ sP0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f276,f277]) ).

tff(f277,plain,
    ! [X0: dB] :
      ( ? [X4: dB,X5: dB,X6: list(dB)] :
          ( pp(aa(dB,bool,it,X5))
          & 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,X4),X5),zero_zero(nat)),X6)))
          & ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X4)),X5),X6) = X0 ) )
     => ( pp(aa(dB,bool,it,sK13(X0)))
        & 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,sK12(X0)),sK13(X0)),zero_zero(nat)),sK14(X0))))
        & ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK12(X0))),sK13(X0)),sK14(X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f276,plain,
    ! [X0: dB] :
      ( ( sP0(X0)
        | ! [X1: dB,X2: dB,X3: list(dB)] :
            ( ~ pp(aa(dB,bool,it,X2))
            | ~ 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,X1),X2),zero_zero(nat)),X3)))
            | ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
      & ( ? [X4: dB,X5: dB,X6: list(dB)] :
            ( pp(aa(dB,bool,it,X5))
            & 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,X4),X5),zero_zero(nat)),X6)))
            & ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X4)),X5),X6) = X0 ) )
        | ~ sP0(X0) ) ),
    inference(rectify,[],[f275]) ).

tff(f275,plain,
    ! [X0: dB] :
      ( ( sP0(X0)
        | ! [X1: dB,X2: dB,X3: list(dB)] :
            ( ~ pp(aa(dB,bool,it,X2))
            | ~ 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,X1),X2),zero_zero(nat)),X3)))
            | ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
      & ( ? [X1: dB,X2: dB,X3: list(dB)] :
            ( pp(aa(dB,bool,it,X2))
            & 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,X1),X2),zero_zero(nat)),X3)))
            & ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) )
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f257]) ).

tff(f257,plain,
    ! [X0: dB] :
      ( sP0(X0)
    <=> ? [X1: dB,X2: dB,X3: list(dB)] :
          ( pp(aa(dB,bool,it,X2))
          & 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,X1),X2),zero_zero(nat)),X3)))
          & ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f1393,plain,
    spl29_109,
    inference(avatar_split_clause,[],[f477,f1391]) ).

tff(f1391,plain,
    ( spl29_109
  <=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
        ( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK26(X0,X1,X2,X3,X4,X5)),sK27(X0,X1,X2,X3,X4,X5)) = X2 )
        | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_109])]) ).

tff(f477,plain,
    ! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
      ( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK26(X0,X1,X2,X3,X4,X5)),sK27(X0,X1,X2,X3,X4,X5)) = X2 )
      | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ),
    inference(cnf_transformation,[],[f318]) ).

tff(f318,plain,
    ! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
      ( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
        | ! [X6: X1,X7: list(X1)] :
            ( ( map(X1,X0,X3,X7) != X4 )
            | ( aa(X1,X0,X3,X6) != X5 )
            | ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) != X2 ) ) )
      & ( ( ( map(X1,X0,X3,sK27(X0,X1,X2,X3,X4,X5)) = X4 )
          & ( aa(X1,X0,X3,sK26(X0,X1,X2,X3,X4,X5)) = X5 )
          & ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK26(X0,X1,X2,X3,X4,X5)),sK27(X0,X1,X2,X3,X4,X5)) = X2 ) )
        | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f316,f317]) ).

tff(f317,plain,
    ! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
      ( ? [X8: X1,X9: list(X1)] :
          ( ( map(X1,X0,X3,X9) = X4 )
          & ( aa(X1,X0,X3,X8) = X5 )
          & ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X8),X9) = X2 ) )
     => ( ( map(X1,X0,X3,sK27(X0,X1,X2,X3,X4,X5)) = X4 )
        & ( aa(X1,X0,X3,sK26(X0,X1,X2,X3,X4,X5)) = X5 )
        & ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),sK26(X0,X1,X2,X3,X4,X5)),sK27(X0,X1,X2,X3,X4,X5)) = X2 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f316,plain,
    ! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
      ( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
        | ! [X6: X1,X7: list(X1)] :
            ( ( map(X1,X0,X3,X7) != X4 )
            | ( aa(X1,X0,X3,X6) != X5 )
            | ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) != X2 ) ) )
      & ( ? [X8: X1,X9: list(X1)] :
            ( ( map(X1,X0,X3,X9) = X4 )
            & ( aa(X1,X0,X3,X8) = X5 )
            & ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X8),X9) = X2 ) )
        | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
    inference(rectify,[],[f315]) ).

tff(f315,plain,
    ! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
      ( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
        | ! [X6: X1,X7: list(X1)] :
            ( ( map(X1,X0,X3,X7) != X4 )
            | ( aa(X1,X0,X3,X6) != X5 )
            | ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) != X2 ) ) )
      & ( ? [X6: X1,X7: list(X1)] :
            ( ( map(X1,X0,X3,X7) = X4 )
            & ( aa(X1,X0,X3,X6) = X5 )
            & ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) = X2 ) )
        | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
    inference(nnf_transformation,[],[f206]) ).

tff(f206,plain,
    ! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
      ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) = map(X1,X0,X3,X2) )
    <=> ? [X6: X1,X7: list(X1)] :
          ( ( map(X1,X0,X3,X7) = X4 )
          & ( aa(X1,X0,X3,X6) = X5 )
          & ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X6),X7) = X2 ) ) ),
    inference(rectify,[],[f75]) ).

tff(f75,axiom,
    ! [X0: $tType,X1: $tType,X67: list(X1),X52: fun(X1,X0),X51: list(X0),X36: X0] :
      ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X36),X51) = map(X1,X0,X52,X67) )
    <=> ? [X68: X1,X69: list(X1)] :
          ( ( map(X1,X0,X52,X69) = X51 )
          & ( aa(X1,X0,X52,X68) = X36 )
          & ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X68),X69) = X67 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Cons__eq__map__conv) ).

tff(f1389,plain,
    spl29_108,
    inference(avatar_split_clause,[],[f473,f1387]) ).

tff(f1387,plain,
    ( spl29_108
  <=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun(X0,X1),X2: list(X1)] :
        ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK24(X0,X1,X2,X3,X4,X5)),sK25(X0,X1,X2,X3,X4,X5)) = X4 )
        | ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_108])]) ).

tff(f473,plain,
    ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
      ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK24(X0,X1,X2,X3,X4,X5)),sK25(X0,X1,X2,X3,X4,X5)) = X4 )
      | ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ),
    inference(cnf_transformation,[],[f314]) ).

tff(f314,plain,
    ! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
      ( ( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
        | ! [X6: X0,X7: list(X0)] :
            ( ( map(X0,X1,X5,X7) != X2 )
            | ( aa(X0,X1,X5,X6) != X3 )
            | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) != X4 ) ) )
      & ( ( ( map(X0,X1,X5,sK25(X0,X1,X2,X3,X4,X5)) = X2 )
          & ( aa(X0,X1,X5,sK24(X0,X1,X2,X3,X4,X5)) = X3 )
          & ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK24(X0,X1,X2,X3,X4,X5)),sK25(X0,X1,X2,X3,X4,X5)) = X4 ) )
        | ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25])],[f312,f313]) ).

tff(f313,plain,
    ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
      ( ? [X8: X0,X9: list(X0)] :
          ( ( map(X0,X1,X5,X9) = X2 )
          & ( aa(X0,X1,X5,X8) = X3 )
          & ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X8),X9) = X4 ) )
     => ( ( map(X0,X1,X5,sK25(X0,X1,X2,X3,X4,X5)) = X2 )
        & ( aa(X0,X1,X5,sK24(X0,X1,X2,X3,X4,X5)) = X3 )
        & ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK24(X0,X1,X2,X3,X4,X5)),sK25(X0,X1,X2,X3,X4,X5)) = X4 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f312,plain,
    ! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
      ( ( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
        | ! [X6: X0,X7: list(X0)] :
            ( ( map(X0,X1,X5,X7) != X2 )
            | ( aa(X0,X1,X5,X6) != X3 )
            | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) != X4 ) ) )
      & ( ? [X8: X0,X9: list(X0)] :
            ( ( map(X0,X1,X5,X9) = X2 )
            & ( aa(X0,X1,X5,X8) = X3 )
            & ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X8),X9) = X4 ) )
        | ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
    inference(rectify,[],[f311]) ).

tff(f311,plain,
    ! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
      ( ( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
        | ! [X6: X0,X7: list(X0)] :
            ( ( map(X0,X1,X5,X7) != X2 )
            | ( aa(X0,X1,X5,X6) != X3 )
            | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) != X4 ) ) )
      & ( ? [X6: X0,X7: list(X0)] :
            ( ( map(X0,X1,X5,X7) = X2 )
            & ( aa(X0,X1,X5,X6) = X3 )
            & ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) = X4 ) )
        | ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
    inference(nnf_transformation,[],[f205]) ).

tff(f205,plain,
    ! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
      ( ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) = map(X0,X1,X5,X4) )
    <=> ? [X6: X0,X7: list(X0)] :
          ( ( map(X0,X1,X5,X7) = X2 )
          & ( aa(X0,X1,X5,X6) = X3 )
          & ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X6),X7) = X4 ) ) ),
    inference(rectify,[],[f80]) ).

tff(f80,axiom,
    ! [X1: $tType,X0: $tType,X67: list(X0),X74: X0,X51: list(X1),X52: fun(X1,X0)] :
      ( ( map(X1,X0,X52,X51) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X74),X67) )
    <=> ? [X68: X1,X69: list(X1)] :
          ( ( map(X1,X0,X52,X69) = X67 )
          & ( aa(X1,X0,X52,X68) = X74 )
          & ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X68),X69) = X51 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_map__eq__Cons__conv) ).

tff(f1374,plain,
    spl29_107,
    inference(avatar_split_clause,[],[f406,f1372]) ).

tff(f1372,plain,
    ( spl29_107
  <=> ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_107])]) ).

tff(f406,plain,
    ! [X2: dB,X0: nat,X1: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) ),
    inference(cnf_transformation,[],[f158]) ).

tff(f158,plain,
    ! [X0: nat,X1: dB,X2: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X0)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)) ),
    inference(rectify,[],[f26]) ).

tff(f26,axiom,
    ! [X24: nat,X10: dB,X23: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),lift,aa(dB,dB,aa(dB,fun(dB,dB),app,X23),X10)),X24) = aa(dB,dB,aa(dB,fun(dB,dB),app,aa(nat,dB,aa(dB,fun(nat,dB),lift,X23),X24)),aa(nat,dB,aa(dB,fun(nat,dB),lift,X10),X24)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_lift_Osimps_I2_J) ).

tff(f1364,plain,
    spl29_106,
    inference(avatar_split_clause,[],[f356,f1361]) ).

tff(f1361,plain,
    ( spl29_106
  <=> 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),sK7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_106])]) ).

tff(f356,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),sK7)),
    inference(cnf_transformation,[],[f265]) ).

tff(f1359,plain,
    spl29_105,
    inference(avatar_split_clause,[],[f354,f1356]) ).

tff(f1356,plain,
    ( spl29_105
  <=> 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)),b),sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_105])]) ).

tff(f354,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)),b),sK6)),
    inference(cnf_transformation,[],[f263]) ).

tff(f1354,plain,
    spl29_104,
    inference(avatar_split_clause,[],[f340,f1351]) ).

tff(f1351,plain,
    ( spl29_104
  <=> 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)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_104])]) ).

tff(f340,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(cnf_transformation,[],[f12]) ).

tff(f12,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/sandbox/benchmark/theBenchmark.p',fact_11_argT) ).

tff(f1215,plain,
    ( spl29_103
    | ~ spl29_10
    | ~ spl29_24 ),
    inference(avatar_split_clause,[],[f664,f650,f569,f1212]) ).

tff(f1212,plain,
    ( spl29_103
  <=> sP1(abs(ua)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_103])]) ).

tff(f569,plain,
    ( spl29_10
  <=> pp(aa(dB,bool,it,ua)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_10])]) ).

tff(f664,plain,
    ( sP1(abs(ua))
    | ~ spl29_10
    | ~ spl29_24 ),
    inference(resolution,[],[f651,f571]) ).

tff(f571,plain,
    ( pp(aa(dB,bool,it,ua))
    | ~ spl29_10 ),
    inference(avatar_component_clause,[],[f569]) ).

tff(f1210,plain,
    spl29_102,
    inference(avatar_split_clause,[],[f471,f1208]) ).

tff(f1208,plain,
    ( spl29_102
  <=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X2,fun(X1,X0)),X4: fun(X2,X1),X3: X2] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X2,fun(X1,X0)),fun(fun(X2,X1),fun(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_102])]) ).

tff(f471,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X2,fun(X1,X0))] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X2,fun(X1,X0)),fun(fun(X2,X1),fun(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ),
    inference(cnf_transformation,[],[f203]) ).

tff(f203,plain,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X2,fun(X1,X0))] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X2,fun(X1,X0)),fun(fun(X2,X1),fun(X2,X0)),combs(X2,X1,X0),X5),X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ),
    inference(rectify,[],[f108]) ).

tff(f108,axiom,
    ! [X2: $tType,X1: $tType,X0: $tType,X90: X0,X91: fun(X0,X1),X89: fun(X0,fun(X1,X2))] : ( aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2)),combs(X0,X1,X2),X89),X91),X90) = aa(X1,X2,aa(X0,fun(X1,X2),X89,X90),aa(X0,X1,X91,X90)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).

tff(f1206,plain,
    spl29_101,
    inference(avatar_split_clause,[],[f456,f1204]) ).

tff(f1204,plain,
    ( spl29_101
  <=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: X1,X2: list(X1)] : ( map(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_101])]) ).

tff(f456,plain,
    ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( map(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) ),
    inference(cnf_transformation,[],[f190]) ).

tff(f190,plain,
    ! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( map(X1,X0,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X4,X3)),map(X1,X0,X4,X2)) ),
    inference(rectify,[],[f64]) ).

tff(f64,axiom,
    ! [X0: $tType,X1: $tType,X51: list(X1),X36: X1,X52: fun(X1,X0)] : ( map(X1,X0,X52,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X36),X51)) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),aa(X1,X0,X52,X36)),map(X1,X0,X52,X51)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_map_Osimps_I2_J) ).

tff(f1201,plain,
    spl29_100,
    inference(avatar_split_clause,[],[f417,f1199]) ).

tff(f1199,plain,
    ( spl29_100
  <=> ! [X2: fun(nat,type),X0: type,X1: dB] :
        ( ( aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2)),sK18(X0,X1,X2)) = X0 )
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_100])]) ).

tff(f417,plain,
    ! [X2: fun(nat,type),X0: type,X1: dB] :
      ( ( aa(type,type,aa(type,fun(type,type),fun1,sK17(X0,X1,X2)),sK18(X0,X1,X2)) = X0 )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),abs(X1)),X0)) ),
    inference(cnf_transformation,[],[f285]) ).

tff(f1195,plain,
    spl29_99,
    inference(avatar_split_clause,[],[f434,f1193]) ).

tff(f1193,plain,
    ( spl29_99
  <=> ! [X0: type,X3: fun(nat,type),X2: nat,X1: list(dB)] :
        ( pp(aa(list(type),bool,typings(X3,X1),sK21(X0,X1,X2,X3)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_99])]) ).

tff(f434,plain,
    ! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
      ( pp(aa(list(type),bool,typings(X3,X1),sK21(X0,X1,X2,X3)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0)) ),
    inference(cnf_transformation,[],[f293]) ).

tff(f1187,plain,
    spl29_98,
    inference(avatar_split_clause,[],[f432,f1185]) ).

tff(f1185,plain,
    ( spl29_98
  <=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
        ( pp(aa(list(type),bool,typings(X3,X1),sK20(X0,X1,X2,X3)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_98])]) ).

tff(f432,plain,
    ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
      ( pp(aa(list(type),bool,typings(X3,X1),sK20(X0,X1,X2,X3)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
    inference(cnf_transformation,[],[f291]) ).

tff(f1183,plain,
    spl29_97,
    inference(avatar_split_clause,[],[f430,f1181]) ).

tff(f1181,plain,
    ( spl29_97
  <=> ! [X0: type,X3: fun(nat,type),X2: dB,X1: list(dB)] :
        ( pp(aa(list(type),bool,typings(X3,X1),sK19(X0,X1,X2,X3)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_97])]) ).

tff(f430,plain,
    ! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
      ( pp(aa(list(type),bool,typings(X3,X1),sK19(X0,X1,X2,X3)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
    inference(cnf_transformation,[],[f289]) ).

tff(f1179,plain,
    ( spl29_96
    | ~ spl29_11
    | ~ spl29_24 ),
    inference(avatar_split_clause,[],[f663,f650,f574,f1176]) ).

tff(f1176,plain,
    ( spl29_96
  <=> sP1(abs(u)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_96])]) ).

tff(f574,plain,
    ( spl29_11
  <=> pp(aa(dB,bool,it,u)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_11])]) ).

tff(f663,plain,
    ( sP1(abs(u))
    | ~ spl29_11
    | ~ spl29_24 ),
    inference(resolution,[],[f651,f576]) ).

tff(f576,plain,
    ( pp(aa(dB,bool,it,u))
    | ~ spl29_11 ),
    inference(avatar_component_clause,[],[f574]) ).

tff(f1098,plain,
    spl29_95,
    inference(avatar_split_clause,[],[f470,f1096]) ).

tff(f1096,plain,
    ( spl29_95
  <=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X1,X0),X4: fun(X2,X1),X3: X2] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_95])]) ).

tff(f470,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
    inference(cnf_transformation,[],[f202]) ).

tff(f202,plain,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,aa(fun(X2,X1),fun(X2,X0),aa(fun(X1,X0),fun(fun(X2,X1),fun(X2,X0)),combb(X1,X0,X2),X5),X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
    inference(rectify,[],[f105]) ).

tff(f105,axiom,
    ! [X2: $tType,X1: $tType,X0: $tType,X90: X0,X91: fun(X0,X1),X89: fun(X1,X2)] : ( aa(X0,X2,aa(fun(X0,X1),fun(X0,X2),aa(fun(X1,X2),fun(fun(X0,X1),fun(X0,X2)),combb(X1,X2,X0),X89),X91),X90) = aa(X1,X2,X89,aa(X0,X1,X91,X90)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).

tff(f1094,plain,
    spl29_94,
    inference(avatar_split_clause,[],[f469,f1092]) ).

tff(f1092,plain,
    ( spl29_94
  <=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_94])]) ).

tff(f469,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
    inference(cnf_transformation,[],[f201]) ).

tff(f201,plain,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,aa(X2,fun(X0,X1),aa(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X5),X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
    inference(rectify,[],[f106]) ).

tff(f106,axiom,
    ! [X0: $tType,X2: $tType,X1: $tType,X90: X0,X91: X1,X89: fun(X0,fun(X1,X2))] : ( aa(X0,X2,aa(X1,fun(X0,X2),aa(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2)),combc(X0,X1,X2),X89),X91),X90) = aa(X1,X2,aa(X0,fun(X1,X2),X89,X90),X91) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).

tff(f1090,plain,
    spl29_93,
    inference(avatar_split_clause,[],[f468,f1088]) ).

tff(f1088,plain,
    ( spl29_93
  <=> ! [X1: $tType,X0: $tType,X3: X1,X4: X0,X5: fun(X0,fun(X1,X0)),X2: list(X1)] : ( foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_93])]) ).

tff(f468,plain,
    ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) ),
    inference(cnf_transformation,[],[f200]) ).

tff(f200,plain,
    ! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) ),
    inference(rectify,[],[f70]) ).

tff(f70,axiom,
    ! [X0: $tType,X1: $tType,X51: list(X1),X36: X1,X53: X0,X52: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X52,X53,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X36),X51)) = foldl(X0,X1,X52,aa(X1,X0,aa(X0,fun(X1,X0),X52,X53),X36),X51) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_foldl__Cons) ).

tff(f1086,plain,
    spl29_92,
    inference(avatar_split_clause,[],[f467,f1084]) ).

tff(f1084,plain,
    ( spl29_92
  <=> ! [X1: $tType,X0: $tType,X3: list(X0),X4: X0,X5: fun(X0,fun(X1,X1)),X2: X1] : ( foldr(X0,X1,X5,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),X2) = aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_92])]) ).

tff(f467,plain,
    ! [X1: $tType,X0: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun(X0,fun(X1,X1))] : ( foldr(X0,X1,X5,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),X2) = aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) ),
    inference(cnf_transformation,[],[f199]) ).

tff(f199,plain,
    ! [X0: $tType,X1: $tType,X2: X1,X3: list(X0),X4: X0,X5: fun(X0,fun(X1,X1))] : ( foldr(X0,X1,X5,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3),X2) = aa(X1,X1,aa(X0,fun(X1,X1),X5,X4),foldr(X0,X1,X5,X3,X2)) ),
    inference(rectify,[],[f67]) ).

tff(f67,axiom,
    ! [X1: $tType,X0: $tType,X53: X0,X51: list(X1),X36: X1,X52: fun(X1,fun(X0,X0))] : ( foldr(X1,X0,X52,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X36),X51),X53) = aa(X0,X0,aa(X1,fun(X0,X0),X52,X36),foldr(X1,X0,X52,X51,X53)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_foldr_Osimps_I2_J) ).

tff(f1082,plain,
    spl29_91,
    inference(avatar_split_clause,[],[f464,f1080]) ).

tff(f1080,plain,
    ( spl29_91
  <=> ! [X0: $tType,X2: X0,X4: X0,X3: list(X0),X1: list(X0)] :
        ( ( X1 = X3 )
        | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_91])]) ).

tff(f464,plain,
    ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
      ( ( X1 = X3 )
      | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ),
    inference(cnf_transformation,[],[f310]) ).

tff(f310,plain,
    ! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
      ( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
        | ( X1 != X3 )
        | ( X2 != X4 ) )
      & ( ( ( X1 = X3 )
          & ( X2 = X4 ) )
        | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
    inference(flattening,[],[f309]) ).

tff(f309,plain,
    ! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
      ( ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
        | ( X1 != X3 )
        | ( X2 != X4 ) )
      & ( ( ( X1 = X3 )
          & ( X2 = X4 ) )
        | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
    inference(nnf_transformation,[],[f197]) ).

tff(f197,plain,
    ! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
      ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) )
    <=> ( ( X1 = X3 )
        & ( X2 = X4 ) ) ),
    inference(rectify,[],[f63]) ).

tff(f63,axiom,
    ! [X0: $tType,X57: list(X0),X58: X0,X59: list(X0),X53: X0] :
      ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X53),X59) = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X58),X57) )
    <=> ( ( X57 = X59 )
        & ( X53 = X58 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_list_Oinject) ).

tff(f1078,plain,
    ( spl29_90
    | ~ spl29_9
    | ~ spl29_24 ),
    inference(avatar_split_clause,[],[f662,f650,f564,f1075]) ).

tff(f1075,plain,
    ( spl29_90
  <=> sP1(abs(t3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_90])]) ).

tff(f564,plain,
    ( spl29_9
  <=> pp(aa(dB,bool,it,t3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_9])]) ).

tff(f662,plain,
    ( sP1(abs(t3))
    | ~ spl29_9
    | ~ spl29_24 ),
    inference(resolution,[],[f651,f566]) ).

tff(f566,plain,
    ( pp(aa(dB,bool,it,t3))
    | ~ spl29_9 ),
    inference(avatar_component_clause,[],[f564]) ).

tff(f1066,plain,
    spl29_89,
    inference(avatar_split_clause,[],[f479,f1064]) ).

tff(f1064,plain,
    ( spl29_89
  <=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
        ( ( map(X1,X0,X3,sK27(X0,X1,X2,X3,X4,X5)) = X4 )
        | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_89])]) ).

tff(f479,plain,
    ! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
      ( ( map(X1,X0,X3,sK27(X0,X1,X2,X3,X4,X5)) = X4 )
      | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ),
    inference(cnf_transformation,[],[f318]) ).

tff(f1062,plain,
    spl29_88,
    inference(avatar_split_clause,[],[f475,f1060]) ).

tff(f1060,plain,
    ( spl29_88
  <=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun(X0,X1),X2: list(X1)] :
        ( ( map(X0,X1,X5,sK25(X0,X1,X2,X3,X4,X5)) = X2 )
        | ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_88])]) ).

tff(f475,plain,
    ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
      ( ( map(X0,X1,X5,sK25(X0,X1,X2,X3,X4,X5)) = X2 )
      | ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ),
    inference(cnf_transformation,[],[f314]) ).

tff(f1058,plain,
    spl29_87,
    inference(avatar_split_clause,[],[f463,f1056]) ).

tff(f1056,plain,
    ( spl29_87
  <=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] :
        ( ( X2 = X4 )
        | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_87])]) ).

tff(f463,plain,
    ! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
      ( ( X2 = X4 )
      | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X4),X3) ) ),
    inference(cnf_transformation,[],[f310]) ).

tff(f1046,plain,
    ( spl29_86
    | ~ spl29_14
    | ~ spl29_16 ),
    inference(avatar_split_clause,[],[f629,f605,f596,f1044]) ).

tff(f1044,plain,
    ( spl29_86
  <=> ! [X0: nat] : sP1(var(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_86])]) ).

tff(f629,plain,
    ( ! [X0: nat] : sP1(var(X0))
    | ~ spl29_14
    | ~ spl29_16 ),
    inference(resolution,[],[f606,f597]) ).

tff(f1042,plain,
    spl29_85,
    inference(avatar_split_clause,[],[f478,f1040]) ).

tff(f1040,plain,
    ( spl29_85
  <=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
        ( ( aa(X1,X0,X3,sK26(X0,X1,X2,X3,X4,X5)) = X5 )
        | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_85])]) ).

tff(f478,plain,
    ! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
      ( ( aa(X1,X0,X3,sK26(X0,X1,X2,X3,X4,X5)) = X5 )
      | ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X4) != map(X1,X0,X3,X2) ) ),
    inference(cnf_transformation,[],[f318]) ).

tff(f1038,plain,
    spl29_84,
    inference(avatar_split_clause,[],[f474,f1036]) ).

tff(f1036,plain,
    ( spl29_84
  <=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun(X0,X1),X2: list(X1)] :
        ( ( aa(X0,X1,X5,sK24(X0,X1,X2,X3,X4,X5)) = X3 )
        | ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_84])]) ).

tff(f474,plain,
    ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
      ( ( aa(X0,X1,X5,sK24(X0,X1,X2,X3,X4,X5)) = X3 )
      | ( aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2) != map(X0,X1,X5,X4) ) ),
    inference(cnf_transformation,[],[f314]) ).

tff(f1034,plain,
    spl29_83,
    inference(avatar_split_clause,[],[f358,f1031]) ).

tff(f1031,plain,
    ( spl29_83
  <=> 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),sK8)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_83])]) ).

tff(f358,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),sK8)),
    inference(cnf_transformation,[],[f267]) ).

tff(f1029,plain,
    spl29_82,
    inference(avatar_split_clause,[],[f338,f1026]) ).

tff(f1026,plain,
    ( spl29_82
  <=> 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)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_82])]) ).

tff(f338,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(cnf_transformation,[],[f16]) ).

tff(f16,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/sandbox/benchmark/theBenchmark.p',fact_15_argsT) ).

tff(f1012,plain,
    spl29_81,
    inference(avatar_split_clause,[],[f466,f1010]) ).

tff(f466,plain,
    ! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( list_case(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) ),
    inference(cnf_transformation,[],[f198]) ).

tff(f198,plain,
    ! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun(X1,fun(list(X1),X0)),X5: X0] : ( list_case(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X4,X3),X2) ),
    inference(rectify,[],[f79]) ).

tff(f79,axiom,
    ! [X0: $tType,X1: $tType,X59: list(X1),X53: X1,X72: fun(X1,fun(list(X1),X0)),X73: X0] : ( list_case(X0,X1,X73,X72,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X53),X59)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X72,X53),X59) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_list_Osimps_I5_J) ).

tff(f1008,plain,
    spl29_80,
    inference(avatar_split_clause,[],[f374,f1006]) ).

tff(f1006,plain,
    ( spl29_80
  <=> ! [X0: 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,sK12(X0)),sK13(X0)),zero_zero(nat)),sK14(X0))))
        | ~ sP0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_80])]) ).

tff(f374,plain,
    ! [X0: 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,sK12(X0)),sK13(X0)),zero_zero(nat)),sK14(X0))))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f278]) ).

tff(f996,plain,
    spl29_79,
    inference(avatar_split_clause,[],[f513,f994]) ).

tff(f994,plain,
    ( spl29_79
  <=> ! [X0: $tType,X2: fun(nat,X0),X4: nat,X1: X0] : ( aa(nat,X0,aa(X0,fun(nat,X0),aa(nat,fun(X0,fun(nat,X0)),aa(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0))),shift(X0),X2),X4),X1),X4) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_79])]) ).

tff(f513,plain,
    ! [X0: $tType,X2: fun(nat,X0),X1: X0,X4: nat] : ( aa(nat,X0,aa(X0,fun(nat,X0),aa(nat,fun(X0,fun(nat,X0)),aa(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0))),shift(X0),X2),X4),X1),X4) = X1 ),
    inference(equality_resolution,[],[f457]) ).

tff(f457,plain,
    ! [X0: $tType,X2: fun(nat,X0),X3: nat,X1: X0,X4: nat] :
      ( ( aa(nat,X0,aa(X0,fun(nat,X0),aa(nat,fun(X0,fun(nat,X0)),aa(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0))),shift(X0),X2),X4),X1),X3) = X1 )
      | ( X3 != X4 ) ),
    inference(cnf_transformation,[],[f238]) ).

tff(f238,plain,
    ! [X0: $tType,X1: X0,X2: fun(nat,X0),X3: nat,X4: nat] :
      ( ( aa(nat,X0,aa(X0,fun(nat,X0),aa(nat,fun(X0,fun(nat,X0)),aa(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0))),shift(X0),X2),X4),X1),X3) = X1 )
      | ( X3 != X4 ) ),
    inference(ennf_transformation,[],[f191]) ).

tff(f191,plain,
    ! [X0: $tType,X1: X0,X2: fun(nat,X0),X3: nat,X4: nat] :
      ( ( X3 = X4 )
     => ( aa(nat,X0,aa(X0,fun(nat,X0),aa(nat,fun(X0,fun(nat,X0)),aa(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0))),shift(X0),X2),X4),X1),X3) = X1 ) ),
    inference(rectify,[],[f13]) ).

tff(f13,axiom,
    ! [X0: $tType,X12: X0,X14: fun(nat,X0),X20: nat,X13: nat] :
      ( ( X13 = X20 )
     => ( aa(nat,X0,aa(X0,fun(nat,X0),aa(nat,fun(X0,fun(nat,X0)),aa(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0))),shift(X0),X14),X13),X12),X20) = X12 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_shift__eq) ).

tff(f992,plain,
    spl29_78,
    inference(avatar_split_clause,[],[f364,f990]) ).

tff(f990,plain,
    ( spl29_78
  <=> ! [X0: list(dB)] :
        ( listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),X0))
        | ~ listsp(dB,it,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_78])]) ).

tff(f364,plain,
    ! [X0: list(dB)] :
      ( listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),X0))
      | ~ listsp(dB,it,X0) ),
    inference(cnf_transformation,[],[f219]) ).

tff(f219,plain,
    ! [X0: list(dB)] :
      ( listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),X0))
      | ~ listsp(dB,it,X0) ),
    inference(ennf_transformation,[],[f129]) ).

tff(f129,plain,
    ! [X0: list(dB)] :
      ( listsp(dB,it,X0)
     => listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),X0)) ),
    inference(rectify,[],[f48]) ).

tff(f48,axiom,
    ! [X45: list(dB)] :
      ( listsp(dB,it,X45)
     => listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),lift),zero_zero(nat)),X45)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_lifts__IT) ).

tff(f988,plain,
    spl29_77,
    inference(avatar_split_clause,[],[f337,f985]) ).

tff(f985,plain,
    ( spl29_77
  <=> 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)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_77])]) ).

tff(f337,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(cnf_transformation,[],[f18]) ).

tff(f18,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/sandbox/benchmark/theBenchmark.p',fact_17__096IT_A_Iu_A_092_060degree_062_Aa_091u_Pi_093_J_096) ).

tff(f977,plain,
    spl29_76,
    inference(avatar_split_clause,[],[f413,f975]) ).

tff(f975,plain,
    ( spl29_76
  <=> ! [X2: dB,X0: nat,X1: nat] :
        ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
        | ~ pp(aa(dB,bool,it,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_76])]) ).

tff(f413,plain,
    ! [X2: dB,X0: nat,X1: nat] :
      ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
      | ~ pp(aa(dB,bool,it,X2)) ),
    inference(cnf_transformation,[],[f224]) ).

tff(f224,plain,
    ! [X0: nat,X1: nat,X2: dB] :
      ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0)))
      | ~ pp(aa(dB,bool,it,X2)) ),
    inference(ennf_transformation,[],[f165]) ).

tff(f165,plain,
    ! [X0: nat,X1: nat,X2: dB] :
      ( pp(aa(dB,bool,it,X2))
     => pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X2),var(X1)),X0))) ),
    inference(rectify,[],[f14]) ).

tff(f14,axiom,
    ! [X21: nat,X9: nat,X22: dB] :
      ( pp(aa(dB,bool,it,X22))
     => pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X22),var(X9)),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_subst__Var__IT) ).

tff(f973,plain,
    spl29_75,
    inference(avatar_split_clause,[],[f404,f971]) ).

tff(f971,plain,
    ( spl29_75
  <=> ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_75])]) ).

tff(f404,plain,
    ! [X2: dB,X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 ),
    inference(cnf_transformation,[],[f156]) ).

tff(f156,plain,
    ! [X0: dB,X1: nat,X2: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X2),X1)),X0),X1) = X2 ),
    inference(rectify,[],[f15]) ).

tff(f15,axiom,
    ! [X23: dB,X24: nat,X10: dB] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,aa(nat,dB,aa(dB,fun(nat,dB),lift,X10),X24)),X23),X24) = X10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_subst__lift) ).

tff(f967,plain,
    spl29_74,
    inference(avatar_split_clause,[],[f419,f965]) ).

tff(f965,plain,
    ( spl29_74
  <=> ! [X2: fun(nat,type),X0: type,X1: nat] :
        ( ( aa(nat,type,X2,X1) = X0 )
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_74])]) ).

tff(f419,plain,
    ! [X2: fun(nat,type),X0: type,X1: nat] :
      ( ( aa(nat,type,X2,X1) = X0 )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0)) ),
    inference(cnf_transformation,[],[f229]) ).

tff(f229,plain,
    ! [X0: type,X1: nat,X2: fun(nat,type)] :
      ( ( aa(nat,type,X2,X1) = X0 )
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0)) ),
    inference(ennf_transformation,[],[f170]) ).

tff(f170,plain,
    ! [X0: type,X1: nat,X2: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0))
     => ( aa(nat,type,X2,X1) = X0 ) ),
    inference(rectify,[],[f24]) ).

tff(f24,axiom,
    ! [X12: type,X13: nat,X14: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X14),var(X13)),X12))
     => ( aa(nat,type,X14,X13) = X12 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_typing__elims_I1_J) ).

tff(f960,plain,
    spl29_73,
    inference(avatar_split_clause,[],[f503,f958]) ).

tff(f958,plain,
    ( spl29_73
  <=> ! [X2: fun(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),aa(nat,type,X2,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_73])]) ).

tff(f503,plain,
    ! [X2: fun(nat,type),X1: nat] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),aa(nat,type,X2,X1))),
    inference(equality_resolution,[],[f414]) ).

tff(f414,plain,
    ! [X2: fun(nat,type),X0: type,X1: nat] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0))
      | ( aa(nat,type,X2,X1) != X0 ) ),
    inference(cnf_transformation,[],[f225]) ).

tff(f225,plain,
    ! [X0: type,X1: nat,X2: fun(nat,type)] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0))
      | ( aa(nat,type,X2,X1) != X0 ) ),
    inference(ennf_transformation,[],[f166]) ).

tff(f166,plain,
    ! [X0: type,X1: nat,X2: fun(nat,type)] :
      ( ( aa(nat,type,X2,X1) = X0 )
     => pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2),var(X1)),X0)) ),
    inference(rectify,[],[f25]) ).

tff(f25,axiom,
    ! [X12: type,X36: nat,X37: fun(nat,type)] :
      ( ( aa(nat,type,X37,X36) = X12 )
     => pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X37),var(X36)),X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_typing_OVar) ).

tff(f948,plain,
    spl29_72,
    inference(avatar_split_clause,[],[f449,f946]) ).

tff(f946,plain,
    ( spl29_72
  <=> ! [X2: type,X0: type,X1: type,X3: type] :
        ( ( X0 = X2 )
        | ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_72])]) ).

tff(f449,plain,
    ! [X2: type,X3: type,X0: type,X1: type] :
      ( ( X0 = X2 )
      | ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ),
    inference(cnf_transformation,[],[f305]) ).

tff(f305,plain,
    ! [X0: type,X1: type,X2: type,X3: type] :
      ( ( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
        | ( X0 != X2 )
        | ( X1 != X3 ) )
      & ( ( ( X0 = X2 )
          & ( X1 = X3 ) )
        | ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ) ),
    inference(flattening,[],[f304]) ).

tff(f304,plain,
    ! [X0: type,X1: type,X2: type,X3: type] :
      ( ( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
        | ( X0 != X2 )
        | ( X1 != X3 ) )
      & ( ( ( X0 = X2 )
          & ( X1 = X3 ) )
        | ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ) ),
    inference(nnf_transformation,[],[f187]) ).

tff(f187,plain,
    ! [X0: type,X1: type,X2: type,X3: type] :
      ( ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) = aa(type,type,aa(type,fun(type,type),fun1,X1),X0) )
    <=> ( ( X0 = X2 )
        & ( X1 = X3 ) ) ),
    inference(rectify,[],[f21]) ).

tff(f21,axiom,
    ! [X31: type,X32: type,X33: type,X34: type] :
      ( ( aa(type,type,aa(type,fun(type,type),fun1,X34),X33) = aa(type,type,aa(type,fun(type,type),fun1,X32),X31) )
    <=> ( ( X31 = X33 )
        & ( X32 = X34 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_type_Osimps_I2_J) ).

tff(f944,plain,
    spl29_71,
    inference(avatar_split_clause,[],[f448,f942]) ).

tff(f942,plain,
    ( spl29_71
  <=> ! [X0: type,X3: type,X2: type,X1: type] :
        ( ( X1 = X3 )
        | ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_71])]) ).

tff(f448,plain,
    ! [X2: type,X3: type,X0: type,X1: type] :
      ( ( X1 = X3 )
      | ( aa(type,type,aa(type,fun(type,type),fun1,X3),X2) != aa(type,type,aa(type,fun(type,type),fun1,X1),X0) ) ),
    inference(cnf_transformation,[],[f305]) ).

tff(f940,plain,
    spl29_70,
    inference(avatar_split_clause,[],[f446,f938]) ).

tff(f938,plain,
    ( spl29_70
  <=> ! [X2: dB,X0: dB,X1: dB,X3: dB] :
        ( ( X0 = X2 )
        | ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_70])]) ).

tff(f446,plain,
    ! [X2: dB,X3: dB,X0: dB,X1: dB] :
      ( ( X0 = X2 )
      | ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ),
    inference(cnf_transformation,[],[f303]) ).

tff(f303,plain,
    ! [X0: dB,X1: dB,X2: dB,X3: dB] :
      ( ( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
        | ( X0 != X2 )
        | ( X1 != X3 ) )
      & ( ( ( X0 = X2 )
          & ( X1 = X3 ) )
        | ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
    inference(flattening,[],[f302]) ).

tff(f302,plain,
    ! [X0: dB,X1: dB,X2: dB,X3: dB] :
      ( ( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
        | ( X0 != X2 )
        | ( X1 != X3 ) )
      & ( ( ( X0 = X2 )
          & ( X1 = X3 ) )
        | ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
    inference(nnf_transformation,[],[f186]) ).

tff(f186,plain,
    ! [X0: dB,X1: dB,X2: dB,X3: dB] :
      ( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) )
    <=> ( ( X0 = X2 )
        & ( X1 = X3 ) ) ),
    inference(rectify,[],[f19]) ).

tff(f19,axiom,
    ! [X25: dB,X26: dB,X27: dB,X28: dB] :
      ( ( aa(dB,dB,aa(dB,fun(dB,dB),app,X28),X27) = aa(dB,dB,aa(dB,fun(dB,dB),app,X26),X25) )
    <=> ( ( X25 = X27 )
        & ( X26 = X28 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_dB_Osimps_I2_J) ).

tff(f936,plain,
    spl29_69,
    inference(avatar_split_clause,[],[f445,f934]) ).

tff(f934,plain,
    ( spl29_69
  <=> ! [X0: dB,X3: dB,X2: dB,X1: dB] :
        ( ( X1 = X3 )
        | ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_69])]) ).

tff(f445,plain,
    ! [X2: dB,X3: dB,X0: dB,X1: dB] :
      ( ( X1 = X3 )
      | ( aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) ) ),
    inference(cnf_transformation,[],[f303]) ).

tff(f925,plain,
    spl29_68,
    inference(avatar_split_clause,[],[f438,f923]) ).

tff(f923,plain,
    ( spl29_68
  <=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
        ( ( X2 = X3 )
        | ( aa(X1,X0,X3,sK23(X0,X1,X2,X3)) != aa(X1,X0,X2,sK23(X0,X1,X2,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_68])]) ).

tff(f438,plain,
    ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
      ( ( X2 = X3 )
      | ( aa(X1,X0,X3,sK23(X0,X1,X2,X3)) != aa(X1,X0,X2,sK23(X0,X1,X2,X3)) ) ),
    inference(cnf_transformation,[],[f297]) ).

tff(f297,plain,
    ! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
      ( ( X2 = X3 )
      | ( aa(X1,X0,X3,sK23(X0,X1,X2,X3)) != aa(X1,X0,X2,sK23(X0,X1,X2,X3)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f237,f296]) ).

tff(f296,plain,
    ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
      ( ? [X4: X1] : ( aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) )
     => ( aa(X1,X0,X3,sK23(X0,X1,X2,X3)) != aa(X1,X0,X2,sK23(X0,X1,X2,X3)) ) ),
    introduced(choice_axiom,[]) ).

tff(f237,plain,
    ! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
      ( ( X2 = X3 )
      | ? [X4: X1] : ( aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) ) ),
    inference(ennf_transformation,[],[f183]) ).

tff(f183,plain,
    ! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
      ( ! [X4: X1] : ( aa(X1,X0,X3,X4) = aa(X1,X0,X2,X4) )
     => ( X2 = X3 ) ),
    inference(rectify,[],[f76]) ).

tff(f76,axiom,
    ! [X1: $tType,X0: $tType,X54: fun(X0,X1),X52: fun(X0,X1)] :
      ( ! [X70: X0] : ( aa(X0,X1,X52,X70) = aa(X0,X1,X54,X70) )
     => ( X52 = X54 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).

tff(f921,plain,
    spl29_67,
    inference(avatar_split_clause,[],[f373,f919]) ).

tff(f919,plain,
    ( spl29_67
  <=> ! [X0: dB] :
        ( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK12(X0))),sK13(X0)),sK14(X0)) = X0 )
        | ~ sP0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_67])]) ).

tff(f373,plain,
    ! [X0: dB] :
      ( ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK12(X0))),sK13(X0)),sK14(X0)) = X0 )
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f278]) ).

tff(f909,plain,
    spl29_66,
    inference(avatar_split_clause,[],[f424,f907]) ).

tff(f907,plain,
    ( spl29_66
  <=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
        | ~ pp(aa(X0,bool,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_66])]) ).

tff(f424,plain,
    ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
      ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
      | ~ pp(aa(X0,bool,X1,X2)) ),
    inference(cnf_transformation,[],[f287]) ).

tff(f287,plain,
    ! [X0: $tType,X1: fun(X0,bool),X2: X0] :
      ( ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
        | ~ pp(aa(X0,bool,X1,X2)) )
      & ( pp(aa(X0,bool,X1,X2))
        | ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
    inference(nnf_transformation,[],[f173]) ).

tff(f173,plain,
    ! [X0: $tType,X1: fun(X0,bool),X2: X0] :
      ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
    <=> pp(aa(X0,bool,X1,X2)) ),
    inference(rectify,[],[f77]) ).

tff(f77,axiom,
    ! [X0: $tType,X49: fun(X0,bool),X36: X0] :
      ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X36),X49))
    <=> pp(aa(X0,bool,X49,X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).

tff(f905,plain,
    spl29_65,
    inference(avatar_split_clause,[],[f423,f903]) ).

tff(f903,plain,
    ( spl29_65
  <=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( pp(aa(X0,bool,X1,X2))
        | ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_65])]) ).

tff(f423,plain,
    ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
      ( pp(aa(X0,bool,X1,X2))
      | ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ),
    inference(cnf_transformation,[],[f287]) ).

tff(f901,plain,
    spl29_64,
    inference(avatar_split_clause,[],[f393,f899]) ).

tff(f899,plain,
    ( spl29_64
  <=> ! [X0: nat,X1: dB] :
        ( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))
        | ~ pp(aa(dB,bool,it,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_64])]) ).

tff(f393,plain,
    ! [X0: nat,X1: dB] :
      ( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))
      | ~ pp(aa(dB,bool,it,X1)) ),
    inference(cnf_transformation,[],[f223]) ).

tff(f223,plain,
    ! [X0: nat,X1: dB] :
      ( pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))
      | ~ pp(aa(dB,bool,it,X1)) ),
    inference(ennf_transformation,[],[f147]) ).

tff(f147,plain,
    ! [X0: nat,X1: dB] :
      ( pp(aa(dB,bool,it,X1))
     => pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0)))) ),
    inference(rectify,[],[f33]) ).

tff(f33,axiom,
    ! [X9: nat,X10: dB] :
      ( pp(aa(dB,bool,it,X10))
     => pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,X10),var(X9)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_app__Var__IT) ).

tff(f897,plain,
    ( spl29_63
    | ~ spl29_10
    | ~ spl29_16 ),
    inference(avatar_split_clause,[],[f632,f605,f569,f894]) ).

tff(f894,plain,
    ( spl29_63
  <=> sP1(ua) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_63])]) ).

tff(f632,plain,
    ( sP1(ua)
    | ~ spl29_10
    | ~ spl29_16 ),
    inference(resolution,[],[f606,f571]) ).

tff(f880,plain,
    spl29_62,
    inference(avatar_split_clause,[],[f392,f878]) ).

tff(f878,plain,
    ( spl29_62
  <=> ! [X0: nat,X1: dB] :
        ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
        | ~ pp(aa(dB,bool,it,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_62])]) ).

tff(f392,plain,
    ! [X0: nat,X1: dB] :
      ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
      | ~ pp(aa(dB,bool,it,X1)) ),
    inference(cnf_transformation,[],[f222]) ).

tff(f222,plain,
    ! [X0: nat,X1: dB] :
      ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0)))
      | ~ pp(aa(dB,bool,it,X1)) ),
    inference(ennf_transformation,[],[f146]) ).

tff(f146,plain,
    ! [X0: nat,X1: dB] :
      ( pp(aa(dB,bool,it,X1))
     => pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X1),X0))) ),
    inference(rectify,[],[f7]) ).

tff(f7,axiom,
    ! [X9: nat,X10: dB] :
      ( pp(aa(dB,bool,it,X10))
     => pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),lift,X10),X9))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_lift__IT) ).

tff(f876,plain,
    spl29_61,
    inference(avatar_split_clause,[],[f384,f874]) ).

tff(f874,plain,
    ( spl29_61
  <=> ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X1)),X0),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_61])]) ).

tff(f384,plain,
    ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X1)),X0),X1) = X0 ),
    inference(cnf_transformation,[],[f137]) ).

tff(f137,plain,
    ! [X0: dB,X1: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X1)),X0),X1) = X0 ),
    inference(rectify,[],[f34]) ).

tff(f34,axiom,
    ! [X35: dB,X24: nat] : ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,var(X24)),X35),X24) = X35 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_subst__eq) ).

tff(f872,plain,
    spl29_60,
    inference(avatar_split_clause,[],[f368,f870]) ).

tff(f870,plain,
    ( spl29_60
  <=> ! [X0: dB] :
        ( sP0(X0)
        | pp(aa(dB,bool,it,sK9(X0)))
        | ( foldl(dB,dB,app,var(sK11(X0)),sK10(X0)) = X0 )
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_60])]) ).

tff(f368,plain,
    ! [X0: dB] :
      ( sP0(X0)
      | pp(aa(dB,bool,it,sK9(X0)))
      | ( foldl(dB,dB,app,var(sK11(X0)),sK10(X0)) = X0 )
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f274]) ).

tff(f274,plain,
    ! [X0: dB] :
      ( ( sP1(X0)
        | ( ~ sP0(X0)
          & ! [X1: dB] :
              ( ~ pp(aa(dB,bool,it,X1))
              | ( abs(X1) != X0 ) )
          & ! [X2: list(dB),X3: nat] :
              ( ~ listsp(dB,it,X2)
              | ( foldl(dB,dB,app,var(X3),X2) != X0 ) ) ) )
      & ( sP0(X0)
        | ( pp(aa(dB,bool,it,sK9(X0)))
          & ( abs(sK9(X0)) = X0 ) )
        | ( listsp(dB,it,sK10(X0))
          & ( foldl(dB,dB,app,var(sK11(X0)),sK10(X0)) = X0 ) )
        | ~ sP1(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f271,f273,f272]) ).

tff(f272,plain,
    ! [X0: dB] :
      ( ? [X4: dB] :
          ( pp(aa(dB,bool,it,X4))
          & ( abs(X4) = X0 ) )
     => ( pp(aa(dB,bool,it,sK9(X0)))
        & ( abs(sK9(X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f273,plain,
    ! [X0: dB] :
      ( ? [X5: list(dB),X6: nat] :
          ( listsp(dB,it,X5)
          & ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
     => ( listsp(dB,it,sK10(X0))
        & ( foldl(dB,dB,app,var(sK11(X0)),sK10(X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f271,plain,
    ! [X0: dB] :
      ( ( sP1(X0)
        | ( ~ sP0(X0)
          & ! [X1: dB] :
              ( ~ pp(aa(dB,bool,it,X1))
              | ( abs(X1) != X0 ) )
          & ! [X2: list(dB),X3: nat] :
              ( ~ listsp(dB,it,X2)
              | ( foldl(dB,dB,app,var(X3),X2) != X0 ) ) ) )
      & ( sP0(X0)
        | ? [X4: dB] :
            ( pp(aa(dB,bool,it,X4))
            & ( abs(X4) = X0 ) )
        | ? [X5: list(dB),X6: nat] :
            ( listsp(dB,it,X5)
            & ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
        | ~ sP1(X0) ) ),
    inference(rectify,[],[f270]) ).

tff(f270,plain,
    ! [X0: dB] :
      ( ( sP1(X0)
        | ( ~ sP0(X0)
          & ! [X4: dB] :
              ( ~ pp(aa(dB,bool,it,X4))
              | ( abs(X4) != X0 ) )
          & ! [X5: list(dB),X6: nat] :
              ( ~ listsp(dB,it,X5)
              | ( foldl(dB,dB,app,var(X6),X5) != X0 ) ) ) )
      & ( sP0(X0)
        | ? [X4: dB] :
            ( pp(aa(dB,bool,it,X4))
            & ( abs(X4) = X0 ) )
        | ? [X5: list(dB),X6: nat] :
            ( listsp(dB,it,X5)
            & ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
        | ~ sP1(X0) ) ),
    inference(flattening,[],[f269]) ).

tff(f269,plain,
    ! [X0: dB] :
      ( ( sP1(X0)
        | ( ~ sP0(X0)
          & ! [X4: dB] :
              ( ~ pp(aa(dB,bool,it,X4))
              | ( abs(X4) != X0 ) )
          & ! [X5: list(dB),X6: nat] :
              ( ~ listsp(dB,it,X5)
              | ( foldl(dB,dB,app,var(X6),X5) != X0 ) ) ) )
      & ( sP0(X0)
        | ? [X4: dB] :
            ( pp(aa(dB,bool,it,X4))
            & ( abs(X4) = X0 ) )
        | ? [X5: list(dB),X6: nat] :
            ( listsp(dB,it,X5)
            & ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
        | ~ sP1(X0) ) ),
    inference(nnf_transformation,[],[f258]) ).

tff(f258,plain,
    ! [X0: dB] :
      ( sP1(X0)
    <=> ( sP0(X0)
        | ? [X4: dB] :
            ( pp(aa(dB,bool,it,X4))
            & ( abs(X4) = X0 ) )
        | ? [X5: list(dB),X6: nat] :
            ( listsp(dB,it,X5)
            & ( foldl(dB,dB,app,var(X6),X5) = X0 ) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

tff(f868,plain,
    spl29_59,
    inference(avatar_split_clause,[],[f336,f865]) ).

tff(f865,plain,
    ( spl29_59
  <=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,e),u),t)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_59])]) ).

tff(f336,plain,
    pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,e),u),t)),
    inference(cnf_transformation,[],[f5]) ).

tff(f5,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/sandbox/benchmark/theBenchmark.p',fact_4_uT) ).

tff(f863,plain,
    spl29_58,
    inference(avatar_split_clause,[],[f335,f860]) ).

tff(f860,plain,
    ( spl29_58
  <=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,ea),ua),t)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_58])]) ).

tff(f335,plain,
    pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,ea),ua),t)),
    inference(cnf_transformation,[],[f17]) ).

tff(f17,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/sandbox/benchmark/theBenchmark.p',fact_16_Var_I4_J) ).

tff(f858,plain,
    ( spl29_57
    | ~ spl29_11
    | ~ spl29_16 ),
    inference(avatar_split_clause,[],[f631,f605,f574,f855]) ).

tff(f855,plain,
    ( spl29_57
  <=> sP1(u) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_57])]) ).

tff(f631,plain,
    ( sP1(u)
    | ~ spl29_11
    | ~ spl29_16 ),
    inference(resolution,[],[f606,f576]) ).

tff(f850,plain,
    spl29_56,
    inference(avatar_split_clause,[],[f426,f848]) ).

tff(f848,plain,
    ( spl29_56
  <=> ! [X2: dB,X0: list(dB),X1: nat,X3: dB] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_56])]) ).

tff(f426,plain,
    ! [X2: dB,X3: dB,X0: list(dB),X1: nat] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2) ),
    inference(cnf_transformation,[],[f175]) ).

tff(f175,plain,
    ! [X0: list(dB),X1: nat,X2: dB,X3: dB] : ( foldl(dB,dB,app,var(X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X3)),X2) ),
    inference(rectify,[],[f92]) ).

tff(f92,axiom,
    ! [X61: list(dB),X55: nat,X15: dB,X38: dB] : ( foldl(dB,dB,app,var(X55),X61) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X38)),X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_Abs__App__neq__Var__apps) ).

tff(f846,plain,
    spl29_55,
    inference(avatar_split_clause,[],[f366,f844]) ).

tff(f366,plain,
    ! [X0: dB] :
      ( sP0(X0)
      | ( abs(sK9(X0)) = X0 )
      | ( foldl(dB,dB,app,var(sK11(X0)),sK10(X0)) = X0 )
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f274]) ).

tff(f839,plain,
    spl29_54,
    inference(avatar_split_clause,[],[f443,f837]) ).

tff(f837,plain,
    ( spl29_54
  <=> ! [X2: list(dB),X0: list(dB),X1: nat,X3: nat] :
        ( ( X0 = X2 )
        | ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_54])]) ).

tff(f443,plain,
    ! [X2: list(dB),X3: nat,X0: list(dB),X1: nat] :
      ( ( X0 = X2 )
      | ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ),
    inference(cnf_transformation,[],[f301]) ).

tff(f301,plain,
    ! [X0: list(dB),X1: nat,X2: list(dB),X3: nat] :
      ( ( ( foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) )
        | ( X0 != X2 )
        | ( X1 != X3 ) )
      & ( ( ( X0 = X2 )
          & ( X1 = X3 ) )
        | ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ) ),
    inference(flattening,[],[f300]) ).

tff(f300,plain,
    ! [X0: list(dB),X1: nat,X2: list(dB),X3: nat] :
      ( ( ( foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) )
        | ( X0 != X2 )
        | ( X1 != X3 ) )
      & ( ( ( X0 = X2 )
          & ( X1 = X3 ) )
        | ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ) ),
    inference(nnf_transformation,[],[f185]) ).

tff(f185,plain,
    ! [X0: list(dB),X1: nat,X2: list(dB),X3: nat] :
      ( ( foldl(dB,dB,app,var(X3),X2) = foldl(dB,dB,app,var(X1),X0) )
    <=> ( ( X0 = X2 )
        & ( X1 = X3 ) ) ),
    inference(rectify,[],[f66]) ).

tff(f66,axiom,
    ! [X61: list(dB),X55: nat,X56: list(dB),X62: nat] :
      ( ( foldl(dB,dB,app,var(X62),X56) = foldl(dB,dB,app,var(X55),X61) )
    <=> ( ( X56 = X61 )
        & ( X55 = X62 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Var__apps__eq__Var__apps__conv) ).

tff(f835,plain,
    spl29_53,
    inference(avatar_split_clause,[],[f440,f833]) ).

tff(f833,plain,
    ( spl29_53
  <=> ! [X2: list(dB),X0: list(dB),X1: dB,X3: dB] :
        ( ( X0 = X2 )
        | ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_53])]) ).

tff(f440,plain,
    ! [X2: list(dB),X3: dB,X0: list(dB),X1: dB] :
      ( ( X0 = X2 )
      | ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ),
    inference(cnf_transformation,[],[f299]) ).

tff(f299,plain,
    ! [X0: list(dB),X1: dB,X2: list(dB),X3: dB] :
      ( ( ( foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) )
        | ( X0 != X2 )
        | ( X1 != X3 ) )
      & ( ( ( X0 = X2 )
          & ( X1 = X3 ) )
        | ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
    inference(flattening,[],[f298]) ).

tff(f298,plain,
    ! [X0: list(dB),X1: dB,X2: list(dB),X3: dB] :
      ( ( ( foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) )
        | ( X0 != X2 )
        | ( X1 != X3 ) )
      & ( ( ( X0 = X2 )
          & ( X1 = X3 ) )
        | ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
    inference(nnf_transformation,[],[f184]) ).

tff(f184,plain,
    ! [X0: list(dB),X1: dB,X2: list(dB),X3: dB] :
      ( ( foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) )
    <=> ( ( X0 = X2 )
        & ( X1 = X3 ) ) ),
    inference(rectify,[],[f86]) ).

tff(f86,axiom,
    ! [X61: list(dB),X38: dB,X56: list(dB),X60: dB] :
      ( ( foldl(dB,dB,app,abs(X60),X56) = foldl(dB,dB,app,abs(X38),X61) )
    <=> ( ( X56 = X61 )
        & ( X38 = X60 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Abs__apps__eq__Abs__apps__conv) ).

tff(f831,plain,
    ( spl29_52
    | ~ spl29_9
    | ~ spl29_16 ),
    inference(avatar_split_clause,[],[f630,f605,f564,f828]) ).

tff(f828,plain,
    ( spl29_52
  <=> sP1(t3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_52])]) ).

tff(f630,plain,
    ( sP1(t3)
    | ~ spl29_9
    | ~ spl29_16 ),
    inference(resolution,[],[f606,f566]) ).

tff(f826,plain,
    spl29_51,
    inference(avatar_split_clause,[],[f402,f824]) ).

tff(f402,plain,
    ! [X0: $tType,X2: X0,X1: list(X0)] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != X1 ),
    inference(cnf_transformation,[],[f154]) ).

tff(f154,plain,
    ! [X0: $tType,X1: list(X0),X2: X0] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X2),X1) != X1 ),
    inference(rectify,[],[f69]) ).

tff(f69,axiom,
    ! [X0: $tType,X64: list(X0),X63: X0] : ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X63),X64) != X64 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_not__Cons__self2) ).

tff(f822,plain,
    spl29_50,
    inference(avatar_split_clause,[],[f334,f819]) ).

tff(f334,plain,
    rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as),
    inference(cnf_transformation,[],[f55]) ).

tff(f55,axiom,
    rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54__096rs_A_061_Aa_A_D_Aas_096) ).

tff(f815,plain,
    spl29_49,
    inference(avatar_split_clause,[],[f442,f813]) ).

tff(f813,plain,
    ( spl29_49
  <=> ! [X0: list(dB),X3: nat,X2: list(dB),X1: nat] :
        ( ( X1 = X3 )
        | ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_49])]) ).

tff(f442,plain,
    ! [X2: list(dB),X3: nat,X0: list(dB),X1: nat] :
      ( ( X1 = X3 )
      | ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) ) ),
    inference(cnf_transformation,[],[f301]) ).

tff(f811,plain,
    spl29_48,
    inference(avatar_split_clause,[],[f439,f809]) ).

tff(f809,plain,
    ( spl29_48
  <=> ! [X0: list(dB),X3: dB,X2: list(dB),X1: dB] :
        ( ( X1 = X3 )
        | ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_48])]) ).

tff(f439,plain,
    ! [X2: list(dB),X3: dB,X0: list(dB),X1: dB] :
      ( ( X1 = X3 )
      | ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ),
    inference(cnf_transformation,[],[f299]) ).

tff(f807,plain,
    spl29_47,
    inference(avatar_split_clause,[],[f333,f804]) ).

tff(f804,plain,
    ( spl29_47
  <=> ( t = aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_47])]) ).

tff(f333,plain,
    t = aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1)),
    inference(cnf_transformation,[],[f44]) ).

tff(f44,axiom,
    t = aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_T) ).

tff(f778,plain,
    spl29_46,
    inference(avatar_split_clause,[],[f421,f776]) ).

tff(f776,plain,
    ( spl29_46
  <=> ! [X2: dB,X0: dB,X1: list(dB)] :
        ( ( X0 = X2 )
        | ( foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_46])]) ).

tff(f421,plain,
    ! [X2: dB,X0: dB,X1: list(dB)] :
      ( ( X0 = X2 )
      | ( foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1) ) ),
    inference(cnf_transformation,[],[f286]) ).

tff(f286,plain,
    ! [X0: dB,X1: list(dB),X2: dB] :
      ( ( ( foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) )
        | ( X0 != X2 ) )
      & ( ( X0 = X2 )
        | ( foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1) ) ) ),
    inference(nnf_transformation,[],[f172]) ).

tff(f172,plain,
    ! [X0: dB,X1: list(dB),X2: dB] :
      ( ( foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) )
    <=> ( X0 = X2 ) ),
    inference(rectify,[],[f65]) ).

tff(f65,axiom,
    ! [X38: dB,X45: list(dB),X60: dB] :
      ( ( foldl(dB,dB,app,X60,X45) = foldl(dB,dB,app,X38,X45) )
    <=> ( X38 = X60 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_apps__eq__tail__conv) ).

tff(f774,plain,
    spl29_45,
    inference(avatar_split_clause,[],[f412,f772]) ).

tff(f772,plain,
    ( spl29_45
  <=> ! [X0: $tType,X2: X0,X1: X0] :
        ( ( X1 = X2 )
        | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_45])]) ).

tff(f412,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( X1 = X2 )
      | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ),
    inference(cnf_transformation,[],[f164]) ).

tff(f164,plain,
    ! [X0: $tType,X1: X0,X2: X0] :
      ( ( X1 = X2 )
      | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ),
    inference(rectify,[],[f114]) ).

tff(f114,axiom,
    ! [X0: $tType,X92: X0,X63: X0] :
      ( ( X63 = X92 )
      | ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X63),X92)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).

tff(f770,plain,
    spl29_44,
    inference(avatar_split_clause,[],[f391,f768]) ).

tff(f768,plain,
    ( spl29_44
  <=> ! [X0: nat,X1: list(dB)] :
        ( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
        | ~ listsp(dB,it,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_44])]) ).

tff(f391,plain,
    ! [X0: nat,X1: list(dB)] :
      ( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
      | ~ listsp(dB,it,X1) ),
    inference(cnf_transformation,[],[f221]) ).

tff(f221,plain,
    ! [X0: nat,X1: list(dB)] :
      ( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
      | ~ listsp(dB,it,X1) ),
    inference(ennf_transformation,[],[f145]) ).

tff(f145,plain,
    ! [X0: nat,X1: list(dB)] :
      ( listsp(dB,it,X1)
     => pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) ),
    inference(rectify,[],[f59]) ).

tff(f59,axiom,
    ! [X55: nat,X56: list(dB)] :
      ( listsp(dB,it,X56)
     => pp(aa(dB,bool,it,foldl(dB,dB,app,var(X55),X56))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_IT_OVar) ).

tff(f766,plain,
    spl29_43,
    inference(avatar_split_clause,[],[f390,f764]) ).

tff(f764,plain,
    ( spl29_43
  <=> ! [X0: bool,X1: bool] :
        ( pp(X0)
        | ~ pp(X1)
        | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_43])]) ).

tff(f390,plain,
    ! [X0: bool,X1: bool] :
      ( pp(X0)
      | ~ pp(X1)
      | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)) ),
    inference(cnf_transformation,[],[f144]) ).

tff(f144,plain,
    ! [X0: bool,X1: bool] :
      ( pp(X0)
      | ~ pp(X1)
      | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0)) ),
    inference(rectify,[],[f118]) ).

tff(f118,axiom,
    ! [X91: bool,X89: bool] :
      ( pp(X91)
      | ~ pp(X89)
      | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X89),X91)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).

tff(f762,plain,
    spl29_42,
    inference(avatar_split_clause,[],[f385,f760]) ).

tff(f760,plain,
    ( spl29_42
  <=> ! [X0: bool,X1: bool] :
        ( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
        | ~ pp(X0)
        | ~ pp(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_42])]) ).

tff(f385,plain,
    ! [X0: bool,X1: bool] :
      ( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
      | ~ pp(X0)
      | ~ pp(X1) ),
    inference(cnf_transformation,[],[f139]) ).

tff(f139,plain,
    ! [X0: bool,X1: bool] :
      ( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
      | ~ pp(X0)
      | ~ pp(X1) ),
    inference(rectify,[],[f109]) ).

tff(f109,axiom,
    ! [X91: bool,X89: bool] :
      ( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X89),X91))
      | ~ pp(X91)
      | ~ pp(X89) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

tff(f758,plain,
    spl29_41,
    inference(avatar_split_clause,[],[f369,f756]) ).

tff(f369,plain,
    ! [X0: dB] :
      ( sP0(X0)
      | pp(aa(dB,bool,it,sK9(X0)))
      | listsp(dB,it,sK10(X0))
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f274]) ).

tff(f738,plain,
    spl29_40,
    inference(avatar_split_clause,[],[f425,f736]) ).

tff(f736,plain,
    ( spl29_40
  <=> ! [X2: list(dB),X0: list(dB),X1: dB,X3: nat] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_40])]) ).

tff(f425,plain,
    ! [X2: list(dB),X3: nat,X0: list(dB),X1: dB] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) ),
    inference(cnf_transformation,[],[f174]) ).

tff(f174,plain,
    ! [X0: list(dB),X1: dB,X2: list(dB),X3: nat] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) ),
    inference(rectify,[],[f93]) ).

tff(f93,axiom,
    ! [X61: list(dB),X60: dB,X45: list(dB),X55: nat] : ( foldl(dB,dB,app,var(X55),X45) != foldl(dB,dB,app,abs(X60),X61) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Var__apps__neq__Abs__apps) ).

tff(f734,plain,
    spl29_39,
    inference(avatar_split_clause,[],[f411,f732]) ).

tff(f732,plain,
    ( spl29_39
  <=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
        ( pp(aa(X0,bool,X2,X1))
        | ~ pp(aa(fun(X0,bool),bool,fAll(X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_39])]) ).

tff(f411,plain,
    ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
      ( pp(aa(X0,bool,X2,X1))
      | ~ pp(aa(fun(X0,bool),bool,fAll(X0),X2)) ),
    inference(cnf_transformation,[],[f163]) ).

tff(f163,plain,
    ! [X0: $tType,X1: X0,X2: fun(X0,bool)] :
      ( pp(aa(X0,bool,X2,X1))
      | ~ pp(aa(fun(X0,bool),bool,fAll(X0),X2)) ),
    inference(rectify,[],[f104]) ).

tff(f104,axiom,
    ! [X0: $tType,X63: X0,X89: fun(X0,bool)] :
      ( pp(aa(X0,bool,X89,X63))
      | ~ pp(aa(fun(X0,bool),bool,fAll(X0),X89)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fAll_1_1_U) ).

tff(f730,plain,
    spl29_38,
    inference(avatar_split_clause,[],[f410,f728]) ).

tff(f410,plain,
    ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
      ( pp(aa(fun(X0,bool),bool,fEx(X0),X2))
      | ~ pp(aa(X0,bool,X2,X1)) ),
    inference(cnf_transformation,[],[f162]) ).

tff(f162,plain,
    ! [X0: $tType,X1: X0,X2: fun(X0,bool)] :
      ( pp(aa(fun(X0,bool),bool,fEx(X0),X2))
      | ~ pp(aa(X0,bool,X2,X1)) ),
    inference(rectify,[],[f103]) ).

tff(f103,axiom,
    ! [X0: $tType,X63: X0,X89: fun(X0,bool)] :
      ( pp(aa(fun(X0,bool),bool,fEx(X0),X89))
      | ~ pp(aa(X0,bool,X89,X63)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fEx_1_1_U) ).

tff(f724,plain,
    ( spl29_37
    | ~ spl29_1
    | ~ spl29_24 ),
    inference(avatar_split_clause,[],[f665,f650,f526,f721]) ).

tff(f721,plain,
    ( spl29_37
  <=> sP1(abs(sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_37])]) ).

tff(f665,plain,
    ( sP1(abs(sK4))
    | ~ spl29_1
    | ~ spl29_24 ),
    inference(resolution,[],[f651,f528]) ).

tff(f717,plain,
    spl29_36,
    inference(avatar_split_clause,[],[f400,f715]) ).

tff(f715,plain,
    ( spl29_36
  <=> ! [X2: dB,X0: nat,X1: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_36])]) ).

tff(f400,plain,
    ! [X2: dB,X0: nat,X1: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
    inference(cnf_transformation,[],[f152]) ).

tff(f152,plain,
    ! [X0: nat,X1: dB,X2: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
    inference(rectify,[],[f32]) ).

tff(f32,axiom,
    ! [X41: nat,X39: dB,X40: dB] : ( var(X41) != aa(dB,dB,aa(dB,fun(dB,dB),app,X40),X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_dB_Osimps_I5_J) ).

tff(f713,plain,
    spl29_35,
    inference(avatar_split_clause,[],[f398,f711]) ).

tff(f711,plain,
    ( spl29_35
  <=> ! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_35])]) ).

tff(f398,plain,
    ! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
    inference(cnf_transformation,[],[f150]) ).

tff(f150,plain,
    ! [X0: dB,X1: dB,X2: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
    inference(rectify,[],[f89]) ).

tff(f89,axiom,
    ! [X79: dB,X77: dB,X78: dB] : ( abs(X79) != aa(dB,dB,aa(dB,fun(dB,dB),app,X78),X77) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_dB_Osimps_I8_J) ).

tff(f709,plain,
    spl29_34,
    inference(avatar_split_clause,[],[f389,f707]) ).

tff(f707,plain,
    ( spl29_34
  <=> ! [X0: bool,X1: bool] :
        ( pp(X0)
        | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_34])]) ).

tff(f389,plain,
    ! [X0: bool,X1: bool] :
      ( pp(X0)
      | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
    inference(cnf_transformation,[],[f143]) ).

tff(f143,plain,
    ! [X0: bool,X1: bool] :
      ( pp(X0)
      | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
    inference(rectify,[],[f111]) ).

tff(f111,axiom,
    ! [X91: bool,X89: bool] :
      ( pp(X91)
      | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X89),X91)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

tff(f705,plain,
    spl29_33,
    inference(avatar_split_clause,[],[f388,f703]) ).

tff(f703,plain,
    ( spl29_33
  <=> ! [X0: bool,X1: bool] :
        ( pp(X1)
        | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_33])]) ).

tff(f388,plain,
    ! [X0: bool,X1: bool] :
      ( pp(X1)
      | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
    inference(cnf_transformation,[],[f142]) ).

tff(f142,plain,
    ! [X0: bool,X1: bool] :
      ( pp(X1)
      | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
    inference(rectify,[],[f110]) ).

tff(f110,axiom,
    ! [X91: bool,X89: bool] :
      ( pp(X89)
      | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X89),X91)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

tff(f701,plain,
    spl29_32,
    inference(avatar_split_clause,[],[f387,f699]) ).

tff(f699,plain,
    ( spl29_32
  <=> ! [X0: bool,X1: bool] :
        ( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0))
        | pp(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_32])]) ).

tff(f387,plain,
    ! [X0: bool,X1: bool] :
      ( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0))
      | pp(X1) ),
    inference(cnf_transformation,[],[f141]) ).

tff(f141,plain,
    ! [X0: bool,X1: bool] :
      ( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0))
      | pp(X1) ),
    inference(rectify,[],[f116]) ).

tff(f116,axiom,
    ! [X91: bool,X89: bool] :
      ( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X89),X91))
      | pp(X89) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).

tff(f697,plain,
    spl29_31,
    inference(avatar_split_clause,[],[f386,f695]) ).

tff(f695,plain,
    ( spl29_31
  <=> ! [X0: bool,X1: bool] :
        ( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1))
        | ~ pp(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_31])]) ).

tff(f386,plain,
    ! [X0: bool,X1: bool] :
      ( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1))
      | ~ pp(X1) ),
    inference(cnf_transformation,[],[f140]) ).

tff(f140,plain,
    ! [X0: bool,X1: bool] :
      ( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1))
      | ~ pp(X1) ),
    inference(rectify,[],[f117]) ).

tff(f117,axiom,
    ! [X89: bool,X91: bool] :
      ( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X89),X91))
      | ~ pp(X91) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).

tff(f693,plain,
    spl29_30,
    inference(avatar_split_clause,[],[f367,f691]) ).

tff(f691,plain,
    ( spl29_30
  <=> ! [X0: dB] :
        ( sP0(X0)
        | ( abs(sK9(X0)) = X0 )
        | listsp(dB,it,sK10(X0))
        | ~ sP1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_30])]) ).

tff(f367,plain,
    ! [X0: dB] :
      ( sP0(X0)
      | ( abs(sK9(X0)) = X0 )
      | listsp(dB,it,sK10(X0))
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f274]) ).

tff(f685,plain,
    spl29_29,
    inference(avatar_split_clause,[],[f502,f683]) ).

tff(f683,plain,
    ( spl29_29
  <=> ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_29])]) ).

tff(f502,plain,
    ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)),
    inference(equality_resolution,[],[f409]) ).

tff(f409,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))
      | ( X1 != X2 ) ),
    inference(cnf_transformation,[],[f161]) ).

tff(f161,plain,
    ! [X0: $tType,X1: X0,X2: X0] :
      ( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))
      | ( X1 != X2 ) ),
    inference(rectify,[],[f115]) ).

tff(f115,axiom,
    ! [X0: $tType,X92: X0,X63: X0] :
      ( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X63),X92))
      | ( X63 != X92 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).

tff(f681,plain,
    spl29_28,
    inference(avatar_split_clause,[],[f365,f679]) ).

tff(f365,plain,
    ! [X0: dB] :
      ( pp(aa(dB,bool,it,abs(X0)))
      | ~ pp(aa(dB,bool,it,X0)) ),
    inference(cnf_transformation,[],[f220]) ).

tff(f220,plain,
    ! [X0: dB] :
      ( pp(aa(dB,bool,it,abs(X0)))
      | ~ pp(aa(dB,bool,it,X0)) ),
    inference(ennf_transformation,[],[f130]) ).

tff(f130,plain,
    ! [X0: dB] :
      ( pp(aa(dB,bool,it,X0))
     => pp(aa(dB,bool,it,abs(X0))) ),
    inference(rectify,[],[f85]) ).

tff(f85,axiom,
    ! [X22: dB] :
      ( pp(aa(dB,bool,it,X22))
     => pp(aa(dB,bool,it,abs(X22))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_Lambda) ).

tff(f676,plain,
    spl29_27,
    inference(avatar_split_clause,[],[f321,f673]) ).

tff(f321,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),sK2),sK5),t)),b),sK3)),
    inference(cnf_transformation,[],[f261]) ).

tff(f261,plain,
    ( ~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),sK4),sK5)))
    & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4),t))
    & pp(aa(dB,bool,it,sK4))
    & 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),sK2),sK5),t)),b),sK3)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f213,f260]) ).

tff(f260,plain,
    ( ? [X0: fun(nat,type),X1: type,X2: dB,X3: nat] :
        ( ~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X2),X3)))
        & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),X2),t))
        & pp(aa(dB,bool,it,X2))
        & 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),X0),X3),t)),b),X1)) )
   => ( ~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),sK4),sK5)))
      & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4),t))
      & pp(aa(dB,bool,it,sK4))
      & 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),sK2),sK5),t)),b),sK3)) ) ),
    introduced(choice_axiom,[]) ).

tff(f213,plain,
    ? [X0: fun(nat,type),X1: type,X2: dB,X3: nat] :
      ( ~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X2),X3)))
      & pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),X2),t))
      & pp(aa(dB,bool,it,X2))
      & 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),X0),X3),t)),b),X1)) ),
    inference(ennf_transformation,[],[f121]) ).

tff(f121,plain,
    ~ ! [X0: fun(nat,type),X1: type,X2: dB,X3: nat] :
        ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X2),X3)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),X2),t))
        | ~ pp(aa(dB,bool,it,X2))
        | ~ 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),X0),X3),t)),b),X1)) ),
    inference(rectify,[],[f120]) ).

tff(f120,negated_conjecture,
    ~ ! [X93: fun(nat,type),X94: type,X95: dB,X96: nat] :
        ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X95),X96)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X93),X95),t))
        | ~ pp(aa(dB,bool,it,X95))
        | ~ 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),X93),X96),t)),b),X94)) ),
    inference(negated_conjecture,[],[f119]) ).

tff(f119,conjecture,
    ! [X93: fun(nat,type),X94: type,X95: dB,X96: nat] :
      ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X95),X96)))
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X93),X95),t))
      | ~ pp(aa(dB,bool,it,X95))
      | ~ 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),X93),X96),t)),b),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(f671,plain,
    spl29_26,
    inference(avatar_split_clause,[],[f498,f669]) ).

tff(f669,plain,
    ( spl29_26
  <=> ! [X2: list(dB),X3: nat] :
        ( sP1(foldl(dB,dB,app,var(X3),X2))
        | ~ listsp(dB,it,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_26])]) ).

tff(f498,plain,
    ! [X2: list(dB),X3: nat] :
      ( sP1(foldl(dB,dB,app,var(X3),X2))
      | ~ listsp(dB,it,X2) ),
    inference(equality_resolution,[],[f370]) ).

tff(f370,plain,
    ! [X2: list(dB),X3: nat,X0: dB] :
      ( sP1(X0)
      | ~ listsp(dB,it,X2)
      | ( foldl(dB,dB,app,var(X3),X2) != X0 ) ),
    inference(cnf_transformation,[],[f274]) ).

tff(f659,plain,
    ( spl29_25
    | ~ spl29_1
    | ~ spl29_16 ),
    inference(avatar_split_clause,[],[f633,f605,f526,f656]) ).

tff(f633,plain,
    ( sP1(sK4)
    | ~ spl29_1
    | ~ spl29_16 ),
    inference(resolution,[],[f606,f528]) ).

tff(f652,plain,
    spl29_24,
    inference(avatar_split_clause,[],[f497,f650]) ).

tff(f497,plain,
    ! [X1: dB] :
      ( sP1(abs(X1))
      | ~ pp(aa(dB,bool,it,X1)) ),
    inference(equality_resolution,[],[f371]) ).

tff(f371,plain,
    ! [X0: dB,X1: dB] :
      ( sP1(X0)
      | ~ pp(aa(dB,bool,it,X1))
      | ( abs(X1) != X0 ) ),
    inference(cnf_transformation,[],[f274]) ).

tff(f648,plain,
    spl29_23,
    inference(avatar_split_clause,[],[f383,f646]) ).

tff(f646,plain,
    ( spl29_23
  <=> ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_23])]) ).

tff(f383,plain,
    ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
    inference(cnf_transformation,[],[f136]) ).

tff(f136,plain,
    ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
    inference(rectify,[],[f53]) ).

tff(f53,axiom,
    ! [X0: $tType,X50: list(X0)] : ( map(X0,X0,combi(X0),X50) = X50 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_map__ident) ).

tff(f644,plain,
    spl29_22,
    inference(avatar_split_clause,[],[f375,f642]) ).

tff(f375,plain,
    ! [X0: dB] :
      ( pp(aa(dB,bool,it,sK13(X0)))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f278]) ).

tff(f628,plain,
    spl29_21,
    inference(avatar_split_clause,[],[f396,f626]) ).

tff(f626,plain,
    ( spl29_21
  <=> ! [X0: nat,X1: nat] :
        ( ( X0 = X1 )
        | ( var(X0) != var(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_21])]) ).

tff(f396,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( var(X0) != var(X1) ) ),
    inference(cnf_transformation,[],[f281]) ).

tff(f281,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( var(X0) = var(X1) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( var(X0) != var(X1) ) ) ),
    inference(nnf_transformation,[],[f149]) ).

tff(f149,plain,
    ! [X0: nat,X1: nat] :
      ( ( var(X0) = var(X1) )
    <=> ( X0 = X1 ) ),
    inference(rectify,[],[f20]) ).

tff(f20,axiom,
    ! [X29: nat,X30: nat] :
      ( ( var(X30) = var(X29) )
    <=> ( X29 = X30 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_dB_Osimps_I1_J) ).

tff(f624,plain,
    ( spl29_20
    | spl29_2
    | ~ spl29_1
    | ~ spl29_13 ),
    inference(avatar_split_clause,[],[f592,f583,f526,f531,f621]) ).

tff(f592,plain,
    ( pp(fFalse)
    | ( fTrue = aa(dB,bool,it,sK4) )
    | ~ spl29_1
    | ~ spl29_13 ),
    inference(superposition,[],[f528,f584]) ).

tff(f619,plain,
    spl29_19,
    inference(avatar_split_clause,[],[f394,f617]) ).

tff(f617,plain,
    ( spl29_19
  <=> ! [X0: dB,X1: dB] :
        ( ( X0 = X1 )
        | ( abs(X0) != abs(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_19])]) ).

tff(f394,plain,
    ! [X0: dB,X1: dB] :
      ( ( X0 = X1 )
      | ( abs(X0) != abs(X1) ) ),
    inference(cnf_transformation,[],[f280]) ).

tff(f280,plain,
    ! [X0: dB,X1: dB] :
      ( ( ( abs(X0) = abs(X1) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( abs(X0) != abs(X1) ) ) ),
    inference(nnf_transformation,[],[f148]) ).

tff(f148,plain,
    ! [X0: dB,X1: dB] :
      ( ( abs(X0) = abs(X1) )
    <=> ( X0 = X1 ) ),
    inference(rectify,[],[f84]) ).

tff(f84,axiom,
    ! [X75: dB,X76: dB] :
      ( ( abs(X76) = abs(X75) )
    <=> ( X75 = X76 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_dB_Osimps_I3_J) ).

tff(f615,plain,
    spl29_18,
    inference(avatar_split_clause,[],[f382,f613]) ).

tff(f382,plain,
    ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
    inference(cnf_transformation,[],[f135]) ).

tff(f135,plain,
    ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
    inference(rectify,[],[f107]) ).

tff(f107,axiom,
    ! [X0: $tType,X89: X0] : ( aa(X0,X0,combi(X0),X89) = X89 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).

tff(f611,plain,
    spl29_17,
    inference(avatar_split_clause,[],[f378,f609]) ).

tff(f378,plain,
    ! [X0: dB] :
      ( pp(aa(dB,bool,it,X0))
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f279]) ).

tff(f279,plain,
    ! [X0: dB] :
      ( ( pp(aa(dB,bool,it,X0))
        | ~ sP1(X0) )
      & ( sP1(X0)
        | ~ pp(aa(dB,bool,it,X0)) ) ),
    inference(nnf_transformation,[],[f259]) ).

tff(f259,plain,
    ! [X0: dB] :
      ( pp(aa(dB,bool,it,X0))
    <=> sP1(X0) ),
    inference(definition_folding,[],[f131,f258,f257]) ).

tff(f131,plain,
    ! [X0: dB] :
      ( pp(aa(dB,bool,it,X0))
    <=> ( ? [X1: dB,X2: dB,X3: list(dB)] :
            ( pp(aa(dB,bool,it,X2))
            & 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,X1),X2),zero_zero(nat)),X3)))
            & ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) )
        | ? [X4: dB] :
            ( pp(aa(dB,bool,it,X4))
            & ( abs(X4) = X0 ) )
        | ? [X5: list(dB),X6: nat] :
            ( listsp(dB,it,X5)
            & ( foldl(dB,dB,app,var(X6),X5) = X0 ) ) ) ),
    inference(rectify,[],[f96]) ).

tff(f96,axiom,
    ! [X53: dB] :
      ( pp(aa(dB,bool,it,X53))
    <=> ( ? [X84: dB,X85: dB,X86: list(dB)] :
            ( pp(aa(dB,bool,it,X85))
            & 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,X84),X85),zero_zero(nat)),X86)))
            & ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X84)),X85),X86) = X53 ) )
        | ? [X84: dB] :
            ( pp(aa(dB,bool,it,X84))
            & ( abs(X84) = X53 ) )
        | ? [X82: list(dB),X83: nat] :
            ( listsp(dB,it,X82)
            & ( foldl(dB,dB,app,var(X83),X82) = X53 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_IT_Osimps) ).

tff(f607,plain,
    spl29_16,
    inference(avatar_split_clause,[],[f377,f605]) ).

tff(f377,plain,
    ! [X0: dB] :
      ( sP1(X0)
      | ~ pp(aa(dB,bool,it,X0)) ),
    inference(cnf_transformation,[],[f279]) ).

tff(f602,plain,
    spl29_15,
    inference(avatar_split_clause,[],[f381,f600]) ).

tff(f600,plain,
    ( spl29_15
  <=> ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_15])]) ).

tff(f381,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f134]) ).

tff(f134,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
    inference(rectify,[],[f78]) ).

tff(f78,axiom,
    ! [X0: $tType,X71: fun(X0,bool)] : ( collect(X0,X71) = X71 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).

tff(f598,plain,
    spl29_14,
    inference(avatar_split_clause,[],[f360,f596]) ).

tff(f360,plain,
    ! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
    inference(cnf_transformation,[],[f126]) ).

tff(f126,plain,
    ! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
    inference(rectify,[],[f35]) ).

tff(f35,axiom,
    ! [X42: nat] : pp(aa(dB,bool,it,var(X42))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_Var__IT) ).

tff(f585,plain,
    spl29_13,
    inference(avatar_split_clause,[],[f361,f583]) ).

tff(f361,plain,
    ! [X0: bool] :
      ( ( fFalse = X0 )
      | ( fTrue = X0 ) ),
    inference(cnf_transformation,[],[f127]) ).

tff(f127,plain,
    ! [X0: bool] :
      ( ( fFalse = X0 )
      | ( fTrue = X0 ) ),
    inference(rectify,[],[f113]) ).

tff(f113,axiom,
    ! [X89: bool] :
      ( ( fFalse = X89 )
      | ( fTrue = X89 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).

tff(f581,plain,
    spl29_12,
    inference(avatar_split_clause,[],[f359,f579]) ).

tff(f579,plain,
    ( spl29_12
  <=> ! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_12])]) ).

tff(f359,plain,
    ! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
    inference(cnf_transformation,[],[f125]) ).

tff(f125,plain,
    ! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
    inference(rectify,[],[f82]) ).

tff(f82,axiom,
    ! [X41: nat] : ( zero_zero(nat) = dB_size(var(X41)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_dB_Osize_I1_J) ).

tff(f577,plain,
    spl29_11,
    inference(avatar_split_clause,[],[f332,f574]) ).

tff(f332,plain,
    pp(aa(dB,bool,it,u)),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    pp(aa(dB,bool,it,u)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_uIT) ).

tff(f572,plain,
    spl29_10,
    inference(avatar_split_clause,[],[f331,f569]) ).

tff(f331,plain,
    pp(aa(dB,bool,it,ua)),
    inference(cnf_transformation,[],[f3]) ).

tff(f3,axiom,
    pp(aa(dB,bool,it,ua)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Var_I3_J) ).

tff(f567,plain,
    spl29_9,
    inference(avatar_split_clause,[],[f330,f564]) ).

tff(f330,plain,
    pp(aa(dB,bool,it,t3)),
    inference(cnf_transformation,[],[f2]) ).

tff(f2,axiom,
    pp(aa(dB,bool,it,t3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096IT_At_096) ).

tff(f562,plain,
    ~ spl29_8,
    inference(avatar_split_clause,[],[f324,f559]) ).

tff(f324,plain,
    ~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),sK4),sK5))),
    inference(cnf_transformation,[],[f261]) ).

tff(f557,plain,
    spl29_7,
    inference(avatar_split_clause,[],[f323,f554]) ).

tff(f323,plain,
    pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,sK2),sK4),t)),
    inference(cnf_transformation,[],[f261]) ).

tff(f552,plain,
    spl29_6,
    inference(avatar_split_clause,[],[f379,f550]) ).

tff(f550,plain,
    ( spl29_6
  <=> ! [X0: nat,X1: dB] : ( var(X0) != abs(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_6])]) ).

tff(f379,plain,
    ! [X0: nat,X1: dB] : ( var(X0) != abs(X1) ),
    inference(cnf_transformation,[],[f132]) ).

tff(f132,plain,
    ! [X0: nat,X1: dB] : ( var(X0) != abs(X1) ),
    inference(rectify,[],[f90]) ).

tff(f90,axiom,
    ! [X41: nat,X79: dB] : ( var(X41) != abs(X79) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_dB_Osimps_I7_J) ).

tff(f548,plain,
    spl29_5,
    inference(avatar_split_clause,[],[f372,f546]) ).

tff(f546,plain,
    ( spl29_5
  <=> ! [X0: dB] :
        ( sP1(X0)
        | ~ sP0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_5])]) ).

tff(f372,plain,
    ! [X0: dB] :
      ( sP1(X0)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f274]) ).

tff(f544,plain,
    spl29_4,
    inference(avatar_split_clause,[],[f328,f541]) ).

tff(f328,plain,
    pp(fTrue),
    inference(cnf_transformation,[],[f102]) ).

tff(f102,axiom,
    pp(fTrue),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).

tff(f539,plain,
    spl29_3,
    inference(avatar_split_clause,[],[f327,f536]) ).

tff(f536,plain,
    ( spl29_3
  <=> zero(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_3])]) ).

tff(f327,plain,
    zero(nat),
    inference(cnf_transformation,[],[f100]) ).

tff(f100,axiom,
    zero(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).

tff(f534,plain,
    ~ spl29_2,
    inference(avatar_split_clause,[],[f325,f531]) ).

tff(f325,plain,
    ~ pp(fFalse),
    inference(cnf_transformation,[],[f112]) ).

tff(f112,axiom,
    ~ pp(fFalse),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

tff(f529,plain,
    spl29_1,
    inference(avatar_split_clause,[],[f322,f526]) ).

tff(f322,plain,
    pp(aa(dB,bool,it,sK4)),
    inference(cnf_transformation,[],[f261]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : LCL806_5 : TPTP v8.1.2. Released v6.0.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n002.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 14:09:27 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (2797)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42  % (2800)WARNING: value z3 for option sas not known
% 0.21/0.42  % (2801)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.42  % (2798)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.42  % (2802)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.42  % (2799)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.42  % (2803)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.42  % (2800)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.42  % (2804)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.43  % (2804)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.43  % Exception at run slice level
% 0.21/0.43  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.43  % Exception at run slice level
% 0.21/0.43  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.43  % Exception at run slice level
% 0.21/0.43  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.44  % (2806)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.21/0.45  % (2805)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.45  % (2807)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.21/0.46  % (2806)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.46  % (2805)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.46  % Exception at run slice level
% 0.21/0.46  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.47  % (2808)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 1.31/0.57  % (2802)First to succeed.
% 1.31/0.60  % (2802)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2797"
% 1.31/0.60  % (2802)Refutation found. Thanks to Tanya!
% 1.31/0.60  % SZS status Theorem for theBenchmark
% 1.31/0.60  % SZS output start Proof for theBenchmark
% See solution above
% 1.31/0.60  % (2802)------------------------------
% 1.31/0.60  % (2802)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.31/0.60  % (2802)Termination reason: Refutation
% 1.31/0.60  
% 1.31/0.60  % (2802)Memory used [KB]: 3058
% 1.31/0.60  % (2802)Time elapsed: 0.181 s
% 1.31/0.60  % (2802)Instructions burned: 478 (million)
% 1.31/0.60  % (2797)Success in time 0.233 s
%------------------------------------------------------------------------------