TSTP Solution File: SWW541_5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWW541_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n028.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 : Tue May 21 07:27:18 EDT 2024

% Result   : Theorem 36.52s 5.55s
% Output   : Refutation 36.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :  838
% Syntax   : Number of formulae    : 2571 ( 259 unt;  59 typ;   0 def)
%            Number of atoms       : 8499 (1710 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives : 9882 (3895   ~;4992   |; 129   &)
%                                         ( 698 <=>; 168  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :   10 (   1 avg)
%            Number of FOOLs       :    1 (   1 fml;   0 var)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :   60 (  40   >;  20   *;   0   +;   0  <<)
%            Number of predicates  :  679 ( 677 usr; 663 prp; 0-3 aty)
%            Number of functors    :   40 (  40 usr;   6 con; 0-5 aty)
%            Number of variables   : 6089 (5989   !;  60   ?;6089   :)
%                                         (  40  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    a1: $tType ).

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

tff(type_def_7,type,
    huffma1450048681e_tree: $tType > $tType ).

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

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

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

tff(func_def_0,type,
    zero_zero: 
      !>[X0: $tType] : X0 ).

tff(func_def_1,type,
    huffma675207370phabet: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > fun(X0,bool) ) ).

tff(func_def_2,type,
    huffma1134658180e_cost: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).

tff(func_def_3,type,
    huffma410068972_depth: 
      !>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * X0 ) > nat ) ).

tff(func_def_4,type,
    huffma1352802255e_freq: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > fun(X0,nat) ) ).

tff(func_def_5,type,
    huffma945805758height: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).

tff(func_def_6,type,
    huffma1401021291ibling: 
      !>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * X0 ) > X0 ) ).

tff(func_def_7,type,
    huffma1146269203erNode: 
      !>[X0: $tType] : ( ( nat * huffma1450048681e_tree(X0) * huffma1450048681e_tree(X0) ) > huffma1450048681e_tree(X0) ) ).

tff(func_def_8,type,
    huffma2021818691e_Leaf: 
      !>[X0: $tType] : ( ( nat * X0 ) > huffma1450048681e_tree(X0) ) ).

tff(func_def_9,type,
    huffma107959123e_case: 
      !>[X0: $tType,X1: $tType] : ( ( fun(nat,fun(X0,X1)) * fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))) * huffma1450048681e_tree(X0) ) > X1 ) ).

tff(func_def_10,type,
    huffma1280178957ee_rec: 
      !>[X0: $tType,X1: $tType] : ( ( fun(nat,fun(X0,X1)) * fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))) * huffma1450048681e_tree(X0) ) > X1 ) ).

tff(func_def_11,type,
    if: 
      !>[X0: $tType] : ( ( bool * X0 * X0 ) > X0 ) ).

tff(func_def_12,type,
    semiring_1_of_nat: 
      !>[X0: $tType] : ( nat > X0 ) ).

tff(func_def_13,type,
    size_size: 
      !>[X0: $tType] : ( X0 > nat ) ).

tff(func_def_14,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_15,type,
    fFalse: bool ).

tff(func_def_16,type,
    fTrue: bool ).

tff(func_def_17,type,
    a: a1 ).

tff(func_def_18,type,
    t_1: huffma1450048681e_tree(a1) ).

tff(func_def_19,type,
    t_2: huffma1450048681e_tree(a1) ).

tff(func_def_20,type,
    w: nat ).

tff(func_def_21,type,
    sK1: int > nat ).

tff(func_def_22,type,
    sK2: fun(int,bool) > nat ).

tff(func_def_23,type,
    sK3: fun(int,bool) > int ).

tff(func_def_24,type,
    sK4: fun(int,bool) > int ).

tff(func_def_25,type,
    sK5: fun(int,bool) > nat ).

tff(func_def_26,type,
    sK6: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).

tff(func_def_27,type,
    sK7: ( nat * fun(nat,bool) ) > nat ).

tff(func_def_28,type,
    sK8: fun(nat,bool) > nat ).

tff(func_def_29,type,
    sK9: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).

tff(func_def_30,type,
    sK10: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > huffma1450048681e_tree(X0) ) ).

tff(func_def_31,type,
    sK11: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > huffma1450048681e_tree(X0) ) ).

tff(func_def_32,type,
    sK12: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).

tff(func_def_33,type,
    sK13: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).

tff(func_def_34,type,
    sK14: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).

tff(func_def_35,type,
    sK15: fun(nat,nat) > nat ).

tff(func_def_36,type,
    sK16: fun(nat,nat) > nat ).

tff(func_def_37,type,
    sK17: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

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

tff(pred_def_2,type,
    ord: 
      !>[X0: $tType] : $o ).

tff(pred_def_3,type,
    order: 
      !>[X0: $tType] : $o ).

tff(pred_def_4,type,
    semiring_1: 
      !>[X0: $tType] : $o ).

tff(pred_def_5,type,
    linorder: 
      !>[X0: $tType] : $o ).

tff(pred_def_6,type,
    preorder: 
      !>[X0: $tType] : $o ).

tff(pred_def_7,type,
    semiring_char_0: 
      !>[X0: $tType] : $o ).

tff(pred_def_8,type,
    linordered_semidom: 
      !>[X0: $tType] : $o ).

tff(pred_def_9,type,
    huffma1518433673istent: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > $o ) ).

tff(pred_def_10,type,
    huffma1393970616ptimum: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > $o ) ).

tff(pred_def_11,type,
    ord_less: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(pred_def_12,type,
    ord_less_eq: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(pred_def_13,type,
    member: 
      !>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).

tff(pred_def_14,type,
    pp: bool > $o ).

tff(pred_def_15,type,
    sP0: ( nat * nat * fun(nat,fun(nat,bool)) ) > $o ).

tff(f36745,plain,
    $false,
    inference(avatar_sat_refutation,[],[f583,f588,f593,f598,f603,f608,f613,f618,f623,f628,f633,f638,f643,f648,f653,f658,f663,f668,f673,f678,f683,f688,f693,f697,f701,f705,f709,f713,f718,f723,f727,f731,f735,f739,f743,f747,f754,f759,f764,f768,f772,f777,f781,f790,f794,f798,f806,f810,f814,f821,f825,f829,f834,f838,f842,f846,f850,f854,f870,f882,f886,f890,f894,f898,f904,f908,f924,f928,f932,f936,f940,f944,f948,f952,f956,f960,f1006,f1010,f1014,f1018,f1022,f1026,f1030,f1034,f1038,f1042,f1046,f1050,f1054,f1201,f1205,f1209,f1213,f1217,f1221,f1225,f1256,f1260,f1264,f1268,f1272,f1276,f1280,f1284,f1288,f1292,f1436,f1450,f1454,f1458,f1481,f1485,f1489,f1493,f1497,f1501,f1505,f1526,f1541,f1545,f1570,f1574,f1578,f1582,f1641,f1645,f1649,f1724,f1742,f1768,f1772,f1797,f1801,f1816,f1842,f1846,f1870,f1875,f1879,f1883,f1887,f1907,f1920,f1933,f1959,f1981,f2036,f2050,f2054,f2058,f2062,f2076,f2080,f2084,f2088,f2092,f2119,f2166,f2170,f2183,f2187,f2196,f2204,f2218,f2222,f2226,f2230,f2234,f2305,f2309,f2321,f2339,f2352,f2356,f2360,f2364,f2398,f2414,f2418,f2422,f2432,f2468,f2482,f2545,f2550,f2554,f2558,f2562,f2566,f2571,f2575,f2676,f2693,f2718,f2722,f2726,f2730,f2766,f2770,f2774,f2778,f2782,f2786,f2790,f2794,f2798,f2933,f2937,f2941,f2945,f2949,f2953,f3014,f3031,f3040,f3064,f3074,f3084,f3088,f3092,f3096,f3100,f3167,f3171,f3175,f3309,f3355,f3359,f3363,f3367,f3379,f3391,f3395,f3408,f3412,f3516,f3520,f3536,f3540,f3560,f3564,f3568,f3572,f3576,f3580,f3591,f3595,f3599,f3603,f4101,f4105,f4113,f4114,f4118,f4122,f4144,f4148,f4206,f4216,f4220,f4224,f4228,f4289,f4293,f4297,f4301,f4305,f4413,f4417,f4421,f4425,f4487,f4491,f4495,f4499,f4508,f4512,f4516,f4520,f4807,f4838,f4856,f4860,f4864,f4868,f4872,f4876,f4955,f4970,f4974,f4983,f4987,f4991,f4995,f4999,f5003,f5007,f5011,f5015,f5019,f5023,f5027,f5031,f5035,f5831,f5835,f5839,f5843,f5896,f5900,f5904,f5908,f5912,f5916,f5920,f5924,f6061,f6065,f6069,f6073,f6077,f6081,f6085,f6089,f6219,f6260,f6264,f6268,f6272,f6334,f6338,f6342,f6346,f6494,f6498,f6536,f6540,f6545,f6549,f6553,f6557,f6561,f6600,f6626,f6630,f6680,f6684,f6755,f6759,f6763,f6767,f6871,f6875,f6885,f6889,f7008,f7012,f7016,f7020,f7030,f7034,f7264,f7268,f7291,f7295,f7405,f7409,f7544,f7621,f7625,f7629,f7633,f7851,f7869,f7891,f7923,f7927,f8090,f8094,f8098,f8102,f8174,f8178,f8182,f8268,f8272,f8359,f8363,f8367,f8527,f8531,f8603,f8607,f8781,f8785,f8789,f8889,f8893,f9066,f9070,f9074,f9178,f9183,f9187,f9191,f9309,f9313,f9317,f9321,f9325,f9329,f9333,f9337,f9341,f9345,f12186,f12256,f12260,f12264,f12268,f12272,f12285,f12289,f12293,f12297,f12308,f12522,f12526,f12530,f12534,f12538,f12542,f12546,f12550,f12561,f12565,f12569,f12573,f12577,f12581,f12607,f12611,f12615,f12619,f12623,f16984,f16988,f16992,f16996,f17000,f17004,f17008,f17012,f17073,f17077,f17081,f17085,f17089,f17093,f17097,f17101,f17105,f17109,f17167,f17171,f17175,f17179,f17183,f17187,f18334,f19593,f20034,f20038,f20159,f20163,f20167,f20171,f20175,f20179,f20221,f20225,f20229,f20233,f20237,f20241,f20245,f20353,f20588,f20619,f20634,f20638,f20653,f20657,f20688,f20745,f20749,f20753,f20757,f20761,f20903,f20915,f20927,f20931,f20935,f20939,f20943,f20947,f20951,f20955,f20959,f20963,f20967,f20971,f20975,f20979,f20983,f20987,f20991,f20995,f21893,f21897,f21901,f21905,f21939,f21943,f21947,f21951,f21955,f21959,f22542,f22546,f22550,f22554,f22558,f22602,f22606,f22629,f22633,f22669,f22673,f22677,f22681,f22685,f22689,f22693,f22697,f22701,f22766,f23432,f23436,f23440,f23444,f23448,f23452,f23456,f23460,f23464,f23468,f23472,f23476,f23480,f23484,f23488,f23492,f23496,f23547,f23551,f23555,f23559,f23563,f23567,f23571,f23575,f23579,f25648,f26800,f26804,f26808,f26812,f26816,f26820,f26837,f26841,f26845,f26849,f26853,f26869,f26873,f26877,f26881,f26915,f26919,f26923,f26947,f30602,f30610,f30613,f30799,f30804,f30816,f30820,f30824,f30828,f31484,f31493,f31497,f31501,f31505,f31509,f31513,f31517,f31521,f31525,f31529,f31534,f31538,f31542,f31546,f31550,f31554,f31558,f31562,f31566,f31570,f31574,f31579,f31583,f31587,f34174,f36468,f36492,f36516,f36556,f36580,f36584,f36588,f36592,f36596,f36600,f36604,f36608,f36612,f36616,f36620,f36624,f36628,f36632,f36636,f36640,f36644,f36649,f36679,f36698,f36717,f36721,f36725,f36729,f36733,f36740,f36741]) ).

tff(f36741,plain,
    ( ~ spl18_27
    | ~ spl18_655 ),
    inference(avatar_contradiction_clause,[],[f36736]) ).

tff(f36736,plain,
    ( $false
    | ~ spl18_27
    | ~ spl18_655 ),
    inference(resolution,[],[f36648,f708]) ).

tff(f708,plain,
    ( ! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat))
    | ~ spl18_27 ),
    inference(avatar_component_clause,[],[f707]) ).

tff(f707,plain,
    ( spl18_27
  <=> ! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_27])]) ).

tff(f36648,plain,
    ( ord_less(nat,zero_zero(nat),zero_zero(nat))
    | ~ spl18_655 ),
    inference(avatar_component_clause,[],[f36646]) ).

tff(f36646,plain,
    ( spl18_655
  <=> ord_less(nat,zero_zero(nat),zero_zero(nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_655])]) ).

tff(f36740,plain,
    ( ~ spl18_24
    | ~ spl18_655 ),
    inference(avatar_contradiction_clause,[],[f36737]) ).

tff(f36737,plain,
    ( $false
    | ~ spl18_24
    | ~ spl18_655 ),
    inference(resolution,[],[f36648,f696]) ).

tff(f696,plain,
    ( ! [X0: nat] : ~ ord_less(nat,X0,X0)
    | ~ spl18_24 ),
    inference(avatar_component_clause,[],[f695]) ).

tff(f695,plain,
    ( spl18_24
  <=> ! [X0: nat] : ~ ord_less(nat,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_24])]) ).

tff(f36733,plain,
    ( spl18_662
    | ~ spl18_90
    | ~ spl18_284 ),
    inference(avatar_split_clause,[],[f4818,f4805,f1052,f36731]) ).

tff(f36731,plain,
    ( spl18_662
  <=> ! [X0: $tType,X3: fun(X0,nat),X2: X0,X1: nat] :
        ( ~ ord_less_eq(nat,X1,aa(X0,nat,X3,X2))
        | ( aa(X0,nat,X3,X2) = X1 )
        | ~ ord_less_eq(fun(X0,nat),X3,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_662])]) ).

tff(f1052,plain,
    ( spl18_90
  <=> ! [X0: $tType,X1: nat,X3: X0] : ( aa(X0,nat,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X3)),X3) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_90])]) ).

tff(f4805,plain,
    ( spl18_284
  <=> ! [X0: $tType,X3: X0,X2: fun(X0,nat),X1: fun(X0,nat)] :
        ( ~ ord_less_eq(fun(X0,nat),X1,X2)
        | ( aa(X0,nat,X2,X3) = aa(X0,nat,X1,X3) )
        | ~ ord_less_eq(nat,aa(X0,nat,X2,X3),aa(X0,nat,X1,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_284])]) ).

tff(f4818,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,nat),X1: nat] :
        ( ~ ord_less_eq(nat,X1,aa(X0,nat,X3,X2))
        | ( aa(X0,nat,X3,X2) = X1 )
        | ~ ord_less_eq(fun(X0,nat),X3,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2))) )
    | ~ spl18_90
    | ~ spl18_284 ),
    inference(superposition,[],[f4806,f1053]) ).

tff(f1053,plain,
    ( ! [X0: $tType,X3: X0,X1: nat] : ( aa(X0,nat,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X3)),X3) = X1 )
    | ~ spl18_90 ),
    inference(avatar_component_clause,[],[f1052]) ).

tff(f4806,plain,
    ( ! [X0: $tType,X2: fun(X0,nat),X3: X0,X1: fun(X0,nat)] :
        ( ~ ord_less_eq(nat,aa(X0,nat,X2,X3),aa(X0,nat,X1,X3))
        | ( aa(X0,nat,X2,X3) = aa(X0,nat,X1,X3) )
        | ~ ord_less_eq(fun(X0,nat),X1,X2) )
    | ~ spl18_284 ),
    inference(avatar_component_clause,[],[f4805]) ).

tff(f36729,plain,
    ( spl18_661
    | ~ spl18_41
    | ~ spl18_274 ),
    inference(avatar_split_clause,[],[f4450,f4419,f770,f36727]) ).

tff(f36727,plain,
    ( spl18_661
  <=> ! [X0: fun(int,bool),X3: nat,X2: nat,X1: nat] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,semiring_1_of_nat(int,X2)),X3,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_661])]) ).

tff(f770,plain,
    ( spl18_41
  <=> ! [X0: nat] : ord_less_eq(int,zero_zero(int),semiring_1_of_nat(int,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_41])]) ).

tff(f4419,plain,
    ( spl18_274
  <=> ! [X0: fun(int,bool),X3: nat,X2: nat,X1: int] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ ord_less_eq(int,zero_zero(int),X1)
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,X1),X3,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_274])]) ).

tff(f4450,plain,
    ( ! [X2: nat,X3: nat,X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,semiring_1_of_nat(int,X2)),X3,X1)) ) )
    | ~ spl18_41
    | ~ spl18_274 ),
    inference(resolution,[],[f4420,f771]) ).

tff(f771,plain,
    ( ! [X0: nat] : ord_less_eq(int,zero_zero(int),semiring_1_of_nat(int,X0))
    | ~ spl18_41 ),
    inference(avatar_component_clause,[],[f770]) ).

tff(f4420,plain,
    ( ! [X2: nat,X3: nat,X0: fun(int,bool),X1: int] :
        ( ~ ord_less_eq(int,zero_zero(int),X1)
        | pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,X1),X3,X2)) ) )
    | ~ spl18_274 ),
    inference(avatar_component_clause,[],[f4419]) ).

tff(f36725,plain,
    ( spl18_660
    | ~ spl18_66
    | ~ spl18_268 ),
    inference(avatar_split_clause,[],[f4346,f4291,f902,f36723]) ).

tff(f36723,plain,
    ( spl18_660
  <=> ! [X2: nat,X0: fun(nat,bool),X1: nat,X3: nat] :
        ( ord_less(nat,zero_zero(nat),sK8(X0))
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X0,zero_zero(nat)),X3,X2)) )
        | member(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_660])]) ).

tff(f902,plain,
    ( spl18_66
  <=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( member(X0,X2,X1)
        | ~ pp(aa(X0,bool,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_66])]) ).

tff(f4291,plain,
    ( spl18_268
  <=> ! [X0: fun(nat,bool),X3: nat,X2: nat,X1: nat] :
        ( ord_less(nat,zero_zero(nat),sK8(X0))
        | pp(aa(nat,bool,X0,X1))
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X0,zero_zero(nat)),X3,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_268])]) ).

tff(f4346,plain,
    ( ! [X2: nat,X3: nat,X0: fun(nat,bool),X1: nat] :
        ( ord_less(nat,zero_zero(nat),sK8(X0))
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X0,zero_zero(nat)),X3,X2)) )
        | member(nat,X1,X0) )
    | ~ spl18_66
    | ~ spl18_268 ),
    inference(resolution,[],[f4292,f903]) ).

tff(f903,plain,
    ( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( ~ pp(aa(X0,bool,X1,X2))
        | member(X0,X2,X1) )
    | ~ spl18_66 ),
    inference(avatar_component_clause,[],[f902]) ).

tff(f4292,plain,
    ( ! [X2: nat,X3: nat,X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ord_less(nat,zero_zero(nat),sK8(X0))
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X0,zero_zero(nat)),X3,X2)) ) )
    | ~ spl18_268 ),
    inference(avatar_component_clause,[],[f4291]) ).

tff(f36721,plain,
    ( spl18_659
    | ~ spl18_66
    | ~ spl18_267 ),
    inference(avatar_split_clause,[],[f4314,f4287,f902,f36719]) ).

tff(f36719,plain,
    ( spl18_659
  <=> ! [X0: fun(nat,bool),X3: nat,X2: nat,X1: nat] :
        ( ord_less_eq(nat,sK7(X1,X0),X1)
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X0,X1),X3,X2)) )
        | member(nat,zero_zero(nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_659])]) ).

tff(f4287,plain,
    ( spl18_267
  <=> ! [X0: nat,X3: nat,X2: nat,X1: fun(nat,bool)] :
        ( ord_less_eq(nat,sK7(X0,X1),X0)
        | pp(aa(nat,bool,X1,zero_zero(nat)))
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X1,X0),X3,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_267])]) ).

tff(f4314,plain,
    ( ! [X2: nat,X3: nat,X0: fun(nat,bool),X1: nat] :
        ( ord_less_eq(nat,sK7(X1,X0),X1)
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X0,X1),X3,X2)) )
        | member(nat,zero_zero(nat),X0) )
    | ~ spl18_66
    | ~ spl18_267 ),
    inference(resolution,[],[f4288,f903]) ).

tff(f4288,plain,
    ( ! [X2: nat,X3: nat,X0: nat,X1: fun(nat,bool)] :
        ( pp(aa(nat,bool,X1,zero_zero(nat)))
        | ord_less_eq(nat,sK7(X0,X1),X0)
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X1,X0),X3,X2)) ) )
    | ~ spl18_267 ),
    inference(avatar_component_clause,[],[f4287]) ).

tff(f36717,plain,
    ( spl18_658
    | ~ spl18_129
    | ~ spl18_261 ),
    inference(avatar_split_clause,[],[f4193,f4146,f1722,f36715]) ).

tff(f36715,plain,
    ( spl18_658
  <=> ! [X0: fun(nat,nat),X3: nat,X2: nat,X1: nat] :
        ( ord_less(nat,sK15(X0),sK16(X0))
        | ~ ord_less_eq(nat,X1,X2)
        | ord_less_eq(nat,aa(nat,nat,X0,X1),aa(nat,nat,X0,X3))
        | ~ ord_less_eq(nat,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_658])]) ).

tff(f1722,plain,
    ( spl18_129
  <=> ! [X2: fun(nat,nat),X0: nat,X1: nat] :
        ( ord_less_eq(nat,aa(nat,nat,X2,X1),aa(nat,nat,X2,X0))
        | ~ ord_less_eq(nat,X1,X0)
        | ord_less(nat,sK15(X2),sK16(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_129])]) ).

tff(f4146,plain,
    ( spl18_261
  <=> ! [X0: nat,X3: nat,X2: fun(nat,nat),X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less(nat,sK15(X2),sK16(X2))
        | ~ ord_less_eq(nat,aa(nat,nat,X2,X1),X3)
        | ord_less_eq(nat,aa(nat,nat,X2,X0),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_261])]) ).

tff(f4193,plain,
    ( ! [X2: nat,X3: nat,X0: fun(nat,nat),X1: nat] :
        ( ord_less(nat,sK15(X0),sK16(X0))
        | ~ ord_less_eq(nat,X1,X2)
        | ord_less_eq(nat,aa(nat,nat,X0,X1),aa(nat,nat,X0,X3))
        | ~ ord_less_eq(nat,X2,X3) )
    | ~ spl18_129
    | ~ spl18_261 ),
    inference(duplicate_literal_removal,[],[f4182]) ).

tff(f4182,plain,
    ( ! [X2: nat,X3: nat,X0: fun(nat,nat),X1: nat] :
        ( ord_less(nat,sK15(X0),sK16(X0))
        | ~ ord_less_eq(nat,X1,X2)
        | ord_less_eq(nat,aa(nat,nat,X0,X1),aa(nat,nat,X0,X3))
        | ~ ord_less_eq(nat,X2,X3)
        | ord_less(nat,sK15(X0),sK16(X0)) )
    | ~ spl18_129
    | ~ spl18_261 ),
    inference(resolution,[],[f4147,f1723]) ).

tff(f1723,plain,
    ( ! [X2: fun(nat,nat),X0: nat,X1: nat] :
        ( ord_less_eq(nat,aa(nat,nat,X2,X1),aa(nat,nat,X2,X0))
        | ~ ord_less_eq(nat,X1,X0)
        | ord_less(nat,sK15(X2),sK16(X2)) )
    | ~ spl18_129 ),
    inference(avatar_component_clause,[],[f1722]) ).

tff(f4147,plain,
    ( ! [X2: fun(nat,nat),X3: nat,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,aa(nat,nat,X2,X1),X3)
        | ord_less(nat,sK15(X2),sK16(X2))
        | ~ ord_less_eq(nat,X0,X1)
        | ord_less_eq(nat,aa(nat,nat,X2,X0),X3) )
    | ~ spl18_261 ),
    inference(avatar_component_clause,[],[f4146]) ).

tff(f36698,plain,
    ( spl18_657
    | spl18_1
    | ~ spl18_168
    | ~ spl18_249 ),
    inference(avatar_split_clause,[],[f3949,f3574,f2216,f580,f36696]) ).

tff(f36696,plain,
    ( spl18_657
  <=> ! [X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK3(aa(nat,fun(int,bool),X0,X1)))
        | ( fTrue = huffma1280178957ee_rec(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,zero_zero(int))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_657])]) ).

tff(f580,plain,
    ( spl18_1
  <=> pp(fFalse) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_1])]) ).

tff(f2216,plain,
    ( spl18_168
  <=> ! [X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,zero_zero(int)))
        | ord_less_eq(int,zero_zero(int),sK3(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_168])]) ).

tff(f3574,plain,
    ( spl18_249
  <=> ! [X0: $tType,X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X3: X0,X2: nat,X1: fun(nat,fun(X0,bool))] :
        ( ( fTrue = huffma1280178957ee_rec(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)) )
        | ( fFalse = aa(X0,bool,aa(nat,fun(X0,bool),X1,X2),X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_249])]) ).

tff(f3949,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( pp(fFalse)
        | ord_less_eq(int,zero_zero(int),sK3(aa(nat,fun(int,bool),X0,X1)))
        | ( fTrue = huffma1280178957ee_rec(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,zero_zero(int))) ) )
    | ~ spl18_168
    | ~ spl18_249 ),
    inference(superposition,[],[f2217,f3575]) ).

tff(f3575,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: fun(nat,fun(X0,bool)),X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))))] :
        ( ( fTrue = huffma1280178957ee_rec(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)) )
        | ( fFalse = aa(X0,bool,aa(nat,fun(X0,bool),X1,X2),X3) ) )
    | ~ spl18_249 ),
    inference(avatar_component_clause,[],[f3574]) ).

tff(f2217,plain,
    ( ! [X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,zero_zero(int)))
        | ord_less_eq(int,zero_zero(int),sK3(X0)) )
    | ~ spl18_168 ),
    inference(avatar_component_clause,[],[f2216]) ).

tff(f36679,plain,
    ( spl18_656
    | spl18_1
    | ~ spl18_168
    | ~ spl18_246 ),
    inference(avatar_split_clause,[],[f3724,f3562,f2216,f580,f36677]) ).

tff(f36677,plain,
    ( spl18_656
  <=> ! [X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK3(aa(nat,fun(int,bool),X0,X1)))
        | ( fTrue = huffma107959123e_case(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,zero_zero(int))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_656])]) ).

tff(f3562,plain,
    ( spl18_246
  <=> ! [X0: $tType,X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X3: X0,X2: nat,X1: fun(nat,fun(X0,bool))] :
        ( ( fTrue = huffma107959123e_case(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)) )
        | ( fFalse = aa(X0,bool,aa(nat,fun(X0,bool),X1,X2),X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_246])]) ).

tff(f3724,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( pp(fFalse)
        | ord_less_eq(int,zero_zero(int),sK3(aa(nat,fun(int,bool),X0,X1)))
        | ( fTrue = huffma107959123e_case(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,zero_zero(int))) ) )
    | ~ spl18_168
    | ~ spl18_246 ),
    inference(superposition,[],[f2217,f3563]) ).

tff(f3563,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: fun(nat,fun(X0,bool)),X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)))] :
        ( ( fTrue = huffma107959123e_case(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)) )
        | ( fFalse = aa(X0,bool,aa(nat,fun(X0,bool),X1,X2),X3) ) )
    | ~ spl18_246 ),
    inference(avatar_component_clause,[],[f3562]) ).

tff(f36649,plain,
    ( spl18_655
    | ~ spl18_38
    | ~ spl18_630 ),
    inference(avatar_split_clause,[],[f36518,f31576,f756,f36646]) ).

tff(f756,plain,
    ( spl18_38
  <=> ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_38])]) ).

tff(f31576,plain,
    ( spl18_630
  <=> ( zero_zero(nat) = huffma945805758height(a1,t_1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_630])]) ).

tff(f36518,plain,
    ( ord_less(nat,zero_zero(nat),zero_zero(nat))
    | ~ spl18_38
    | ~ spl18_630 ),
    inference(superposition,[],[f758,f31578]) ).

tff(f31578,plain,
    ( ( zero_zero(nat) = huffma945805758height(a1,t_1) )
    | ~ spl18_630 ),
    inference(avatar_component_clause,[],[f31576]) ).

tff(f758,plain,
    ( ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_1))
    | ~ spl18_38 ),
    inference(avatar_component_clause,[],[f756]) ).

tff(f36644,plain,
    ( spl18_654
    | spl18_1
    | ~ spl18_225
    | ~ spl18_245 ),
    inference(avatar_split_clause,[],[f3683,f3558,f3090,f580,f36642]) ).

tff(f36642,plain,
    ( spl18_654
  <=> ! [X2: nat,X0: fun(nat,fun(nat,bool)),X3: nat] :
        ( ord_less(nat,X2,X3)
        | ( fTrue = aa(nat,bool,aa(nat,fun(nat,bool),X0,X2),X3) )
        | sP0(X3,X2,X0)
        | ( X2 = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_654])]) ).

tff(f3090,plain,
    ( spl18_225
  <=> ! [X0: fun(nat,fun(nat,bool)),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X2: nat,X1: nat] :
        ( pp(huffma107959123e_case(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ord_less(nat,X1,X2)
        | ( X1 = X2 )
        | sP0(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_225])]) ).

tff(f3558,plain,
    ( spl18_245
  <=> ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X4: X0,X3: nat,X1: fun(nat,fun(X0,bool))] :
        ( ( fTrue = aa(X0,bool,aa(nat,fun(X0,bool),X1,X3),X4) )
        | ( fFalse = huffma107959123e_case(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_245])]) ).

tff(f3683,plain,
    ( ! [X2: nat,X3: nat,X0: fun(nat,fun(nat,bool))] :
        ( pp(fFalse)
        | ord_less(nat,X2,X3)
        | ( X2 = X3 )
        | sP0(X3,X2,X0)
        | ( fTrue = aa(nat,bool,aa(nat,fun(nat,bool),X0,X2),X3) ) )
    | ~ spl18_225
    | ~ spl18_245 ),
    inference(superposition,[],[f3091,f3559]) ).

tff(f3559,plain,
    ( ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X3: nat,X1: fun(nat,fun(X0,bool)),X4: X0] :
        ( ( fTrue = aa(X0,bool,aa(nat,fun(X0,bool),X1,X3),X4) )
        | ( fFalse = huffma107959123e_case(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) ) )
    | ~ spl18_245 ),
    inference(avatar_component_clause,[],[f3558]) ).

tff(f3091,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( pp(huffma107959123e_case(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ord_less(nat,X1,X2)
        | ( X1 = X2 )
        | sP0(X2,X1,X0) )
    | ~ spl18_225 ),
    inference(avatar_component_clause,[],[f3090]) ).

tff(f36640,plain,
    ( spl18_653
    | ~ spl18_31
    | ~ spl18_239 ),
    inference(avatar_split_clause,[],[f3494,f3406,f725,f36638]) ).

tff(f36638,plain,
    ( spl18_653
  <=> ! [X0: fun(bool,bool),X1: fun(bool,bool)] :
        ( ( fTrue != aa(bool,bool,X1,fTrue) )
        | ( X0 = X1 )
        | ( fFalse = sK17(bool,bool,X0,X1) )
        | ( fFalse = aa(bool,bool,X0,fTrue) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_653])]) ).

tff(f725,plain,
    ( spl18_31
  <=> ! [X0: bool] :
        ( ( fFalse = X0 )
        | ( fTrue = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_31])]) ).

tff(f3406,plain,
    ( spl18_239
  <=> ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
        ( ( aa(bool,X0,X2,fTrue) != aa(bool,X0,X1,fTrue) )
        | ( X1 = X2 )
        | ( fFalse = sK17(X0,bool,X1,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_239])]) ).

tff(f3494,plain,
    ( ! [X0: fun(bool,bool),X1: fun(bool,bool)] :
        ( ( fTrue != aa(bool,bool,X1,fTrue) )
        | ( X0 = X1 )
        | ( fFalse = sK17(bool,bool,X0,X1) )
        | ( fFalse = aa(bool,bool,X0,fTrue) ) )
    | ~ spl18_31
    | ~ spl18_239 ),
    inference(superposition,[],[f3407,f726]) ).

tff(f726,plain,
    ( ! [X0: bool] :
        ( ( fTrue = X0 )
        | ( fFalse = X0 ) )
    | ~ spl18_31 ),
    inference(avatar_component_clause,[],[f725]) ).

tff(f3407,plain,
    ( ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
        ( ( aa(bool,X0,X2,fTrue) != aa(bool,X0,X1,fTrue) )
        | ( X1 = X2 )
        | ( fFalse = sK17(X0,bool,X1,X2) ) )
    | ~ spl18_239 ),
    inference(avatar_component_clause,[],[f3406]) ).

tff(f36636,plain,
    ( spl18_652
    | ~ spl18_31
    | ~ spl18_239 ),
    inference(avatar_split_clause,[],[f3480,f3406,f725,f36634]) ).

tff(f36634,plain,
    ( spl18_652
  <=> ! [X0: fun(bool,bool),X1: fun(bool,bool)] :
        ( ( fTrue != aa(bool,bool,X1,fTrue) )
        | ( X0 = X1 )
        | ( fFalse = sK17(bool,bool,X1,X0) )
        | ( fFalse = aa(bool,bool,X0,fTrue) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_652])]) ).

tff(f3480,plain,
    ( ! [X0: fun(bool,bool),X1: fun(bool,bool)] :
        ( ( fTrue != aa(bool,bool,X1,fTrue) )
        | ( X0 = X1 )
        | ( fFalse = sK17(bool,bool,X1,X0) )
        | ( fFalse = aa(bool,bool,X0,fTrue) ) )
    | ~ spl18_31
    | ~ spl18_239 ),
    inference(superposition,[],[f3407,f726]) ).

tff(f36632,plain,
    ( spl18_651
    | ~ spl18_31
    | ~ spl18_238 ),
    inference(avatar_split_clause,[],[f3473,f3393,f725,f36630]) ).

tff(f36630,plain,
    ( spl18_651
  <=> ! [X2: nat,X3: huffma1450048681e_tree(bool),X4: huffma1450048681e_tree(bool),X0: nat,X5: bool,X1: huffma1450048681e_tree(bool)] :
        ( ( fTrue = huffma1401021291ibling(bool,X1,X5) )
        | ( huffma1401021291ibling(bool,X1,X5) = X5 )
        | ( fFalse = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X0,X1,huffma1146269203erNode(bool,X2,X3,X4)),X5) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_651])]) ).

tff(f3393,plain,
    ( spl18_238
  <=> ! [X0: $tType,X5: huffma1450048681e_tree(X0),X3: nat,X4: huffma1450048681e_tree(X0),X6: X0,X2: huffma1450048681e_tree(X0),X1: nat] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),X6) = huffma1401021291ibling(X0,X2,X6) )
        | ( huffma1401021291ibling(X0,X2,X6) = X6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_238])]) ).

tff(f3473,plain,
    ( ! [X2: nat,X3: huffma1450048681e_tree(bool),X0: nat,X1: huffma1450048681e_tree(bool),X4: huffma1450048681e_tree(bool),X5: bool] :
        ( ( fTrue = huffma1401021291ibling(bool,X1,X5) )
        | ( huffma1401021291ibling(bool,X1,X5) = X5 )
        | ( fFalse = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X0,X1,huffma1146269203erNode(bool,X2,X3,X4)),X5) ) )
    | ~ spl18_31
    | ~ spl18_238 ),
    inference(superposition,[],[f3394,f726]) ).

tff(f3394,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: nat,X6: X0,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),X6) = huffma1401021291ibling(X0,X2,X6) )
        | ( huffma1401021291ibling(X0,X2,X6) = X6 ) )
    | ~ spl18_238 ),
    inference(avatar_component_clause,[],[f3393]) ).

tff(f36628,plain,
    ( spl18_650
    | ~ spl18_53
    | ~ spl18_236 ),
    inference(avatar_split_clause,[],[f3384,f3377,f827,f36626]) ).

tff(f36626,plain,
    ( spl18_650
  <=> ! [X0: $tType,X2: X0,X1: nat] :
        ( ( fFalse = aa(X0,bool,semiring_1_of_nat(fun(X0,bool),X1),X2) )
        | ord_less_eq(bool,aa(X0,bool,zero_zero(fun(X0,bool)),X2),fTrue)
        | ~ linordered_semidom(fun(X0,bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_650])]) ).

tff(f827,plain,
    ( spl18_53
  <=> ! [X0: $tType,X1: nat] :
        ( ord_less_eq(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
        | ~ linordered_semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_53])]) ).

tff(f3377,plain,
    ( spl18_236
  <=> ! [X0: $tType,X3: fun(X0,bool),X2: X0,X1: fun(X0,bool)] :
        ( ord_less_eq(bool,aa(X0,bool,X3,X2),fTrue)
        | ( fFalse = aa(X0,bool,X1,X2) )
        | ~ ord_less_eq(fun(X0,bool),X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_236])]) ).

tff(f3384,plain,
    ( ! [X0: $tType,X2: X0,X1: nat] :
        ( ( fFalse = aa(X0,bool,semiring_1_of_nat(fun(X0,bool),X1),X2) )
        | ord_less_eq(bool,aa(X0,bool,zero_zero(fun(X0,bool)),X2),fTrue)
        | ~ linordered_semidom(fun(X0,bool)) )
    | ~ spl18_53
    | ~ spl18_236 ),
    inference(resolution,[],[f3378,f828]) ).

tff(f828,plain,
    ( ! [X0: $tType,X1: nat] :
        ( ord_less_eq(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
        | ~ linordered_semidom(X0) )
    | ~ spl18_53 ),
    inference(avatar_component_clause,[],[f827]) ).

tff(f3378,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: fun(X0,bool)] :
        ( ~ ord_less_eq(fun(X0,bool),X3,X1)
        | ( fFalse = aa(X0,bool,X1,X2) )
        | ord_less_eq(bool,aa(X0,bool,X3,X2),fTrue) )
    | ~ spl18_236 ),
    inference(avatar_component_clause,[],[f3377]) ).

tff(f36624,plain,
    ( spl18_649
    | ~ spl18_53
    | ~ spl18_235 ),
    inference(avatar_split_clause,[],[f3372,f3365,f827,f36622]) ).

tff(f36622,plain,
    ( spl18_649
  <=> ! [X0: $tType,X2: nat,X1: X0] :
        ( ( fFalse = aa(X0,bool,zero_zero(fun(X0,bool)),X1) )
        | ord_less_eq(bool,fTrue,aa(X0,bool,semiring_1_of_nat(fun(X0,bool),X2),X1))
        | ~ linordered_semidom(fun(X0,bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_649])]) ).

tff(f3365,plain,
    ( spl18_235
  <=> ! [X0: $tType,X3: fun(X0,bool),X2: X0,X1: fun(X0,bool)] :
        ( ord_less_eq(bool,fTrue,aa(X0,bool,X3,X2))
        | ( fFalse = aa(X0,bool,X1,X2) )
        | ~ ord_less_eq(fun(X0,bool),X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_235])]) ).

tff(f3372,plain,
    ( ! [X0: $tType,X2: nat,X1: X0] :
        ( ( fFalse = aa(X0,bool,zero_zero(fun(X0,bool)),X1) )
        | ord_less_eq(bool,fTrue,aa(X0,bool,semiring_1_of_nat(fun(X0,bool),X2),X1))
        | ~ linordered_semidom(fun(X0,bool)) )
    | ~ spl18_53
    | ~ spl18_235 ),
    inference(resolution,[],[f3366,f828]) ).

tff(f3366,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: fun(X0,bool)] :
        ( ~ ord_less_eq(fun(X0,bool),X1,X3)
        | ( fFalse = aa(X0,bool,X1,X2) )
        | ord_less_eq(bool,fTrue,aa(X0,bool,X3,X2)) )
    | ~ spl18_235 ),
    inference(avatar_component_clause,[],[f3365]) ).

tff(f36620,plain,
    ( spl18_648
    | ~ spl18_71
    | ~ spl18_228 ),
    inference(avatar_split_clause,[],[f3241,f3165,f934,f36618]) ).

tff(f36618,plain,
    ( spl18_648
  <=> ! [X4: nat,X0: bool,X3: nat,X2: nat,X1: nat] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X1),zero_zero(int))
        | ( zero_zero(nat) = if(nat,X0,X1,X2) )
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,X0,X4,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_648])]) ).

tff(f934,plain,
    ( spl18_71
  <=> ! [X0: nat] :
        ( ( zero_zero(nat) = X0 )
        | ~ ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_71])]) ).

tff(f3165,plain,
    ( spl18_228
  <=> ! [X4: nat,X0: nat,X3: nat,X2: nat,X1: bool] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X1,X2,X0)) )
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,X1,X3,X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_228])]) ).

tff(f3241,plain,
    ( ! [X2: nat,X3: nat,X0: bool,X1: nat,X4: nat] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X1),zero_zero(int))
        | ( zero_zero(nat) = if(nat,X0,X1,X2) )
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,X0,X4,X3)) ) )
    | ~ spl18_71
    | ~ spl18_228 ),
    inference(superposition,[],[f935,f3166]) ).

tff(f3166,plain,
    ( ! [X2: nat,X3: nat,X0: nat,X1: bool,X4: nat] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X1,X2,X0)) )
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,X1,X3,X4)) ) )
    | ~ spl18_228 ),
    inference(avatar_component_clause,[],[f3165]) ).

tff(f935,plain,
    ( ! [X0: nat] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int))
        | ( zero_zero(nat) = X0 ) )
    | ~ spl18_71 ),
    inference(avatar_component_clause,[],[f934]) ).

tff(f36616,plain,
    ( spl18_647
    | ~ spl18_71
    | ~ spl18_228 ),
    inference(avatar_split_clause,[],[f3186,f3165,f934,f36614]) ).

tff(f36614,plain,
    ( spl18_647
  <=> ! [X4: nat,X0: bool,X3: nat,X2: nat,X1: nat] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X2),zero_zero(int))
        | ( zero_zero(nat) = if(nat,X0,X1,X2) )
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,X0,X3,X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_647])]) ).

tff(f3186,plain,
    ( ! [X2: nat,X3: nat,X0: bool,X1: nat,X4: nat] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X2),zero_zero(int))
        | ( zero_zero(nat) = if(nat,X0,X1,X2) )
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,X0,X3,X4)) ) )
    | ~ spl18_71
    | ~ spl18_228 ),
    inference(superposition,[],[f935,f3166]) ).

tff(f36612,plain,
    ( spl18_646
    | ~ spl18_94
    | ~ spl18_196 ),
    inference(avatar_split_clause,[],[f2660,f2573,f1211,f36610]) ).

tff(f36610,plain,
    ( spl18_646
  <=> ! [X0: fun(int,bool),X3: nat,X2: nat,X1: int] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | ~ ord_less_eq(int,zero_zero(int),X1)
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,X1),X2,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_646])]) ).

tff(f1211,plain,
    ( spl18_94
  <=> ! [X2: bool,X0: nat,X1: nat] :
        ( ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) )
        | ~ pp(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_94])]) ).

tff(f2573,plain,
    ( spl18_196
  <=> ! [X0: int,X1: fun(int,bool)] :
        ( ~ ord_less_eq(int,zero_zero(int),X0)
        | pp(aa(int,bool,X1,X0))
        | ord_less_eq(int,zero_zero(int),sK3(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_196])]) ).

tff(f2660,plain,
    ( ! [X2: nat,X3: nat,X0: fun(int,bool),X1: int] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | ~ ord_less_eq(int,zero_zero(int),X1)
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,X1),X2,X3)) ) )
    | ~ spl18_94
    | ~ spl18_196 ),
    inference(resolution,[],[f2574,f1212]) ).

tff(f1212,plain,
    ( ! [X2: bool,X0: nat,X1: nat] :
        ( ~ pp(X2)
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) ) )
    | ~ spl18_94 ),
    inference(avatar_component_clause,[],[f1211]) ).

tff(f2574,plain,
    ( ! [X0: int,X1: fun(int,bool)] :
        ( pp(aa(int,bool,X1,X0))
        | ord_less_eq(int,zero_zero(int),sK3(X1))
        | ~ ord_less_eq(int,zero_zero(int),X0) )
    | ~ spl18_196 ),
    inference(avatar_component_clause,[],[f2573]) ).

tff(f36608,plain,
    ( spl18_645
    | ~ spl18_94
    | ~ spl18_194 ),
    inference(avatar_split_clause,[],[f2640,f2564,f1211,f36606]) ).

tff(f36606,plain,
    ( spl18_645
  <=> ! [X0: fun(nat,bool),X3: nat,X2: nat,X1: nat] :
        ( ord_less(nat,zero_zero(nat),sK8(X0))
        | ~ member(nat,zero_zero(nat),X0)
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X0,X1),X2,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_645])]) ).

tff(f2564,plain,
    ( spl18_194
  <=> ! [X0: fun(nat,bool),X1: nat] :
        ( ord_less(nat,zero_zero(nat),sK8(X0))
        | pp(aa(nat,bool,X0,X1))
        | ~ member(nat,zero_zero(nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_194])]) ).

tff(f2640,plain,
    ( ! [X2: nat,X3: nat,X0: fun(nat,bool),X1: nat] :
        ( ord_less(nat,zero_zero(nat),sK8(X0))
        | ~ member(nat,zero_zero(nat),X0)
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X0,X1),X2,X3)) ) )
    | ~ spl18_94
    | ~ spl18_194 ),
    inference(resolution,[],[f2565,f1212]) ).

tff(f2565,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ord_less(nat,zero_zero(nat),sK8(X0))
        | ~ member(nat,zero_zero(nat),X0) )
    | ~ spl18_194 ),
    inference(avatar_component_clause,[],[f2564]) ).

tff(f36604,plain,
    ( spl18_644
    | ~ spl18_94
    | ~ spl18_193 ),
    inference(avatar_split_clause,[],[f2616,f2560,f1211,f36602]) ).

tff(f36602,plain,
    ( spl18_644
  <=> ! [X0: fun(nat,bool),X3: nat,X2: nat,X1: nat] :
        ( ord_less_eq(nat,sK7(X1,X0),X1)
        | ~ member(nat,X1,X0)
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X0,zero_zero(nat)),X2,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_644])]) ).

tff(f2560,plain,
    ( spl18_193
  <=> ! [X0: nat,X1: fun(nat,bool)] :
        ( ord_less_eq(nat,sK7(X0,X1),X0)
        | pp(aa(nat,bool,X1,zero_zero(nat)))
        | ~ member(nat,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_193])]) ).

tff(f2616,plain,
    ( ! [X2: nat,X3: nat,X0: fun(nat,bool),X1: nat] :
        ( ord_less_eq(nat,sK7(X1,X0),X1)
        | ~ member(nat,X1,X0)
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X0,zero_zero(nat)),X2,X3)) ) )
    | ~ spl18_94
    | ~ spl18_193 ),
    inference(resolution,[],[f2561,f1212]) ).

tff(f2561,plain,
    ( ! [X0: nat,X1: fun(nat,bool)] :
        ( pp(aa(nat,bool,X1,zero_zero(nat)))
        | ord_less_eq(nat,sK7(X0,X1),X0)
        | ~ member(nat,X0,X1) )
    | ~ spl18_193 ),
    inference(avatar_component_clause,[],[f2560]) ).

tff(f36600,plain,
    ( spl18_643
    | ~ spl18_127
    | ~ spl18_178 ),
    inference(avatar_split_clause,[],[f2386,f2354,f1643,f36598]) ).

tff(f36598,plain,
    ( spl18_643
  <=> ! [X4: nat,X0: fun(nat,fun(nat,fun(nat,bool))),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(nat,bool)))),X2: nat,X1: nat] :
        ( ~ member(nat,X4,huffma107959123e_case(nat,fun(nat,bool),X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ~ sP0(X4,X2,aa(nat,fun(nat,fun(nat,bool)),X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_643])]) ).

tff(f1643,plain,
    ( spl18_127
  <=> ! [X1: $tType,X0: $tType,X3: nat,X4: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),X0))),X5: fun(nat,fun(X1,X0)),X2: X1] : ( huffma107959123e_case(X1,X0,X5,X4,huffma2021818691e_Leaf(X1,X3,X2)) = aa(X1,X0,aa(nat,fun(X1,X0),X5,X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_127])]) ).

tff(f2354,plain,
    ( spl18_178
  <=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( ~ sP0(X0,X1,X2)
        | ~ member(nat,X0,aa(nat,fun(nat,bool),X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_178])]) ).

tff(f2386,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(nat,bool)))),X0: fun(nat,fun(nat,fun(nat,bool))),X1: nat,X4: nat] :
        ( ~ member(nat,X4,huffma107959123e_case(nat,fun(nat,bool),X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ~ sP0(X4,X2,aa(nat,fun(nat,fun(nat,bool)),X0,X1)) )
    | ~ spl18_127
    | ~ spl18_178 ),
    inference(superposition,[],[f2355,f1644]) ).

tff(f1644,plain,
    ( ! [X1: $tType,X0: $tType,X2: X1,X3: nat,X4: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),X0))),X5: fun(nat,fun(X1,X0))] : ( huffma107959123e_case(X1,X0,X5,X4,huffma2021818691e_Leaf(X1,X3,X2)) = aa(X1,X0,aa(nat,fun(X1,X0),X5,X3),X2) )
    | ~ spl18_127 ),
    inference(avatar_component_clause,[],[f1643]) ).

tff(f2355,plain,
    ( ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( ~ member(nat,X0,aa(nat,fun(nat,bool),X2,X1))
        | ~ sP0(X0,X1,X2) )
    | ~ spl18_178 ),
    inference(avatar_component_clause,[],[f2354]) ).

tff(f36596,plain,
    ( spl18_642
    | ~ spl18_128
    | ~ spl18_178 ),
    inference(avatar_split_clause,[],[f2385,f2354,f1647,f36594]) ).

tff(f36594,plain,
    ( spl18_642
  <=> ! [X4: nat,X0: fun(nat,fun(nat,fun(nat,bool))),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)))))),X2: nat,X1: nat] :
        ( ~ member(nat,X4,huffma1280178957ee_rec(nat,fun(nat,bool),X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ~ sP0(X4,X2,aa(nat,fun(nat,fun(nat,bool)),X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_642])]) ).

tff(f1647,plain,
    ( spl18_128
  <=> ! [X1: $tType,X0: $tType,X5: fun(nat,fun(X1,X0)),X4: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))))),X3: nat,X2: X1] : ( aa(X1,X0,aa(nat,fun(X1,X0),X5,X3),X2) = huffma1280178957ee_rec(X1,X0,X5,X4,huffma2021818691e_Leaf(X1,X3,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_128])]) ).

tff(f2385,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)))))),X0: fun(nat,fun(nat,fun(nat,bool))),X1: nat,X4: nat] :
        ( ~ member(nat,X4,huffma1280178957ee_rec(nat,fun(nat,bool),X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ~ sP0(X4,X2,aa(nat,fun(nat,fun(nat,bool)),X0,X1)) )
    | ~ spl18_128
    | ~ spl18_178 ),
    inference(superposition,[],[f2355,f1648]) ).

tff(f1648,plain,
    ( ! [X1: $tType,X0: $tType,X2: X1,X3: nat,X4: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))))),X5: fun(nat,fun(X1,X0))] : ( aa(X1,X0,aa(nat,fun(X1,X0),X5,X3),X2) = huffma1280178957ee_rec(X1,X0,X5,X4,huffma2021818691e_Leaf(X1,X3,X2)) )
    | ~ spl18_128 ),
    inference(avatar_component_clause,[],[f1647]) ).

tff(f36592,plain,
    ( spl18_641
    | ~ spl18_129
    | ~ spl18_156 ),
    inference(avatar_split_clause,[],[f2136,f2078,f1722,f36590]) ).

tff(f36590,plain,
    ( spl18_641
  <=> ! [X0: nat,X3: nat,X2: nat,X1: fun(nat,nat)] :
        ( ord_less_eq(nat,X0,aa(nat,nat,X1,X2))
        | ord_less_eq(nat,aa(nat,nat,X1,X3),X0)
        | ~ ord_less_eq(nat,X3,X2)
        | ord_less(nat,sK15(X1),sK16(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_641])]) ).

tff(f2078,plain,
    ( spl18_156
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less_eq(nat,X2,X1)
        | ord_less_eq(nat,X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_156])]) ).

tff(f2136,plain,
    ( ! [X2: nat,X3: nat,X0: nat,X1: fun(nat,nat)] :
        ( ord_less_eq(nat,X0,aa(nat,nat,X1,X2))
        | ord_less_eq(nat,aa(nat,nat,X1,X3),X0)
        | ~ ord_less_eq(nat,X3,X2)
        | ord_less(nat,sK15(X1),sK16(X1)) )
    | ~ spl18_129
    | ~ spl18_156 ),
    inference(resolution,[],[f2079,f1723]) ).

tff(f2079,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less_eq(nat,X2,X1)
        | ord_less_eq(nat,X0,X2) )
    | ~ spl18_156 ),
    inference(avatar_component_clause,[],[f2078]) ).

tff(f36588,plain,
    ( spl18_640
    | ~ spl18_37
    | ~ spl18_136 ),
    inference(avatar_split_clause,[],[f1851,f1840,f752,f36586]) ).

tff(f36586,plain,
    ( spl18_640
  <=> ! [X2: fun(nat,bool),X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,sK7(X1,X2))
        | ~ pp(aa(nat,bool,X2,X1))
        | pp(aa(nat,bool,X2,zero_zero(nat)))
        | ( fFalse = aa(nat,bool,X2,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_640])]) ).

tff(f752,plain,
    ( spl18_37
  <=> ! [X0: bool] :
        ( pp(X0)
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_37])]) ).

tff(f1840,plain,
    ( spl18_136
  <=> ! [X0: nat,X1: fun(nat,bool),X3: nat] :
        ( ~ pp(aa(nat,bool,X1,X3))
        | ~ ord_less(nat,X3,sK7(X0,X1))
        | ~ pp(aa(nat,bool,X1,X0))
        | pp(aa(nat,bool,X1,zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_136])]) ).

tff(f1851,plain,
    ( ! [X2: fun(nat,bool),X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,sK7(X1,X2))
        | ~ pp(aa(nat,bool,X2,X1))
        | pp(aa(nat,bool,X2,zero_zero(nat)))
        | ( fFalse = aa(nat,bool,X2,X0) ) )
    | ~ spl18_37
    | ~ spl18_136 ),
    inference(resolution,[],[f1841,f753]) ).

tff(f753,plain,
    ( ! [X0: bool] :
        ( pp(X0)
        | ( fFalse = X0 ) )
    | ~ spl18_37 ),
    inference(avatar_component_clause,[],[f752]) ).

tff(f1841,plain,
    ( ! [X3: nat,X0: nat,X1: fun(nat,bool)] :
        ( ~ pp(aa(nat,bool,X1,X3))
        | ~ ord_less(nat,X3,sK7(X0,X1))
        | ~ pp(aa(nat,bool,X1,X0))
        | pp(aa(nat,bool,X1,zero_zero(nat))) )
    | ~ spl18_136 ),
    inference(avatar_component_clause,[],[f1840]) ).

tff(f36584,plain,
    ( spl18_639
    | ~ spl18_81
    | ~ spl18_134 ),
    inference(avatar_split_clause,[],[f1827,f1799,f1016,f36582]) ).

tff(f36582,plain,
    ( spl18_639
  <=> ! [X0: $tType,X3: bool,X2: fun(bool,X0),X1: fun(bool,X0)] :
        ( ( aa(bool,X0,X2,X3) != aa(bool,X0,X1,X3) )
        | ( X1 = X2 )
        | ( fFalse = sK17(X0,bool,X1,X2) )
        | ( fFalse = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_639])]) ).

tff(f1016,plain,
    ( spl18_81
  <=> ! [X0: bool,X1: bool] :
        ( ( X0 = X1 )
        | ( fFalse = X1 )
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_81])]) ).

tff(f1799,plain,
    ( spl18_134
  <=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
        ( ( X2 = X3 )
        | ( aa(X1,X0,X3,sK17(X0,X1,X2,X3)) != aa(X1,X0,X2,sK17(X0,X1,X2,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_134])]) ).

tff(f1827,plain,
    ( ! [X0: $tType,X2: fun(bool,X0),X3: bool,X1: fun(bool,X0)] :
        ( ( aa(bool,X0,X2,X3) != aa(bool,X0,X1,X3) )
        | ( X1 = X2 )
        | ( fFalse = sK17(X0,bool,X1,X2) )
        | ( fFalse = X3 ) )
    | ~ spl18_81
    | ~ spl18_134 ),
    inference(superposition,[],[f1800,f1017]) ).

tff(f1017,plain,
    ( ! [X0: bool,X1: bool] :
        ( ( X0 = X1 )
        | ( fFalse = X1 )
        | ( fFalse = X0 ) )
    | ~ spl18_81 ),
    inference(avatar_component_clause,[],[f1016]) ).

tff(f1800,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
        ( ( aa(X1,X0,X3,sK17(X0,X1,X2,X3)) != aa(X1,X0,X2,sK17(X0,X1,X2,X3)) )
        | ( X2 = X3 ) )
    | ~ spl18_134 ),
    inference(avatar_component_clause,[],[f1799]) ).

tff(f36580,plain,
    ( spl18_638
    | ~ spl18_81
    | ~ spl18_134 ),
    inference(avatar_split_clause,[],[f1825,f1799,f1016,f36578]) ).

tff(f36578,plain,
    ( spl18_638
  <=> ! [X0: $tType,X3: bool,X2: fun(bool,X0),X1: fun(bool,X0)] :
        ( ( aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) )
        | ( X1 = X2 )
        | ( sK17(X0,bool,X1,X2) = X3 )
        | ( fFalse = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_638])]) ).

tff(f1825,plain,
    ( ! [X0: $tType,X2: fun(bool,X0),X3: bool,X1: fun(bool,X0)] :
        ( ( aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) )
        | ( X1 = X2 )
        | ( sK17(X0,bool,X1,X2) = X3 )
        | ( fFalse = X3 ) )
    | ~ spl18_81
    | ~ spl18_134 ),
    inference(superposition,[],[f1800,f1017]) ).

tff(f36556,plain,
    ( ~ spl18_19
    | spl18_637
    | ~ spl18_81
    | ~ spl18_124 ),
    inference(avatar_split_clause,[],[f1625,f1576,f1016,f36554,f670]) ).

tff(f670,plain,
    ( spl18_19
  <=> ord(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_19])]) ).

tff(f36554,plain,
    ( spl18_637
  <=> ! [X0: $tType,X4: fun(X0,bool),X3: bool,X2: X0,X1: fun(X0,bool)] :
        ( ord_less_eq(bool,aa(X0,bool,X4,X2),X3)
        | ( fFalse = X3 )
        | ( fFalse = aa(X0,bool,X1,X2) )
        | ~ ord_less_eq(fun(X0,bool),X4,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_637])]) ).

tff(f1576,plain,
    ( spl18_124
  <=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: fun(X1,X0),X2: X1] :
        ( ord_less_eq(X0,aa(X1,X0,X4,X2),aa(X1,X0,X3,X2))
        | ~ ord_less_eq(fun(X1,X0),X4,X3)
        | ~ ord(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_124])]) ).

tff(f1625,plain,
    ( ! [X0: $tType,X2: X0,X3: bool,X1: fun(X0,bool),X4: fun(X0,bool)] :
        ( ord_less_eq(bool,aa(X0,bool,X4,X2),X3)
        | ~ ord_less_eq(fun(X0,bool),X4,X1)
        | ~ ord(bool)
        | ( fFalse = aa(X0,bool,X1,X2) )
        | ( fFalse = X3 ) )
    | ~ spl18_81
    | ~ spl18_124 ),
    inference(superposition,[],[f1577,f1017]) ).

tff(f1577,plain,
    ( ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X1,X0),X4: fun(X1,X0)] :
        ( ord_less_eq(X0,aa(X1,X0,X4,X2),aa(X1,X0,X3,X2))
        | ~ ord_less_eq(fun(X1,X0),X4,X3)
        | ~ ord(X0) )
    | ~ spl18_124 ),
    inference(avatar_component_clause,[],[f1576]) ).

tff(f36516,plain,
    ( ~ spl18_19
    | spl18_636
    | ~ spl18_81
    | ~ spl18_124 ),
    inference(avatar_split_clause,[],[f1623,f1576,f1016,f36514,f670]) ).

tff(f36514,plain,
    ( spl18_636
  <=> ! [X0: $tType,X4: bool,X3: fun(X0,bool),X2: X0,X1: fun(X0,bool)] :
        ( ord_less_eq(bool,aa(X0,bool,X3,X2),fFalse)
        | ( fFalse = X4 )
        | ( aa(X0,bool,X1,X2) = X4 )
        | ~ ord_less_eq(fun(X0,bool),X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_636])]) ).

tff(f1623,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: fun(X0,bool),X4: bool] :
        ( ord_less_eq(bool,aa(X0,bool,X3,X2),fFalse)
        | ~ ord_less_eq(fun(X0,bool),X3,X1)
        | ~ ord(bool)
        | ( aa(X0,bool,X1,X2) = X4 )
        | ( fFalse = X4 ) )
    | ~ spl18_81
    | ~ spl18_124 ),
    inference(superposition,[],[f1577,f1017]) ).

tff(f36492,plain,
    ( ~ spl18_19
    | spl18_635
    | ~ spl18_81
    | ~ spl18_124 ),
    inference(avatar_split_clause,[],[f1618,f1576,f1016,f36490,f670]) ).

tff(f36490,plain,
    ( spl18_635
  <=> ! [X0: $tType,X4: fun(X0,bool),X3: bool,X2: X0,X1: fun(X0,bool)] :
        ( ord_less_eq(bool,X3,aa(X0,bool,X4,X2))
        | ( fFalse = X3 )
        | ( fFalse = aa(X0,bool,X1,X2) )
        | ~ ord_less_eq(fun(X0,bool),X1,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_635])]) ).

tff(f1618,plain,
    ( ! [X0: $tType,X2: X0,X3: bool,X1: fun(X0,bool),X4: fun(X0,bool)] :
        ( ord_less_eq(bool,X3,aa(X0,bool,X4,X2))
        | ~ ord_less_eq(fun(X0,bool),X1,X4)
        | ~ ord(bool)
        | ( fFalse = aa(X0,bool,X1,X2) )
        | ( fFalse = X3 ) )
    | ~ spl18_81
    | ~ spl18_124 ),
    inference(superposition,[],[f1577,f1017]) ).

tff(f36468,plain,
    ( ~ spl18_19
    | spl18_634
    | ~ spl18_81
    | ~ spl18_124 ),
    inference(avatar_split_clause,[],[f1616,f1576,f1016,f36466,f670]) ).

tff(f36466,plain,
    ( spl18_634
  <=> ! [X0: $tType,X4: bool,X3: fun(X0,bool),X2: X0,X1: fun(X0,bool)] :
        ( ord_less_eq(bool,fFalse,aa(X0,bool,X3,X2))
        | ( fFalse = X4 )
        | ( aa(X0,bool,X1,X2) = X4 )
        | ~ ord_less_eq(fun(X0,bool),X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_634])]) ).

tff(f1616,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: fun(X0,bool),X4: bool] :
        ( ord_less_eq(bool,fFalse,aa(X0,bool,X3,X2))
        | ~ ord_less_eq(fun(X0,bool),X1,X3)
        | ~ ord(bool)
        | ( aa(X0,bool,X1,X2) = X4 )
        | ( fFalse = X4 ) )
    | ~ spl18_81
    | ~ spl18_124 ),
    inference(superposition,[],[f1577,f1017]) ).

tff(f34174,plain,
    ( spl18_633
    | ~ spl18_59
    | ~ spl18_600 ),
    inference(avatar_split_clause,[],[f30618,f30604,f852,f34172]) ).

tff(f34172,plain,
    ( spl18_633
  <=> ! [X0: a1] : ( huffma1401021291ibling(a1,t_1,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_633])]) ).

tff(f852,plain,
    ( spl18_59
  <=> ! [X0: $tType,X3: nat,X2: X0,X1: X0] : ( huffma1401021291ibling(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_59])]) ).

tff(f30604,plain,
    ( spl18_600
  <=> ( t_1 = huffma2021818691e_Leaf(a1,sK12(a1,t_1),sK13(a1,t_1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_600])]) ).

tff(f30618,plain,
    ( ! [X0: a1] : ( huffma1401021291ibling(a1,t_1,X0) = X0 )
    | ~ spl18_59
    | ~ spl18_600 ),
    inference(superposition,[],[f853,f30606]) ).

tff(f30606,plain,
    ( ( t_1 = huffma2021818691e_Leaf(a1,sK12(a1,t_1),sK13(a1,t_1)) )
    | ~ spl18_600 ),
    inference(avatar_component_clause,[],[f30604]) ).

tff(f853,plain,
    ( ! [X0: $tType,X2: X0,X3: nat,X1: X0] : ( huffma1401021291ibling(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) = X1 )
    | ~ spl18_59 ),
    inference(avatar_component_clause,[],[f852]) ).

tff(f31587,plain,
    ( spl18_632
    | ~ spl18_129
    | ~ spl18_298 ),
    inference(avatar_split_clause,[],[f5623,f4993,f1722,f31585]) ).

tff(f31585,plain,
    ( spl18_632
  <=> ! [X2: nat,X0: fun(nat,nat),X1: nat] :
        ( ord_less(nat,sK15(X0),sK16(X0))
        | ~ ord_less_eq(nat,X1,X2)
        | ( aa(nat,nat,X0,X1) = aa(nat,nat,X0,X2) )
        | ~ ord_less_eq(nat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_632])]) ).

tff(f4993,plain,
    ( spl18_298
  <=> ! [X2: fun(nat,nat),X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less(nat,sK15(X2),sK16(X2))
        | ~ ord_less_eq(nat,aa(nat,nat,X2,X1),aa(nat,nat,X2,X0))
        | ( aa(nat,nat,X2,X1) = aa(nat,nat,X2,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_298])]) ).

tff(f5623,plain,
    ( ! [X2: nat,X0: fun(nat,nat),X1: nat] :
        ( ord_less(nat,sK15(X0),sK16(X0))
        | ~ ord_less_eq(nat,X1,X2)
        | ( aa(nat,nat,X0,X1) = aa(nat,nat,X0,X2) )
        | ~ ord_less_eq(nat,X2,X1) )
    | ~ spl18_129
    | ~ spl18_298 ),
    inference(duplicate_literal_removal,[],[f5594]) ).

tff(f5594,plain,
    ( ! [X2: nat,X0: fun(nat,nat),X1: nat] :
        ( ord_less(nat,sK15(X0),sK16(X0))
        | ~ ord_less_eq(nat,X1,X2)
        | ( aa(nat,nat,X0,X1) = aa(nat,nat,X0,X2) )
        | ~ ord_less_eq(nat,X2,X1)
        | ord_less(nat,sK15(X0),sK16(X0)) )
    | ~ spl18_129
    | ~ spl18_298 ),
    inference(resolution,[],[f4994,f1723]) ).

tff(f4994,plain,
    ( ! [X2: fun(nat,nat),X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,aa(nat,nat,X2,X1),aa(nat,nat,X2,X0))
        | ord_less(nat,sK15(X2),sK16(X2))
        | ~ ord_less_eq(nat,X0,X1)
        | ( aa(nat,nat,X2,X1) = aa(nat,nat,X2,X0) ) )
    | ~ spl18_298 ),
    inference(avatar_component_clause,[],[f4993]) ).

tff(f31583,plain,
    ( spl18_631
    | ~ spl18_30
    | ~ spl18_274 ),
    inference(avatar_split_clause,[],[f4449,f4419,f720,f31581]) ).

tff(f31581,plain,
    ( spl18_631
  <=> ! [X2: nat,X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,zero_zero(int)),X2,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_631])]) ).

tff(f720,plain,
    ( spl18_30
  <=> ord_less_eq(int,zero_zero(int),zero_zero(int)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_30])]) ).

tff(f4449,plain,
    ( ! [X2: nat,X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,zero_zero(int)),X2,X1)) ) )
    | ~ spl18_30
    | ~ spl18_274 ),
    inference(resolution,[],[f4420,f722]) ).

tff(f722,plain,
    ( ord_less_eq(int,zero_zero(int),zero_zero(int))
    | ~ spl18_30 ),
    inference(avatar_component_clause,[],[f720]) ).

tff(f31579,plain,
    ( spl18_630
    | ~ spl18_57
    | ~ spl18_600 ),
    inference(avatar_split_clause,[],[f30617,f30604,f844,f31576]) ).

tff(f844,plain,
    ( spl18_57
  <=> ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_57])]) ).

tff(f30617,plain,
    ( ( zero_zero(nat) = huffma945805758height(a1,t_1) )
    | ~ spl18_57
    | ~ spl18_600 ),
    inference(superposition,[],[f845,f30606]) ).

tff(f845,plain,
    ( ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X2,X1)) )
    | ~ spl18_57 ),
    inference(avatar_component_clause,[],[f844]) ).

tff(f31574,plain,
    ( spl18_629
    | ~ spl18_37
    | ~ spl18_251 ),
    inference(avatar_split_clause,[],[f4052,f3589,f752,f31572]) ).

tff(f31572,plain,
    ( spl18_629
  <=> ! [X0: fun(nat,fun(int,bool)),X3: nat,X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK4(aa(nat,fun(int,bool),X0,X1)))
        | ( fFalse = huffma1280178957ee_rec(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,X3))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_629])]) ).

tff(f3589,plain,
    ( spl18_251
  <=> ! [X0: fun(nat,fun(int,bool)),X3: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X2: nat,X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(int,bool,X0,X3,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,X2))))
        | ord_less_eq(int,zero_zero(int),sK4(aa(nat,fun(int,bool),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_251])]) ).

tff(f4052,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X3: nat,X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK4(aa(nat,fun(int,bool),X0,X1)))
        | ( fFalse = huffma1280178957ee_rec(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,X3))) ) )
    | ~ spl18_37
    | ~ spl18_251 ),
    inference(resolution,[],[f3590,f753]) ).

tff(f3590,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(int,bool,X0,X3,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,X2))))
        | ord_less_eq(int,zero_zero(int),sK4(aa(nat,fun(int,bool),X0,X1))) )
    | ~ spl18_251 ),
    inference(avatar_component_clause,[],[f3589]) ).

tff(f31570,plain,
    ( spl18_628
    | ~ spl18_37
    | ~ spl18_247 ),
    inference(avatar_split_clause,[],[f3757,f3566,f752,f31568]) ).

tff(f31568,plain,
    ( spl18_628
  <=> ! [X0: fun(nat,fun(int,bool)),X3: nat,X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK4(aa(nat,fun(int,bool),X0,X1)))
        | ( fFalse = huffma107959123e_case(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,X3))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_628])]) ).

tff(f3566,plain,
    ( spl18_247
  <=> ! [X0: fun(nat,fun(int,bool)),X3: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X2: nat,X1: nat] :
        ( ~ pp(huffma107959123e_case(int,bool,X0,X3,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,X2))))
        | ord_less_eq(int,zero_zero(int),sK4(aa(nat,fun(int,bool),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_247])]) ).

tff(f3757,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X3: nat,X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK4(aa(nat,fun(int,bool),X0,X1)))
        | ( fFalse = huffma107959123e_case(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,X3))) ) )
    | ~ spl18_37
    | ~ spl18_247 ),
    inference(resolution,[],[f3567,f753]) ).

tff(f3567,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ~ pp(huffma107959123e_case(int,bool,X0,X3,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,X2))))
        | ord_less_eq(int,zero_zero(int),sK4(aa(nat,fun(int,bool),X0,X1))) )
    | ~ spl18_247 ),
    inference(avatar_component_clause,[],[f3566]) ).

tff(f31566,plain,
    ( spl18_627
    | ~ spl18_126
    | ~ spl18_240 ),
    inference(avatar_split_clause,[],[f3512,f3410,f1639,f31564]) ).

tff(f31564,plain,
    ( spl18_627
  <=> ! [X2: fun(nat,bool),X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,sK7(sK7(X1,X2),X2))
        | pp(aa(nat,bool,X2,zero_zero(nat)))
        | ~ member(nat,X0,X2)
        | ~ pp(aa(nat,bool,X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_627])]) ).

tff(f1639,plain,
    ( spl18_126
  <=> ! [X0: nat,X1: fun(nat,bool)] :
        ( pp(aa(nat,bool,X1,sK7(X0,X1)))
        | ~ pp(aa(nat,bool,X1,X0))
        | pp(aa(nat,bool,X1,zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_126])]) ).

tff(f3410,plain,
    ( spl18_240
  <=> ! [X2: fun(nat,bool),X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,sK7(X1,X2))
        | ~ pp(aa(nat,bool,X2,X1))
        | pp(aa(nat,bool,X2,zero_zero(nat)))
        | ~ member(nat,X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_240])]) ).

tff(f3512,plain,
    ( ! [X2: fun(nat,bool),X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,sK7(sK7(X1,X2),X2))
        | pp(aa(nat,bool,X2,zero_zero(nat)))
        | ~ member(nat,X0,X2)
        | ~ pp(aa(nat,bool,X2,X1)) )
    | ~ spl18_126
    | ~ spl18_240 ),
    inference(duplicate_literal_removal,[],[f3498]) ).

tff(f3498,plain,
    ( ! [X2: fun(nat,bool),X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,sK7(sK7(X1,X2),X2))
        | pp(aa(nat,bool,X2,zero_zero(nat)))
        | ~ member(nat,X0,X2)
        | ~ pp(aa(nat,bool,X2,X1))
        | pp(aa(nat,bool,X2,zero_zero(nat))) )
    | ~ spl18_126
    | ~ spl18_240 ),
    inference(resolution,[],[f3411,f1640]) ).

tff(f1640,plain,
    ( ! [X0: nat,X1: fun(nat,bool)] :
        ( pp(aa(nat,bool,X1,sK7(X0,X1)))
        | ~ pp(aa(nat,bool,X1,X0))
        | pp(aa(nat,bool,X1,zero_zero(nat))) )
    | ~ spl18_126 ),
    inference(avatar_component_clause,[],[f1639]) ).

tff(f3411,plain,
    ( ! [X2: fun(nat,bool),X0: nat,X1: nat] :
        ( ~ pp(aa(nat,bool,X2,X1))
        | ~ ord_less(nat,X0,sK7(X1,X2))
        | pp(aa(nat,bool,X2,zero_zero(nat)))
        | ~ member(nat,X0,X2) )
    | ~ spl18_240 ),
    inference(avatar_component_clause,[],[f3410]) ).

tff(f31562,plain,
    ( spl18_626
    | ~ spl18_61
    | ~ spl18_236 ),
    inference(avatar_split_clause,[],[f3382,f3377,f880,f31560]) ).

tff(f31560,plain,
    ( spl18_626
  <=> ! [X0: $tType,X3: fun(X0,bool),X2: X0,X1: fun(X0,bool)] :
        ( ( fFalse = aa(X0,bool,X1,X2) )
        | ord_less_eq(bool,aa(X0,bool,X3,X2),fTrue)
        | ord_less_eq(fun(X0,bool),X1,X3)
        | ~ linorder(fun(X0,bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_626])]) ).

tff(f880,plain,
    ( spl18_61
  <=> ! [X0: $tType,X2: X0,X1: X0] :
        ( ord_less_eq(X0,X1,X2)
        | ord_less_eq(X0,X2,X1)
        | ~ linorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_61])]) ).

tff(f3382,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: fun(X0,bool)] :
        ( ( fFalse = aa(X0,bool,X1,X2) )
        | ord_less_eq(bool,aa(X0,bool,X3,X2),fTrue)
        | ord_less_eq(fun(X0,bool),X1,X3)
        | ~ linorder(fun(X0,bool)) )
    | ~ spl18_61
    | ~ spl18_236 ),
    inference(resolution,[],[f3378,f881]) ).

tff(f881,plain,
    ( ! [X0: $tType,X2: X0,X1: X0] :
        ( ord_less_eq(X0,X2,X1)
        | ord_less_eq(X0,X1,X2)
        | ~ linorder(X0) )
    | ~ spl18_61 ),
    inference(avatar_component_clause,[],[f880]) ).

tff(f31558,plain,
    ( spl18_625
    | ~ spl18_61
    | ~ spl18_235 ),
    inference(avatar_split_clause,[],[f3370,f3365,f880,f31556]) ).

tff(f31556,plain,
    ( spl18_625
  <=> ! [X0: $tType,X3: fun(X0,bool),X2: X0,X1: fun(X0,bool)] :
        ( ( fFalse = aa(X0,bool,X1,X2) )
        | ord_less_eq(bool,fTrue,aa(X0,bool,X3,X2))
        | ord_less_eq(fun(X0,bool),X3,X1)
        | ~ linorder(fun(X0,bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_625])]) ).

tff(f3370,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: fun(X0,bool)] :
        ( ( fFalse = aa(X0,bool,X1,X2) )
        | ord_less_eq(bool,fTrue,aa(X0,bool,X3,X2))
        | ord_less_eq(fun(X0,bool),X3,X1)
        | ~ linorder(fun(X0,bool)) )
    | ~ spl18_61
    | ~ spl18_235 ),
    inference(resolution,[],[f3366,f881]) ).

tff(f31554,plain,
    ( spl18_624
    | ~ spl18_63
    | ~ spl18_228 ),
    inference(avatar_split_clause,[],[f3239,f3165,f888,f31552]) ).

tff(f31552,plain,
    ( spl18_624
  <=> ! [X5: nat,X4: nat,X0: bool,X3: nat,X2: nat,X1: nat] :
        ( ( semiring_1_of_nat(int,X1) != semiring_1_of_nat(int,X3) )
        | ( if(nat,X0,X1,X2) = X3 )
        | ( semiring_1_of_nat(int,X4) = semiring_1_of_nat(int,if(nat,X0,X5,X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_624])]) ).

tff(f888,plain,
    ( spl18_63
  <=> ! [X0: nat,X1: nat] :
        ( ( X0 = X1 )
        | ( semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_63])]) ).

tff(f3239,plain,
    ( ! [X2: nat,X3: nat,X0: bool,X1: nat,X4: nat,X5: nat] :
        ( ( semiring_1_of_nat(int,X1) != semiring_1_of_nat(int,X3) )
        | ( if(nat,X0,X1,X2) = X3 )
        | ( semiring_1_of_nat(int,X4) = semiring_1_of_nat(int,if(nat,X0,X5,X4)) ) )
    | ~ spl18_63
    | ~ spl18_228 ),
    inference(superposition,[],[f889,f3166]) ).

tff(f889,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) )
        | ( X0 = X1 ) )
    | ~ spl18_63 ),
    inference(avatar_component_clause,[],[f888]) ).

tff(f31550,plain,
    ( spl18_623
    | ~ spl18_62
    | ~ spl18_228 ),
    inference(avatar_split_clause,[],[f3238,f3165,f884,f31548]) ).

tff(f31548,plain,
    ( spl18_623
  <=> ! [X4: nat,X0: bool,X3: nat,X2: nat,X1: nat] :
        ( ( zero_zero(int) != semiring_1_of_nat(int,X1) )
        | ( zero_zero(nat) = if(nat,X0,X1,X2) )
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,X0,X4,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_623])]) ).

tff(f884,plain,
    ( spl18_62
  <=> ! [X0: nat] :
        ( ( zero_zero(nat) = X0 )
        | ( zero_zero(int) != semiring_1_of_nat(int,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_62])]) ).

tff(f3238,plain,
    ( ! [X2: nat,X3: nat,X0: bool,X1: nat,X4: nat] :
        ( ( zero_zero(int) != semiring_1_of_nat(int,X1) )
        | ( zero_zero(nat) = if(nat,X0,X1,X2) )
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,X0,X4,X3)) ) )
    | ~ spl18_62
    | ~ spl18_228 ),
    inference(superposition,[],[f885,f3166]) ).

tff(f885,plain,
    ( ! [X0: nat] :
        ( ( zero_zero(int) != semiring_1_of_nat(int,X0) )
        | ( zero_zero(nat) = X0 ) )
    | ~ spl18_62 ),
    inference(avatar_component_clause,[],[f884]) ).

tff(f31546,plain,
    ( spl18_622
    | ~ spl18_63
    | ~ spl18_228 ),
    inference(avatar_split_clause,[],[f3184,f3165,f888,f31544]) ).

tff(f31544,plain,
    ( spl18_622
  <=> ! [X5: nat,X4: nat,X0: bool,X3: nat,X2: nat,X1: nat] :
        ( ( semiring_1_of_nat(int,X2) != semiring_1_of_nat(int,X3) )
        | ( if(nat,X0,X1,X2) = X3 )
        | ( semiring_1_of_nat(int,X4) = semiring_1_of_nat(int,if(nat,X0,X4,X5)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_622])]) ).

tff(f3184,plain,
    ( ! [X2: nat,X3: nat,X0: bool,X1: nat,X4: nat,X5: nat] :
        ( ( semiring_1_of_nat(int,X2) != semiring_1_of_nat(int,X3) )
        | ( if(nat,X0,X1,X2) = X3 )
        | ( semiring_1_of_nat(int,X4) = semiring_1_of_nat(int,if(nat,X0,X4,X5)) ) )
    | ~ spl18_63
    | ~ spl18_228 ),
    inference(superposition,[],[f889,f3166]) ).

tff(f31542,plain,
    ( spl18_621
    | ~ spl18_62
    | ~ spl18_228 ),
    inference(avatar_split_clause,[],[f3183,f3165,f884,f31540]) ).

tff(f31540,plain,
    ( spl18_621
  <=> ! [X4: nat,X0: bool,X3: nat,X2: nat,X1: nat] :
        ( ( zero_zero(int) != semiring_1_of_nat(int,X2) )
        | ( zero_zero(nat) = if(nat,X0,X1,X2) )
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,X0,X3,X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_621])]) ).

tff(f3183,plain,
    ( ! [X2: nat,X3: nat,X0: bool,X1: nat,X4: nat] :
        ( ( zero_zero(int) != semiring_1_of_nat(int,X2) )
        | ( zero_zero(nat) = if(nat,X0,X1,X2) )
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,X0,X3,X4)) ) )
    | ~ spl18_62
    | ~ spl18_228 ),
    inference(superposition,[],[f885,f3166]) ).

tff(f31538,plain,
    ( spl18_620
    | ~ spl18_81
    | ~ spl18_226 ),
    inference(avatar_split_clause,[],[f3137,f3094,f1016,f31536]) ).

tff(f31536,plain,
    ( spl18_620
  <=> ! [X2: nat,X3: nat,X4: huffma1450048681e_tree(bool),X0: huffma1450048681e_tree(bool),X5: huffma1450048681e_tree(bool),X1: bool] :
        ( ( huffma1401021291ibling(bool,X0,X1) = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X2,X0,huffma1146269203erNode(bool,X3,X4,X5)),X1) )
        | ( fFalse = sK14(bool,X0) )
        | ( fFalse = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_620])]) ).

tff(f3094,plain,
    ( spl18_226
  <=> ! [X0: $tType,X3: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X1: nat] : ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),sK14(X0,X2)) = huffma1401021291ibling(X0,X2,sK14(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_226])]) ).

tff(f3137,plain,
    ( ! [X2: nat,X3: nat,X0: huffma1450048681e_tree(bool),X1: bool,X4: huffma1450048681e_tree(bool),X5: huffma1450048681e_tree(bool)] :
        ( ( huffma1401021291ibling(bool,X0,X1) = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X2,X0,huffma1146269203erNode(bool,X3,X4,X5)),X1) )
        | ( fFalse = sK14(bool,X0) )
        | ( fFalse = X1 ) )
    | ~ spl18_81
    | ~ spl18_226 ),
    inference(superposition,[],[f3095,f1017]) ).

tff(f3095,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] : ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),sK14(X0,X2)) = huffma1401021291ibling(X0,X2,sK14(X0,X2)) )
    | ~ spl18_226 ),
    inference(avatar_component_clause,[],[f3094]) ).

tff(f31534,plain,
    ( spl18_619
    | ~ spl18_56
    | ~ spl18_600 ),
    inference(avatar_split_clause,[],[f30616,f30604,f840,f31531]) ).

tff(f31531,plain,
    ( spl18_619
  <=> ( zero_zero(nat) = huffma1134658180e_cost(a1,t_1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_619])]) ).

tff(f840,plain,
    ( spl18_56
  <=> ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma1134658180e_cost(X0,huffma2021818691e_Leaf(X0,X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_56])]) ).

tff(f30616,plain,
    ( ( zero_zero(nat) = huffma1134658180e_cost(a1,t_1) )
    | ~ spl18_56
    | ~ spl18_600 ),
    inference(superposition,[],[f841,f30606]) ).

tff(f841,plain,
    ( ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma1134658180e_cost(X0,huffma2021818691e_Leaf(X0,X2,X1)) )
    | ~ spl18_56 ),
    inference(avatar_component_clause,[],[f840]) ).

tff(f31529,plain,
    ( spl18_618
    | ~ spl18_81
    | ~ spl18_226 ),
    inference(avatar_split_clause,[],[f3135,f3094,f1016,f31527]) ).

tff(f31527,plain,
    ( spl18_618
  <=> ! [X5: bool,X4: huffma1450048681e_tree(bool),X0: huffma1450048681e_tree(bool),X3: huffma1450048681e_tree(bool),X2: nat,X1: nat] :
        ( ( huffma1401021291ibling(bool,huffma1146269203erNode(bool,X1,X0,huffma1146269203erNode(bool,X2,X3,X4)),fFalse) = huffma1401021291ibling(bool,X0,fFalse) )
        | ( sK14(bool,X0) = X5 )
        | ( fFalse = X5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_618])]) ).

tff(f3135,plain,
    ( ! [X2: nat,X3: huffma1450048681e_tree(bool),X0: huffma1450048681e_tree(bool),X1: nat,X4: huffma1450048681e_tree(bool),X5: bool] :
        ( ( huffma1401021291ibling(bool,huffma1146269203erNode(bool,X1,X0,huffma1146269203erNode(bool,X2,X3,X4)),fFalse) = huffma1401021291ibling(bool,X0,fFalse) )
        | ( sK14(bool,X0) = X5 )
        | ( fFalse = X5 ) )
    | ~ spl18_81
    | ~ spl18_226 ),
    inference(superposition,[],[f3095,f1017]) ).

tff(f31525,plain,
    ( spl18_617
    | ~ spl18_81
    | ~ spl18_211 ),
    inference(avatar_split_clause,[],[f2908,f2796,f1016,f31523]) ).

tff(f31523,plain,
    ( spl18_617
  <=> ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X6: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X4: X0,X5: bool,X3: nat,X1: fun(nat,fun(X0,bool))] :
        ( ( huffma1280178957ee_rec(X0,bool,X1,X6,huffma2021818691e_Leaf(X0,X3,X4)) = X5 )
        | ( fFalse = huffma107959123e_case(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) )
        | ( fFalse = X5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_617])]) ).

tff(f2796,plain,
    ( spl18_211
  <=> ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X4: X0,X6: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X3: nat] : ( huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,X4)) = huffma1280178957ee_rec(X0,X1,X2,X6,huffma2021818691e_Leaf(X0,X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_211])]) ).

tff(f2908,plain,
    ( ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X3: nat,X1: fun(nat,fun(X0,bool)),X6: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X4: X0,X5: bool] :
        ( ( huffma1280178957ee_rec(X0,bool,X1,X6,huffma2021818691e_Leaf(X0,X3,X4)) = X5 )
        | ( fFalse = huffma107959123e_case(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) )
        | ( fFalse = X5 ) )
    | ~ spl18_81
    | ~ spl18_211 ),
    inference(superposition,[],[f2797,f1017]) ).

tff(f2797,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X6: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)))] : ( huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,X4)) = huffma1280178957ee_rec(X0,X1,X2,X6,huffma2021818691e_Leaf(X0,X3,X4)) )
    | ~ spl18_211 ),
    inference(avatar_component_clause,[],[f2796]) ).

tff(f31521,plain,
    ( spl18_616
    | ~ spl18_81
    | ~ spl18_211 ),
    inference(avatar_split_clause,[],[f2906,f2796,f1016,f31519]) ).

tff(f31519,plain,
    ( spl18_616
  <=> ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X6: bool,X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X3: nat,X1: fun(nat,fun(X0,bool))] :
        ( ( fFalse = huffma1280178957ee_rec(X0,bool,X1,X5,huffma2021818691e_Leaf(X0,X3,X4)) )
        | ( huffma107959123e_case(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) = X6 )
        | ( fFalse = X6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_616])]) ).

tff(f2906,plain,
    ( ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X3: nat,X1: fun(nat,fun(X0,bool)),X6: bool,X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))))] :
        ( ( fFalse = huffma1280178957ee_rec(X0,bool,X1,X5,huffma2021818691e_Leaf(X0,X3,X4)) )
        | ( huffma107959123e_case(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) = X6 )
        | ( fFalse = X6 ) )
    | ~ spl18_81
    | ~ spl18_211 ),
    inference(superposition,[],[f2797,f1017]) ).

tff(f31517,plain,
    ( spl18_615
    | ~ spl18_81
    | ~ spl18_210 ),
    inference(avatar_split_clause,[],[f2881,f2792,f1016,f31515]) ).

tff(f31515,plain,
    ( spl18_615
  <=> ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X6: bool,X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X3: nat,X1: fun(nat,fun(X0,bool))] :
        ( ( fFalse = huffma1280178957ee_rec(X0,bool,X1,X5,huffma2021818691e_Leaf(X0,X3,X4)) )
        | ( huffma1280178957ee_rec(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) = X6 )
        | ( fFalse = X6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_615])]) ).

tff(f2792,plain,
    ( spl18_210
  <=> ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X4: X0,X6: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X3: nat] : ( huffma1280178957ee_rec(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,X4)) = huffma1280178957ee_rec(X0,X1,X2,X6,huffma2021818691e_Leaf(X0,X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_210])]) ).

tff(f2881,plain,
    ( ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X3: nat,X1: fun(nat,fun(X0,bool)),X6: bool,X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))))] :
        ( ( fFalse = huffma1280178957ee_rec(X0,bool,X1,X5,huffma2021818691e_Leaf(X0,X3,X4)) )
        | ( huffma1280178957ee_rec(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) = X6 )
        | ( fFalse = X6 ) )
    | ~ spl18_81
    | ~ spl18_210 ),
    inference(superposition,[],[f2793,f1017]) ).

tff(f2793,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X6: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))))] : ( huffma1280178957ee_rec(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,X4)) = huffma1280178957ee_rec(X0,X1,X2,X6,huffma2021818691e_Leaf(X0,X3,X4)) )
    | ~ spl18_210 ),
    inference(avatar_component_clause,[],[f2792]) ).

tff(f31513,plain,
    ( spl18_614
    | ~ spl18_81
    | ~ spl18_209 ),
    inference(avatar_split_clause,[],[f2861,f2788,f1016,f31511]) ).

tff(f31511,plain,
    ( spl18_614
  <=> ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X6: bool,X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X3: nat,X1: fun(nat,fun(X0,bool))] :
        ( ( fFalse = huffma107959123e_case(X0,bool,X1,X5,huffma2021818691e_Leaf(X0,X3,X4)) )
        | ( huffma107959123e_case(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) = X6 )
        | ( fFalse = X6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_614])]) ).

tff(f2788,plain,
    ( spl18_209
  <=> ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X4: X0,X6: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X3: nat] : ( huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,X4)) = huffma107959123e_case(X0,X1,X2,X6,huffma2021818691e_Leaf(X0,X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_209])]) ).

tff(f2861,plain,
    ( ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X3: nat,X1: fun(nat,fun(X0,bool)),X6: bool,X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)))] :
        ( ( fFalse = huffma107959123e_case(X0,bool,X1,X5,huffma2021818691e_Leaf(X0,X3,X4)) )
        | ( huffma107959123e_case(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) = X6 )
        | ( fFalse = X6 ) )
    | ~ spl18_81
    | ~ spl18_209 ),
    inference(superposition,[],[f2789,f1017]) ).

tff(f2789,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X6: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)))] : ( huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,X4)) = huffma107959123e_case(X0,X1,X2,X6,huffma2021818691e_Leaf(X0,X3,X4)) )
    | ~ spl18_209 ),
    inference(avatar_component_clause,[],[f2788]) ).

tff(f31509,plain,
    ( spl18_613
    | ~ spl18_173
    | ~ spl18_205 ),
    inference(avatar_split_clause,[],[f2814,f2772,f2303,f31507]) ).

tff(f31507,plain,
    ( spl18_613
  <=> ! [X2: nat,X0: nat,X1: huffma1450048681e_tree(bool)] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(bool,bool,huffma675207370phabet(bool,X1),fTrue),X0,X2)) )
        | ~ huffma1518433673istent(bool,X1)
        | ( fFalse = sK6(bool,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_613])]) ).

tff(f2303,plain,
    ( spl18_173
  <=> ! [X0: huffma1450048681e_tree(bool)] :
        ( member(bool,fTrue,huffma675207370phabet(bool,X0))
        | ~ huffma1518433673istent(bool,X0)
        | ( fFalse = sK6(bool,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_173])]) ).

tff(f2772,plain,
    ( spl18_205
  <=> ! [X1: $tType,X4: nat,X0: nat,X3: X1,X2: fun(X1,bool)] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(X1,bool,X2,X3),X0,X4)) )
        | ~ member(X1,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_205])]) ).

tff(f2814,plain,
    ( ! [X2: nat,X0: nat,X1: huffma1450048681e_tree(bool)] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(bool,bool,huffma675207370phabet(bool,X1),fTrue),X0,X2)) )
        | ~ huffma1518433673istent(bool,X1)
        | ( fFalse = sK6(bool,X1) ) )
    | ~ spl18_173
    | ~ spl18_205 ),
    inference(resolution,[],[f2773,f2304]) ).

tff(f2304,plain,
    ( ! [X0: huffma1450048681e_tree(bool)] :
        ( member(bool,fTrue,huffma675207370phabet(bool,X0))
        | ~ huffma1518433673istent(bool,X0)
        | ( fFalse = sK6(bool,X0) ) )
    | ~ spl18_173 ),
    inference(avatar_component_clause,[],[f2303]) ).

tff(f2773,plain,
    ( ! [X1: $tType,X2: fun(X1,bool),X3: X1,X0: nat,X4: nat] :
        ( ~ member(X1,X3,X2)
        | ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(X1,bool,X2,X3),X0,X4)) ) )
    | ~ spl18_205 ),
    inference(avatar_component_clause,[],[f2772]) ).

tff(f31505,plain,
    ( spl18_612
    | ~ spl18_196
    | ~ spl18_200 ),
    inference(avatar_split_clause,[],[f2740,f2720,f2573,f31503]) ).

tff(f31503,plain,
    ( spl18_612
  <=> ! [X2: int,X0: fun(int,bool),X1: fun(int,bool)] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ member(int,sK3(X1),X0)
        | pp(aa(int,bool,X1,X2))
        | ~ ord_less_eq(int,zero_zero(int),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_612])]) ).

tff(f2720,plain,
    ( spl18_200
  <=> ! [X0: fun(int,bool),X1: int] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ ord_less_eq(int,zero_zero(int),X1)
        | ~ member(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_200])]) ).

tff(f2740,plain,
    ( ! [X2: int,X0: fun(int,bool),X1: fun(int,bool)] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ member(int,sK3(X1),X0)
        | pp(aa(int,bool,X1,X2))
        | ~ ord_less_eq(int,zero_zero(int),X2) )
    | ~ spl18_196
    | ~ spl18_200 ),
    inference(resolution,[],[f2721,f2574]) ).

tff(f2721,plain,
    ( ! [X0: fun(int,bool),X1: int] :
        ( ~ ord_less_eq(int,zero_zero(int),X1)
        | pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ member(int,X1,X0) )
    | ~ spl18_200 ),
    inference(avatar_component_clause,[],[f2720]) ).

tff(f31501,plain,
    ( spl18_611
    | ~ spl18_132
    | ~ spl18_173 ),
    inference(avatar_split_clause,[],[f2366,f2303,f1770,f31499]) ).

tff(f31499,plain,
    ( spl18_611
  <=> ! [X4: huffma1450048681e_tree(bool),X0: huffma1450048681e_tree(bool),X3: huffma1450048681e_tree(bool),X2: nat,X1: nat] :
        ( ~ huffma1518433673istent(bool,X0)
        | ( fFalse = sK6(bool,X0) )
        | ( huffma1401021291ibling(bool,X0,fTrue) = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X1,X0,huffma1146269203erNode(bool,X2,X3,X4)),fTrue) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_611])]) ).

tff(f1770,plain,
    ( spl18_132
  <=> ! [X0: $tType,X5: huffma1450048681e_tree(X0),X3: nat,X2: huffma1450048681e_tree(X0),X4: nat,X6: X0,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X5,huffma1146269203erNode(X0,X3,X2,X1)),X6) = huffma1401021291ibling(X0,X5,X6) )
        | ~ member(X0,X6,huffma675207370phabet(X0,X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_132])]) ).

tff(f2366,plain,
    ( ! [X2: nat,X3: huffma1450048681e_tree(bool),X0: huffma1450048681e_tree(bool),X1: nat,X4: huffma1450048681e_tree(bool)] :
        ( ~ huffma1518433673istent(bool,X0)
        | ( fFalse = sK6(bool,X0) )
        | ( huffma1401021291ibling(bool,X0,fTrue) = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X1,X0,huffma1146269203erNode(bool,X2,X3,X4)),fTrue) ) )
    | ~ spl18_132
    | ~ spl18_173 ),
    inference(resolution,[],[f2304,f1771]) ).

tff(f1771,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X6: X0,X4: nat,X5: huffma1450048681e_tree(X0)] :
        ( ~ member(X0,X6,huffma675207370phabet(X0,X5))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X5,huffma1146269203erNode(X0,X3,X2,X1)),X6) = huffma1401021291ibling(X0,X5,X6) ) )
    | ~ spl18_132 ),
    inference(avatar_component_clause,[],[f1770]) ).

tff(f31497,plain,
    ( spl18_610
    | ~ spl18_37
    | ~ spl18_133 ),
    inference(avatar_split_clause,[],[f1805,f1795,f752,f31495]) ).

tff(f31495,plain,
    ( spl18_610
  <=> ! [X2: nat,X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ ord_less(nat,X1,sK8(X0))
        | pp(aa(nat,bool,X0,X2))
        | ( fFalse = aa(nat,bool,X0,zero_zero(nat)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_610])]) ).

tff(f1795,plain,
    ( spl18_133
  <=> ! [X0: nat,X1: fun(nat,bool),X3: nat] :
        ( pp(aa(nat,bool,X1,X0))
        | pp(aa(nat,bool,X1,X3))
        | ~ ord_less(nat,X3,sK8(X1))
        | ~ pp(aa(nat,bool,X1,zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_133])]) ).

tff(f1805,plain,
    ( ! [X2: nat,X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ ord_less(nat,X1,sK8(X0))
        | pp(aa(nat,bool,X0,X2))
        | ( fFalse = aa(nat,bool,X0,zero_zero(nat)) ) )
    | ~ spl18_37
    | ~ spl18_133 ),
    inference(resolution,[],[f1796,f753]) ).

tff(f1796,plain,
    ( ! [X3: nat,X0: nat,X1: fun(nat,bool)] :
        ( ~ pp(aa(nat,bool,X1,zero_zero(nat)))
        | pp(aa(nat,bool,X1,X3))
        | ~ ord_less(nat,X3,sK8(X1))
        | pp(aa(nat,bool,X1,X0)) )
    | ~ spl18_133 ),
    inference(avatar_component_clause,[],[f1795]) ).

tff(f31493,plain,
    ( spl18_609
    | ~ spl18_81
    | ~ spl18_121 ),
    inference(avatar_split_clause,[],[f1564,f1543,f1016,f31491]) ).

tff(f31491,plain,
    ( spl18_609
  <=> ! [X3: nat,X4: bool,X0: nat,X5: bool,X2: bool,X1: nat] :
        ( ( X2 = X5 )
        | ( X2 = X4 )
        | ( fFalse = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X0,huffma2021818691e_Leaf(bool,X1,X2),huffma2021818691e_Leaf(bool,X3,X4)),X4) )
        | ( fFalse = X5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_609])]) ).

tff(f1543,plain,
    ( spl18_121
  <=> ! [X0: $tType,X5: X0,X3: nat,X4: nat,X6: X0,X2: nat] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,huffma2021818691e_Leaf(X0,X3,X5),huffma2021818691e_Leaf(X0,X2,X6)),X6) = X5 )
        | ( X5 = X6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_121])]) ).

tff(f1564,plain,
    ( ! [X2: bool,X3: nat,X0: nat,X1: nat,X4: bool,X5: bool] :
        ( ( X2 = X5 )
        | ( X2 = X4 )
        | ( fFalse = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X0,huffma2021818691e_Leaf(bool,X1,X2),huffma2021818691e_Leaf(bool,X3,X4)),X4) )
        | ( fFalse = X5 ) )
    | ~ spl18_81
    | ~ spl18_121 ),
    inference(superposition,[],[f1544,f1017]) ).

tff(f1544,plain,
    ( ! [X0: $tType,X2: nat,X3: nat,X6: X0,X4: nat,X5: X0] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,huffma2021818691e_Leaf(X0,X3,X5),huffma2021818691e_Leaf(X0,X2,X6)),X6) = X5 )
        | ( X5 = X6 ) )
    | ~ spl18_121 ),
    inference(avatar_component_clause,[],[f1543]) ).

tff(f31484,plain,
    ( spl18_608
    | ~ spl18_81
    | ~ spl18_121 ),
    inference(avatar_split_clause,[],[f1562,f1543,f1016,f31482]) ).

tff(f31482,plain,
    ( spl18_608
  <=> ! [X3: nat,X4: bool,X0: nat,X5: bool,X2: bool,X1: nat] :
        ( ( fFalse = X2 )
        | ( X2 = X4 )
        | ( huffma1401021291ibling(bool,huffma1146269203erNode(bool,X0,huffma2021818691e_Leaf(bool,X1,X2),huffma2021818691e_Leaf(bool,X3,X4)),X4) = X5 )
        | ( fFalse = X5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_608])]) ).

tff(f1562,plain,
    ( ! [X2: bool,X3: nat,X0: nat,X1: nat,X4: bool,X5: bool] :
        ( ( fFalse = X2 )
        | ( X2 = X4 )
        | ( huffma1401021291ibling(bool,huffma1146269203erNode(bool,X0,huffma2021818691e_Leaf(bool,X1,X2),huffma2021818691e_Leaf(bool,X3,X4)),X4) = X5 )
        | ( fFalse = X5 ) )
    | ~ spl18_81
    | ~ spl18_121 ),
    inference(superposition,[],[f1544,f1017]) ).

tff(f30828,plain,
    ( spl18_607
    | ~ spl18_37
    | ~ spl18_240 ),
    inference(avatar_split_clause,[],[f3504,f3410,f752,f30826]) ).

tff(f30826,plain,
    ( spl18_607
  <=> ! [X2: fun(nat,bool),X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,sK7(X1,X2))
        | pp(aa(nat,bool,X2,zero_zero(nat)))
        | ~ member(nat,X0,X2)
        | ( fFalse = aa(nat,bool,X2,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_607])]) ).

tff(f3504,plain,
    ( ! [X2: fun(nat,bool),X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,sK7(X1,X2))
        | pp(aa(nat,bool,X2,zero_zero(nat)))
        | ~ member(nat,X0,X2)
        | ( fFalse = aa(nat,bool,X2,X1) ) )
    | ~ spl18_37
    | ~ spl18_240 ),
    inference(resolution,[],[f3411,f753]) ).

tff(f30824,plain,
    ( spl18_606
    | ~ spl18_137
    | ~ spl18_227 ),
    inference(avatar_split_clause,[],[f3153,f3098,f1844,f30822]) ).

tff(f30822,plain,
    ( spl18_606
  <=> ! [X0: $tType,X2: $tType,X3: fun(nat,fun(X0,X2)),X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X2))),X5: fun(nat,fun(X0,X2)),X1: huffma1450048681e_tree(X0)] :
        ( ( huffma107959123e_case(X0,X2,X3,X4,X1) = huffma107959123e_case(X0,X2,X5,X4,X1) )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_606])]) ).

tff(f1844,plain,
    ( spl18_137
  <=> ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma1146269203erNode(X0,sK9(X0,X1),sK10(X0,X1),sK11(X0,X1)) = X1 )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_137])]) ).

tff(f3098,plain,
    ( spl18_227
  <=> ! [X0: $tType,X1: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X4: huffma1450048681e_tree(X0),X6: fun(nat,fun(X0,X1)),X5: huffma1450048681e_tree(X0),X3: nat,X7: fun(nat,fun(X0,X1))] : ( huffma107959123e_case(X0,X1,X6,X2,huffma1146269203erNode(X0,X3,X4,X5)) = huffma107959123e_case(X0,X1,X7,X2,huffma1146269203erNode(X0,X3,X4,X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_227])]) ).

tff(f3153,plain,
    ( ! [X0: $tType,X2: $tType,X3: fun(nat,fun(X0,X2)),X1: huffma1450048681e_tree(X0),X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X2))),X5: fun(nat,fun(X0,X2))] :
        ( ( huffma107959123e_case(X0,X2,X3,X4,X1) = huffma107959123e_case(X0,X2,X5,X4,X1) )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) )
    | ~ spl18_137
    | ~ spl18_227 ),
    inference(superposition,[],[f3099,f1845]) ).

tff(f1845,plain,
    ( ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma1146269203erNode(X0,sK9(X0,X1),sK10(X0,X1),sK11(X0,X1)) = X1 )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) )
    | ~ spl18_137 ),
    inference(avatar_component_clause,[],[f1844]) ).

tff(f3099,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X3: nat,X6: fun(nat,fun(X0,X1)),X7: fun(nat,fun(X0,X1)),X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] : ( huffma107959123e_case(X0,X1,X6,X2,huffma1146269203erNode(X0,X3,X4,X5)) = huffma107959123e_case(X0,X1,X7,X2,huffma1146269203erNode(X0,X3,X4,X5)) )
    | ~ spl18_227 ),
    inference(avatar_component_clause,[],[f3098]) ).

tff(f30820,plain,
    ( spl18_605
    | ~ spl18_31
    | ~ spl18_227 ),
    inference(avatar_split_clause,[],[f3152,f3098,f725,f30818]) ).

tff(f30818,plain,
    ( spl18_605
  <=> ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X6: fun(nat,fun(X0,bool)),X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0),X3: nat,X1: fun(nat,fun(X0,bool))] :
        ( ( fTrue = huffma107959123e_case(X0,bool,X6,X2,huffma1146269203erNode(X0,X3,X4,X5)) )
        | ( fFalse = huffma107959123e_case(X0,bool,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_605])]) ).

tff(f3152,plain,
    ( ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X3: nat,X1: fun(nat,fun(X0,bool)),X6: fun(nat,fun(X0,bool)),X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( fTrue = huffma107959123e_case(X0,bool,X6,X2,huffma1146269203erNode(X0,X3,X4,X5)) )
        | ( fFalse = huffma107959123e_case(X0,bool,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)) ) )
    | ~ spl18_31
    | ~ spl18_227 ),
    inference(superposition,[],[f3099,f726]) ).

tff(f30816,plain,
    ( spl18_604
    | ~ spl18_31
    | ~ spl18_226 ),
    inference(avatar_split_clause,[],[f3144,f3094,f725,f30814]) ).

tff(f30814,plain,
    ( spl18_604
  <=> ! [X4: huffma1450048681e_tree(bool),X0: nat,X3: huffma1450048681e_tree(bool),X2: nat,X1: huffma1450048681e_tree(bool)] :
        ( ( fTrue = huffma1401021291ibling(bool,X1,sK14(bool,X1)) )
        | ( fFalse = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X0,X1,huffma1146269203erNode(bool,X2,X3,X4)),sK14(bool,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_604])]) ).

tff(f3144,plain,
    ( ! [X2: nat,X3: huffma1450048681e_tree(bool),X0: nat,X1: huffma1450048681e_tree(bool),X4: huffma1450048681e_tree(bool)] :
        ( ( fTrue = huffma1401021291ibling(bool,X1,sK14(bool,X1)) )
        | ( fFalse = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X0,X1,huffma1146269203erNode(bool,X2,X3,X4)),sK14(bool,X1)) ) )
    | ~ spl18_31
    | ~ spl18_226 ),
    inference(superposition,[],[f3095,f726]) ).

tff(f30804,plain,
    ( spl18_603
    | ~ spl18_36
    | ~ spl18_600 ),
    inference(avatar_split_clause,[],[f30615,f30604,f745,f30801]) ).

tff(f30801,plain,
    ( spl18_603
  <=> huffma1518433673istent(a1,t_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_603])]) ).

tff(f745,plain,
    ( spl18_36
  <=> ! [X0: $tType,X2: nat,X1: X0] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_36])]) ).

tff(f30615,plain,
    ( huffma1518433673istent(a1,t_1)
    | ~ spl18_36
    | ~ spl18_600 ),
    inference(superposition,[],[f746,f30606]) ).

tff(f746,plain,
    ( ! [X0: $tType,X2: nat,X1: X0] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1))
    | ~ spl18_36 ),
    inference(avatar_component_clause,[],[f745]) ).

tff(f30799,plain,
    ( ~ spl18_16
    | spl18_602
    | ~ spl18_92
    | ~ spl18_196 ),
    inference(avatar_split_clause,[],[f2664,f2573,f1203,f30797,f655]) ).

tff(f655,plain,
    ( spl18_16
  <=> order(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_16])]) ).

tff(f30797,plain,
    ( spl18_602
  <=> ! [X0: fun(int,bool),X1: int] :
        ( pp(aa(int,bool,X0,X1))
        | ( zero_zero(int) = sK3(X0) )
        | ~ ord_less_eq(int,sK3(X0),zero_zero(int))
        | ~ ord_less_eq(int,zero_zero(int),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_602])]) ).

tff(f1203,plain,
    ( spl18_92
  <=> ! [X0: $tType,X2: X0,X1: X0] :
        ( ( X1 = X2 )
        | ~ ord_less_eq(X0,X1,X2)
        | ~ ord_less_eq(X0,X2,X1)
        | ~ order(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_92])]) ).

tff(f2664,plain,
    ( ! [X0: fun(int,bool),X1: int] :
        ( pp(aa(int,bool,X0,X1))
        | ~ ord_less_eq(int,zero_zero(int),X1)
        | ~ ord_less_eq(int,sK3(X0),zero_zero(int))
        | ( zero_zero(int) = sK3(X0) )
        | ~ order(int) )
    | ~ spl18_92
    | ~ spl18_196 ),
    inference(resolution,[],[f2574,f1204]) ).

tff(f1204,plain,
    ( ! [X0: $tType,X2: X0,X1: X0] :
        ( ~ ord_less_eq(X0,X2,X1)
        | ~ ord_less_eq(X0,X1,X2)
        | ( X1 = X2 )
        | ~ order(X0) )
    | ~ spl18_92 ),
    inference(avatar_component_clause,[],[f1203]) ).

tff(f30613,plain,
    ( spl18_23
    | ~ spl18_601 ),
    inference(avatar_contradiction_clause,[],[f30612]) ).

tff(f30612,plain,
    ( $false
    | spl18_23
    | ~ spl18_601 ),
    inference(trivial_inequality_removal,[],[f30611]) ).

tff(f30611,plain,
    ( ( huffma1401021291ibling(a1,t_1,a) != huffma1401021291ibling(a1,t_1,a) )
    | spl18_23
    | ~ spl18_601 ),
    inference(superposition,[],[f692,f30609]) ).

tff(f30609,plain,
    ( ! [X0: nat,X1: huffma1450048681e_tree(a1)] : ( huffma1401021291ibling(a1,t_1,a) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,X1),a) )
    | ~ spl18_601 ),
    inference(avatar_component_clause,[],[f30608]) ).

tff(f30608,plain,
    ( spl18_601
  <=> ! [X0: nat,X1: huffma1450048681e_tree(a1)] : ( huffma1401021291ibling(a1,t_1,a) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,X1),a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_601])]) ).

tff(f692,plain,
    ( ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) != huffma1401021291ibling(a1,t_1,a) )
    | spl18_23 ),
    inference(avatar_component_clause,[],[f690]) ).

tff(f690,plain,
    ( spl18_23
  <=> ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) = huffma1401021291ibling(a1,t_1,a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_23])]) ).

tff(f30610,plain,
    ( spl18_600
    | spl18_601
    | ~ spl18_29
    | ~ spl18_281 ),
    inference(avatar_split_clause,[],[f4703,f4510,f715,f30608,f30604]) ).

tff(f715,plain,
    ( spl18_29
  <=> member(a1,a,huffma675207370phabet(a1,t_1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_29])]) ).

tff(f4510,plain,
    ( spl18_281
  <=> ! [X0: $tType,X4: huffma1450048681e_tree(X0),X3: nat,X2: X0,X1: huffma1450048681e_tree(X0)] :
        ( ~ member(X0,X2,huffma675207370phabet(X0,X1))
        | ( huffma1401021291ibling(X0,X1,X2) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X1,X4),X2) )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_281])]) ).

tff(f4703,plain,
    ( ! [X0: nat,X1: huffma1450048681e_tree(a1)] :
        ( ( huffma1401021291ibling(a1,t_1,a) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,X1),a) )
        | ( t_1 = huffma2021818691e_Leaf(a1,sK12(a1,t_1),sK13(a1,t_1)) ) )
    | ~ spl18_29
    | ~ spl18_281 ),
    inference(resolution,[],[f4511,f717]) ).

tff(f717,plain,
    ( member(a1,a,huffma675207370phabet(a1,t_1))
    | ~ spl18_29 ),
    inference(avatar_component_clause,[],[f715]) ).

tff(f4511,plain,
    ( ! [X0: $tType,X2: X0,X3: nat,X1: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0)] :
        ( ~ member(X0,X2,huffma675207370phabet(X0,X1))
        | ( huffma1401021291ibling(X0,X1,X2) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X1,X4),X2) )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) )
    | ~ spl18_281 ),
    inference(avatar_component_clause,[],[f4510]) ).

tff(f30602,plain,
    ( spl18_599
    | ~ spl18_137
    | ~ spl18_189 ),
    inference(avatar_split_clause,[],[f2546,f2543,f1844,f30600]) ).

tff(f30600,plain,
    ( spl18_599
  <=> ! [X0: huffma1450048681e_tree(a1),X1: nat] :
        ( ( huffma1401021291ibling(a1,t_1,a) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X1,t_1,X0),a) )
        | ( huffma2021818691e_Leaf(a1,sK12(a1,X0),sK13(a1,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_599])]) ).

tff(f2543,plain,
    ( spl18_189
  <=> ! [X2: huffma1450048681e_tree(a1),X0: nat,X1: nat,X3: huffma1450048681e_tree(a1)] : ( huffma1401021291ibling(a1,t_1,a) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,huffma1146269203erNode(a1,X1,X2,X3)),a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_189])]) ).

tff(f2546,plain,
    ( ! [X0: huffma1450048681e_tree(a1),X1: nat] :
        ( ( huffma1401021291ibling(a1,t_1,a) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X1,t_1,X0),a) )
        | ( huffma2021818691e_Leaf(a1,sK12(a1,X0),sK13(a1,X0)) = X0 ) )
    | ~ spl18_137
    | ~ spl18_189 ),
    inference(superposition,[],[f2544,f1845]) ).

tff(f2544,plain,
    ( ! [X2: huffma1450048681e_tree(a1),X3: huffma1450048681e_tree(a1),X0: nat,X1: nat] : ( huffma1401021291ibling(a1,t_1,a) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,huffma1146269203erNode(a1,X1,X2,X3)),a) )
    | ~ spl18_189 ),
    inference(avatar_component_clause,[],[f2543]) ).

tff(f26947,plain,
    ( spl18_598
    | spl18_1
    | ~ spl18_65
    | ~ spl18_249 ),
    inference(avatar_split_clause,[],[f3944,f3574,f896,f580,f26945]) ).

tff(f26945,plain,
    ( spl18_598
  <=> ! [X0: $tType,X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X3: X0,X2: nat,X1: fun(nat,fun(X0,bool))] :
        ( ~ member(X0,X3,aa(nat,fun(X0,bool),X1,X2))
        | ( fTrue = huffma1280178957ee_rec(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_598])]) ).

tff(f896,plain,
    ( spl18_65
  <=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( pp(aa(X0,bool,X1,X2))
        | ~ member(X0,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_65])]) ).

tff(f3944,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: fun(nat,fun(X0,bool)),X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))))] :
        ( pp(fFalse)
        | ~ member(X0,X3,aa(nat,fun(X0,bool),X1,X2))
        | ( fTrue = huffma1280178957ee_rec(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)) ) )
    | ~ spl18_65
    | ~ spl18_249 ),
    inference(superposition,[],[f897,f3575]) ).

tff(f897,plain,
    ( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( pp(aa(X0,bool,X1,X2))
        | ~ member(X0,X2,X1) )
    | ~ spl18_65 ),
    inference(avatar_component_clause,[],[f896]) ).

tff(f26923,plain,
    ( spl18_597
    | spl18_1
    | ~ spl18_65
    | ~ spl18_246 ),
    inference(avatar_split_clause,[],[f3719,f3562,f896,f580,f26921]) ).

tff(f26921,plain,
    ( spl18_597
  <=> ! [X0: $tType,X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X3: X0,X2: nat,X1: fun(nat,fun(X0,bool))] :
        ( ~ member(X0,X3,aa(nat,fun(X0,bool),X1,X2))
        | ( fTrue = huffma107959123e_case(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_597])]) ).

tff(f3719,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: fun(nat,fun(X0,bool)),X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)))] :
        ( pp(fFalse)
        | ~ member(X0,X3,aa(nat,fun(X0,bool),X1,X2))
        | ( fTrue = huffma107959123e_case(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)) ) )
    | ~ spl18_65
    | ~ spl18_246 ),
    inference(superposition,[],[f897,f3563]) ).

tff(f26919,plain,
    ( spl18_596
    | ~ spl18_39
    | ~ spl18_241 ),
    inference(avatar_split_clause,[],[f3611,f3514,f761,f26917]) ).

tff(f26917,plain,
    ( spl18_596
  <=> ! [X2: nat,X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,zero_zero(int)))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,sK3(X0)),X2,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_596])]) ).

tff(f761,plain,
    ( spl18_39
  <=> ( zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_39])]) ).

tff(f3514,plain,
    ( spl18_241
  <=> ! [X0: fun(int,bool),X3: nat,X2: nat,X1: nat] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,X1)))
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,sK3(X0)),X3,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_241])]) ).

tff(f3611,plain,
    ( ! [X2: nat,X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,zero_zero(int)))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,sK3(X0)),X2,X1)) ) )
    | ~ spl18_39
    | ~ spl18_241 ),
    inference(superposition,[],[f3515,f763]) ).

tff(f763,plain,
    ( ( zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)) )
    | ~ spl18_39 ),
    inference(avatar_component_clause,[],[f761]) ).

tff(f3515,plain,
    ( ! [X2: nat,X3: nat,X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,X1)))
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,sK3(X0)),X3,X2)) ) )
    | ~ spl18_241 ),
    inference(avatar_component_clause,[],[f3514]) ).

tff(f26915,plain,
    ( spl18_595
    | ~ spl18_110
    | ~ spl18_241 ),
    inference(avatar_split_clause,[],[f3604,f3514,f1452,f26913]) ).

tff(f26913,plain,
    ( spl18_595
  <=> ! [X2: nat,X0: nat,X1: fun(int,bool)] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(int,bool,X1,sK3(X1)),X2,X0)) )
        | pp(aa(int,bool,X1,sK4(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_595])]) ).

tff(f1452,plain,
    ( spl18_110
  <=> ! [X2: nat,X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,sK4(X0)))
        | ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_110])]) ).

tff(f3604,plain,
    ( ! [X2: nat,X0: nat,X1: fun(int,bool)] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(int,bool,X1,sK3(X1)),X2,X0)) )
        | pp(aa(int,bool,X1,sK4(X1))) )
    | ~ spl18_110
    | ~ spl18_241 ),
    inference(resolution,[],[f3515,f1453]) ).

tff(f1453,plain,
    ( ! [X2: nat,X0: fun(int,bool)] :
        ( ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,X2)))
        | pp(aa(int,bool,X0,sK4(X0))) )
    | ~ spl18_110 ),
    inference(avatar_component_clause,[],[f1452]) ).

tff(f26881,plain,
    ( spl18_594
    | ~ spl18_90
    | ~ spl18_244 ),
    inference(avatar_split_clause,[],[f3551,f3538,f1052,f26879]) ).

tff(f26879,plain,
    ( spl18_594
  <=> ! [X0: $tType,X4: fun(X0,nat),X3: nat,X2: X0,X1: nat] :
        ( ~ ord_less_eq(nat,X1,X3)
        | ord_less_eq(nat,aa(X0,nat,X4,X2),X3)
        | ~ ord_less_eq(fun(X0,nat),X4,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_594])]) ).

tff(f3538,plain,
    ( spl18_244
  <=> ! [X0: $tType,X4: nat,X3: X0,X2: fun(X0,nat),X1: fun(X0,nat)] :
        ( ~ ord_less_eq(fun(X0,nat),X1,X2)
        | ord_less_eq(nat,aa(X0,nat,X1,X3),X4)
        | ~ ord_less_eq(nat,aa(X0,nat,X2,X3),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_244])]) ).

tff(f3551,plain,
    ( ! [X0: $tType,X2: X0,X3: nat,X1: nat,X4: fun(X0,nat)] :
        ( ~ ord_less_eq(nat,X1,X3)
        | ord_less_eq(nat,aa(X0,nat,X4,X2),X3)
        | ~ ord_less_eq(fun(X0,nat),X4,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2))) )
    | ~ spl18_90
    | ~ spl18_244 ),
    inference(superposition,[],[f3539,f1053]) ).

tff(f3539,plain,
    ( ! [X0: $tType,X2: fun(X0,nat),X3: X0,X1: fun(X0,nat),X4: nat] :
        ( ~ ord_less_eq(nat,aa(X0,nat,X2,X3),X4)
        | ord_less_eq(nat,aa(X0,nat,X1,X3),X4)
        | ~ ord_less_eq(fun(X0,nat),X1,X2) )
    | ~ spl18_244 ),
    inference(avatar_component_clause,[],[f3538]) ).

tff(f26877,plain,
    ( spl18_593
    | ~ spl18_61
    | ~ spl18_222 ),
    inference(avatar_split_clause,[],[f3077,f3072,f880,f26875]) ).

tff(f26875,plain,
    ( spl18_593
  <=> ! [X0: $tType,X3: nat,X2: X0,X1: fun(X0,nat)] :
        ( ord_less_eq(nat,aa(X0,nat,X1,X2),X3)
        | ord_less_eq(fun(X0,nat),huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X3,X2)),X1)
        | ~ linorder(fun(X0,nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_593])]) ).

tff(f3072,plain,
    ( spl18_222
  <=> ! [X0: $tType,X3: fun(X0,nat),X2: X0,X1: nat] :
        ( ord_less_eq(nat,aa(X0,nat,X3,X2),X1)
        | ~ ord_less_eq(fun(X0,nat),X3,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_222])]) ).

tff(f3077,plain,
    ( ! [X0: $tType,X2: X0,X3: nat,X1: fun(X0,nat)] :
        ( ord_less_eq(nat,aa(X0,nat,X1,X2),X3)
        | ord_less_eq(fun(X0,nat),huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X3,X2)),X1)
        | ~ linorder(fun(X0,nat)) )
    | ~ spl18_61
    | ~ spl18_222 ),
    inference(resolution,[],[f3073,f881]) ).

tff(f3073,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,nat),X1: nat] :
        ( ~ ord_less_eq(fun(X0,nat),X3,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)))
        | ord_less_eq(nat,aa(X0,nat,X3,X2),X1) )
    | ~ spl18_222 ),
    inference(avatar_component_clause,[],[f3072]) ).

tff(f26873,plain,
    ( spl18_592
    | ~ spl18_61
    | ~ spl18_221 ),
    inference(avatar_split_clause,[],[f3067,f3062,f880,f26871]) ).

tff(f26871,plain,
    ( spl18_592
  <=> ! [X1: $tType,X0: nat,X3: X1,X2: fun(X1,nat)] :
        ( ord_less_eq(nat,X0,aa(X1,nat,X2,X3))
        | ord_less_eq(fun(X1,nat),X2,huffma1352802255e_freq(X1,huffma2021818691e_Leaf(X1,X0,X3)))
        | ~ linorder(fun(X1,nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_592])]) ).

tff(f3062,plain,
    ( spl18_221
  <=> ! [X0: $tType,X3: fun(X0,nat),X2: X0,X1: nat] :
        ( ord_less_eq(nat,X1,aa(X0,nat,X3,X2))
        | ~ ord_less_eq(fun(X0,nat),huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_221])]) ).

tff(f3067,plain,
    ( ! [X1: $tType,X2: fun(X1,nat),X3: X1,X0: nat] :
        ( ord_less_eq(nat,X0,aa(X1,nat,X2,X3))
        | ord_less_eq(fun(X1,nat),X2,huffma1352802255e_freq(X1,huffma2021818691e_Leaf(X1,X0,X3)))
        | ~ linorder(fun(X1,nat)) )
    | ~ spl18_61
    | ~ spl18_221 ),
    inference(resolution,[],[f3063,f881]) ).

tff(f3063,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,nat),X1: nat] :
        ( ~ ord_less_eq(fun(X0,nat),huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3)
        | ord_less_eq(nat,X1,aa(X0,nat,X3,X2)) )
    | ~ spl18_221 ),
    inference(avatar_component_clause,[],[f3062]) ).

tff(f26869,plain,
    ( spl18_591
    | ~ spl18_88
    | ~ spl18_205 ),
    inference(avatar_split_clause,[],[f2811,f2772,f1044,f26867]) ).

tff(f26867,plain,
    ( spl18_591
  <=> ! [X1: $tType,X4: nat,X0: nat,X3: X1,X2: huffma1450048681e_tree(X1)] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(X1,bool,huffma675207370phabet(X1,X2),X3),X0,X4)) )
        | ( huffma1401021291ibling(X1,X2,X3) = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_591])]) ).

tff(f1044,plain,
    ( spl18_88
  <=> ! [X0: $tType,X2: X0,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,X1,X2) = X2 )
        | member(X0,X2,huffma675207370phabet(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_88])]) ).

tff(f2811,plain,
    ( ! [X1: $tType,X2: huffma1450048681e_tree(X1),X3: X1,X0: nat,X4: nat] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(X1,bool,huffma675207370phabet(X1,X2),X3),X0,X4)) )
        | ( huffma1401021291ibling(X1,X2,X3) = X3 ) )
    | ~ spl18_88
    | ~ spl18_205 ),
    inference(resolution,[],[f2773,f1045]) ).

tff(f1045,plain,
    ( ! [X0: $tType,X2: X0,X1: huffma1450048681e_tree(X0)] :
        ( member(X0,X2,huffma675207370phabet(X0,X1))
        | ( huffma1401021291ibling(X0,X1,X2) = X2 ) )
    | ~ spl18_88 ),
    inference(avatar_component_clause,[],[f1044]) ).

tff(f26853,plain,
    ( ~ spl18_15
    | spl18_590
    | ~ spl18_104
    | ~ spl18_196 ),
    inference(avatar_split_clause,[],[f2663,f2573,f1278,f26851,f650]) ).

tff(f650,plain,
    ( spl18_15
  <=> preorder(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_15])]) ).

tff(f26851,plain,
    ( spl18_590
  <=> ! [X2: int,X0: fun(int,bool),X1: int] :
        ( pp(aa(int,bool,X0,X1))
        | ord_less_eq(int,zero_zero(int),X2)
        | ~ ord_less_eq(int,sK3(X0),X2)
        | ~ ord_less_eq(int,zero_zero(int),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_590])]) ).

tff(f1278,plain,
    ( spl18_104
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ord_less_eq(X0,X3,X1)
        | ~ ord_less_eq(X0,X2,X1)
        | ~ ord_less_eq(X0,X3,X2)
        | ~ preorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_104])]) ).

tff(f2663,plain,
    ( ! [X2: int,X0: fun(int,bool),X1: int] :
        ( pp(aa(int,bool,X0,X1))
        | ~ ord_less_eq(int,zero_zero(int),X1)
        | ~ ord_less_eq(int,sK3(X0),X2)
        | ord_less_eq(int,zero_zero(int),X2)
        | ~ preorder(int) )
    | ~ spl18_104
    | ~ spl18_196 ),
    inference(resolution,[],[f2574,f1279]) ).

tff(f1279,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( ~ ord_less_eq(X0,X3,X2)
        | ~ ord_less_eq(X0,X2,X1)
        | ord_less_eq(X0,X3,X1)
        | ~ preorder(X0) )
    | ~ spl18_104 ),
    inference(avatar_component_clause,[],[f1278]) ).

tff(f26849,plain,
    ( spl18_589
    | ~ spl18_184
    | ~ spl18_194 ),
    inference(avatar_split_clause,[],[f2641,f2564,f2416,f26847]) ).

tff(f26847,plain,
    ( spl18_589
  <=> ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ member(nat,zero_zero(nat),X0)
        | ( semiring_1_of_nat(int,sK8(X0)) = semiring_1_of_nat(int,sK1(semiring_1_of_nat(int,sK8(X0)))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_589])]) ).

tff(f2416,plain,
    ( spl18_184
  <=> ! [X0: nat] :
        ( ~ ord_less(nat,zero_zero(nat),X0)
        | ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,sK1(semiring_1_of_nat(int,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_184])]) ).

tff(f2641,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ member(nat,zero_zero(nat),X0)
        | ( semiring_1_of_nat(int,sK8(X0)) = semiring_1_of_nat(int,sK1(semiring_1_of_nat(int,sK8(X0)))) ) )
    | ~ spl18_184
    | ~ spl18_194 ),
    inference(resolution,[],[f2565,f2417]) ).

tff(f2417,plain,
    ( ! [X0: nat] :
        ( ~ ord_less(nat,zero_zero(nat),X0)
        | ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,sK1(semiring_1_of_nat(int,X0))) ) )
    | ~ spl18_184 ),
    inference(avatar_component_clause,[],[f2416]) ).

tff(f26845,plain,
    ( spl18_588
    | ~ spl18_95
    | ~ spl18_180 ),
    inference(avatar_split_clause,[],[f2399,f2362,f1215,f26843]) ).

tff(f26843,plain,
    ( spl18_588
  <=> ! [X5: nat,X4: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X0: nat,X3: nat,X2: fun(nat,fun(nat,bool)),X1: nat] :
        ( ~ sP0(X0,X1,X2)
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,huffma1280178957ee_rec(nat,bool,X2,X4,huffma2021818691e_Leaf(nat,X1,X0)),X5,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_588])]) ).

tff(f1215,plain,
    ( spl18_95
  <=> ! [X2: bool,X0: nat,X1: nat] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) )
        | pp(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_95])]) ).

tff(f2362,plain,
    ( spl18_180
  <=> ! [X0: fun(nat,fun(nat,bool)),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X2: nat,X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ~ sP0(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_180])]) ).

tff(f2399,plain,
    ( ! [X2: fun(nat,fun(nat,bool)),X3: nat,X0: nat,X1: nat,X4: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X5: nat] :
        ( ~ sP0(X0,X1,X2)
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,huffma1280178957ee_rec(nat,bool,X2,X4,huffma2021818691e_Leaf(nat,X1,X0)),X5,X3)) ) )
    | ~ spl18_95
    | ~ spl18_180 ),
    inference(resolution,[],[f2363,f1216]) ).

tff(f1216,plain,
    ( ! [X2: bool,X0: nat,X1: nat] :
        ( pp(X2)
        | ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) ) )
    | ~ spl18_95 ),
    inference(avatar_component_clause,[],[f1215]) ).

tff(f2363,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ~ sP0(X2,X1,X0) )
    | ~ spl18_180 ),
    inference(avatar_component_clause,[],[f2362]) ).

tff(f26841,plain,
    ( spl18_587
    | ~ spl18_95
    | ~ spl18_179 ),
    inference(avatar_split_clause,[],[f2387,f2358,f1215,f26839]) ).

tff(f26839,plain,
    ( spl18_587
  <=> ! [X5: nat,X4: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X0: nat,X3: nat,X2: fun(nat,fun(nat,bool)),X1: nat] :
        ( ~ sP0(X0,X1,X2)
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,huffma107959123e_case(nat,bool,X2,X4,huffma2021818691e_Leaf(nat,X1,X0)),X5,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_587])]) ).

tff(f2358,plain,
    ( spl18_179
  <=> ! [X0: fun(nat,fun(nat,bool)),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X2: nat,X1: nat] :
        ( ~ pp(huffma107959123e_case(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ~ sP0(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_179])]) ).

tff(f2387,plain,
    ( ! [X2: fun(nat,fun(nat,bool)),X3: nat,X0: nat,X1: nat,X4: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X5: nat] :
        ( ~ sP0(X0,X1,X2)
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,huffma107959123e_case(nat,bool,X2,X4,huffma2021818691e_Leaf(nat,X1,X0)),X5,X3)) ) )
    | ~ spl18_95
    | ~ spl18_179 ),
    inference(resolution,[],[f2359,f1216]) ).

tff(f2359,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( ~ pp(huffma107959123e_case(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ~ sP0(X2,X1,X0) )
    | ~ spl18_179 ),
    inference(avatar_component_clause,[],[f2358]) ).

tff(f26837,plain,
    ( spl18_586
    | ~ spl18_95
    | ~ spl18_177 ),
    inference(avatar_split_clause,[],[f2376,f2350,f1215,f26835]) ).

tff(f26835,plain,
    ( spl18_586
  <=> ! [X2: nat,X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,sK4(X0)))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,zero_zero(int)),X2,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_586])]) ).

tff(f2350,plain,
    ( spl18_177
  <=> ! [X0: fun(int,bool)] :
        ( ~ pp(aa(int,bool,X0,zero_zero(int)))
        | pp(aa(int,bool,X0,sK4(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_177])]) ).

tff(f2376,plain,
    ( ! [X2: nat,X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,sK4(X0)))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,zero_zero(int)),X2,X1)) ) )
    | ~ spl18_95
    | ~ spl18_177 ),
    inference(resolution,[],[f2351,f1216]) ).

tff(f2351,plain,
    ( ! [X0: fun(int,bool)] :
        ( ~ pp(aa(int,bool,X0,zero_zero(int)))
        | pp(aa(int,bool,X0,sK4(X0))) )
    | ~ spl18_177 ),
    inference(avatar_component_clause,[],[f2350]) ).

tff(f26820,plain,
    ( spl18_585
    | ~ spl18_112
    | ~ spl18_172 ),
    inference(avatar_split_clause,[],[f2296,f2232,f1479,f26818]) ).

tff(f26818,plain,
    ( spl18_585
  <=> ! [X0: huffma1450048681e_tree(int),X1: nat] :
        ( pp(aa(int,bool,huffma675207370phabet(int,X0),sK4(huffma675207370phabet(int,X0))))
        | ( zero_zero(nat) = aa(int,nat,huffma1352802255e_freq(int,X0),semiring_1_of_nat(int,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_585])]) ).

tff(f1479,plain,
    ( spl18_112
  <=> ! [X0: $tType,X2: X0,X1: huffma1450048681e_tree(X0)] :
        ( ( zero_zero(nat) = aa(X0,nat,huffma1352802255e_freq(X0,X1),X2) )
        | member(X0,X2,huffma675207370phabet(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_112])]) ).

tff(f2232,plain,
    ( spl18_172
  <=> ! [X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,sK4(X0)))
        | ~ member(int,semiring_1_of_nat(int,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_172])]) ).

tff(f2296,plain,
    ( ! [X0: huffma1450048681e_tree(int),X1: nat] :
        ( pp(aa(int,bool,huffma675207370phabet(int,X0),sK4(huffma675207370phabet(int,X0))))
        | ( zero_zero(nat) = aa(int,nat,huffma1352802255e_freq(int,X0),semiring_1_of_nat(int,X1)) ) )
    | ~ spl18_112
    | ~ spl18_172 ),
    inference(resolution,[],[f2233,f1480]) ).

tff(f1480,plain,
    ( ! [X0: $tType,X2: X0,X1: huffma1450048681e_tree(X0)] :
        ( member(X0,X2,huffma675207370phabet(X0,X1))
        | ( zero_zero(nat) = aa(X0,nat,huffma1352802255e_freq(X0,X1),X2) ) )
    | ~ spl18_112 ),
    inference(avatar_component_clause,[],[f1479]) ).

tff(f2233,plain,
    ( ! [X0: fun(int,bool),X1: nat] :
        ( ~ member(int,semiring_1_of_nat(int,X1),X0)
        | pp(aa(int,bool,X0,sK4(X0))) )
    | ~ spl18_172 ),
    inference(avatar_component_clause,[],[f2232]) ).

tff(f26816,plain,
    ( spl18_584
    | ~ spl18_112
    | ~ spl18_170 ),
    inference(avatar_split_clause,[],[f2279,f2224,f1479,f26814]) ).

tff(f26814,plain,
    ( spl18_584
  <=> ! [X0: huffma1450048681e_tree(int),X1: nat] :
        ( pp(aa(int,bool,huffma675207370phabet(int,X0),semiring_1_of_nat(int,X1)))
        | ( zero_zero(nat) = aa(int,nat,huffma1352802255e_freq(int,X0),sK3(huffma675207370phabet(int,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_584])]) ).

tff(f2224,plain,
    ( spl18_170
  <=> ! [X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,X1)))
        | ~ member(int,sK3(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_170])]) ).

tff(f2279,plain,
    ( ! [X0: huffma1450048681e_tree(int),X1: nat] :
        ( pp(aa(int,bool,huffma675207370phabet(int,X0),semiring_1_of_nat(int,X1)))
        | ( zero_zero(nat) = aa(int,nat,huffma1352802255e_freq(int,X0),sK3(huffma675207370phabet(int,X0))) ) )
    | ~ spl18_112
    | ~ spl18_170 ),
    inference(resolution,[],[f2225,f1480]) ).

tff(f2225,plain,
    ( ! [X0: fun(int,bool),X1: nat] :
        ( ~ member(int,sK3(X0),X0)
        | pp(aa(int,bool,X0,semiring_1_of_nat(int,X1))) )
    | ~ spl18_170 ),
    inference(avatar_component_clause,[],[f2224]) ).

tff(f26812,plain,
    ( spl18_583
    | ~ spl18_127
    | ~ spl18_169 ),
    inference(avatar_split_clause,[],[f2276,f2220,f1643,f26810]) ).

tff(f26810,plain,
    ( spl18_583
  <=> ! [X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ~ pp(huffma107959123e_case(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,zero_zero(int))))
        | ord_less_eq(int,zero_zero(int),sK4(aa(nat,fun(int,bool),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_583])]) ).

tff(f2220,plain,
    ( spl18_169
  <=> ! [X0: fun(int,bool)] :
        ( ~ pp(aa(int,bool,X0,zero_zero(int)))
        | ord_less_eq(int,zero_zero(int),sK4(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_169])]) ).

tff(f2276,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ~ pp(huffma107959123e_case(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,zero_zero(int))))
        | ord_less_eq(int,zero_zero(int),sK4(aa(nat,fun(int,bool),X0,X1))) )
    | ~ spl18_127
    | ~ spl18_169 ),
    inference(superposition,[],[f2221,f1644]) ).

tff(f2221,plain,
    ( ! [X0: fun(int,bool)] :
        ( ~ pp(aa(int,bool,X0,zero_zero(int)))
        | ord_less_eq(int,zero_zero(int),sK4(X0)) )
    | ~ spl18_169 ),
    inference(avatar_component_clause,[],[f2220]) ).

tff(f26808,plain,
    ( spl18_582
    | ~ spl18_128
    | ~ spl18_169 ),
    inference(avatar_split_clause,[],[f2275,f2220,f1647,f26806]) ).

tff(f26806,plain,
    ( spl18_582
  <=> ! [X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,zero_zero(int))))
        | ord_less_eq(int,zero_zero(int),sK4(aa(nat,fun(int,bool),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_582])]) ).

tff(f2275,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,zero_zero(int))))
        | ord_less_eq(int,zero_zero(int),sK4(aa(nat,fun(int,bool),X0,X1))) )
    | ~ spl18_128
    | ~ spl18_169 ),
    inference(superposition,[],[f2221,f1648]) ).

tff(f26804,plain,
    ( spl18_581
    | ~ spl18_127
    | ~ spl18_168 ),
    inference(avatar_split_clause,[],[f2265,f2216,f1643,f26802]) ).

tff(f26802,plain,
    ( spl18_581
  <=> ! [X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( pp(huffma107959123e_case(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,zero_zero(int))))
        | ord_less_eq(int,zero_zero(int),sK3(aa(nat,fun(int,bool),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_581])]) ).

tff(f2265,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( pp(huffma107959123e_case(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,zero_zero(int))))
        | ord_less_eq(int,zero_zero(int),sK3(aa(nat,fun(int,bool),X0,X1))) )
    | ~ spl18_127
    | ~ spl18_168 ),
    inference(superposition,[],[f2217,f1644]) ).

tff(f26800,plain,
    ( spl18_580
    | ~ spl18_128
    | ~ spl18_168 ),
    inference(avatar_split_clause,[],[f2264,f2216,f1647,f26798]) ).

tff(f26798,plain,
    ( spl18_580
  <=> ! [X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( pp(huffma1280178957ee_rec(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,zero_zero(int))))
        | ord_less_eq(int,zero_zero(int),sK3(aa(nat,fun(int,bool),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_580])]) ).

tff(f2264,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( pp(huffma1280178957ee_rec(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,zero_zero(int))))
        | ord_less_eq(int,zero_zero(int),sK3(aa(nat,fun(int,bool),X0,X1))) )
    | ~ spl18_128
    | ~ spl18_168 ),
    inference(superposition,[],[f2217,f1648]) ).

tff(f25648,plain,
    ( spl18_579
    | ~ spl18_22
    | ~ spl18_475 ),
    inference(avatar_split_clause,[],[f24068,f19591,f685,f25646]) ).

tff(f25646,plain,
    ( spl18_579
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: bool] :
        ( ( if(X0,X1,X2,X3) = X3 )
        | ( fTrue = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_579])]) ).

tff(f685,plain,
    ( spl18_22
  <=> pp(fTrue) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_22])]) ).

tff(f19591,plain,
    ( spl18_475
  <=> ! [X1: $tType,X4: X1,X0: bool,X3: X1,X2: bool] :
        ( ~ pp(X0)
        | ( if(X1,X2,X3,X4) = X4 )
        | ( X0 = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_475])]) ).

tff(f24068,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: bool] :
        ( ( if(X0,X1,X2,X3) = X3 )
        | ( fTrue = X1 ) )
    | ~ spl18_22
    | ~ spl18_475 ),
    inference(resolution,[],[f19592,f687]) ).

tff(f687,plain,
    ( pp(fTrue)
    | ~ spl18_22 ),
    inference(avatar_component_clause,[],[f685]) ).

tff(f19592,plain,
    ( ! [X1: $tType,X2: bool,X3: X1,X0: bool,X4: X1] :
        ( ~ pp(X0)
        | ( if(X1,X2,X3,X4) = X4 )
        | ( X0 = X2 ) )
    | ~ spl18_475 ),
    inference(avatar_component_clause,[],[f19591]) ).

tff(f23579,plain,
    ( spl18_578
    | ~ spl18_66
    | ~ spl18_243 ),
    inference(avatar_split_clause,[],[f3622,f3534,f902,f23577]) ).

tff(f23577,plain,
    ( spl18_578
  <=> ! [X0: nat,X3: nat,X2: nat,X1: fun(int,bool)] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(int,bool,X1,semiring_1_of_nat(int,X2)),X3,X0)) )
        | member(int,sK4(X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_578])]) ).

tff(f3534,plain,
    ( spl18_243
  <=> ! [X0: fun(int,bool),X3: nat,X2: nat,X1: nat] :
        ( pp(aa(int,bool,X0,sK4(X0)))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,semiring_1_of_nat(int,X2)),X3,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_243])]) ).

tff(f3622,plain,
    ( ! [X2: nat,X3: nat,X0: nat,X1: fun(int,bool)] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(int,bool,X1,semiring_1_of_nat(int,X2)),X3,X0)) )
        | member(int,sK4(X1),X1) )
    | ~ spl18_66
    | ~ spl18_243 ),
    inference(resolution,[],[f3535,f903]) ).

tff(f3535,plain,
    ( ! [X2: nat,X3: nat,X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,sK4(X0)))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,semiring_1_of_nat(int,X2)),X3,X1)) ) )
    | ~ spl18_243 ),
    inference(avatar_component_clause,[],[f3534]) ).

tff(f23575,plain,
    ( spl18_577
    | ~ spl18_66
    | ~ spl18_241 ),
    inference(avatar_split_clause,[],[f3608,f3514,f902,f23573]) ).

tff(f23573,plain,
    ( spl18_577
  <=> ! [X2: nat,X0: nat,X1: fun(int,bool),X3: nat] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(int,bool,X1,sK3(X1)),X2,X0)) )
        | member(int,semiring_1_of_nat(int,X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_577])]) ).

tff(f3608,plain,
    ( ! [X2: nat,X3: nat,X0: nat,X1: fun(int,bool)] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(int,bool,X1,sK3(X1)),X2,X0)) )
        | member(int,semiring_1_of_nat(int,X3),X1) )
    | ~ spl18_66
    | ~ spl18_241 ),
    inference(resolution,[],[f3515,f903]) ).

tff(f23571,plain,
    ( spl18_576
    | ~ spl18_107
    | ~ spl18_241 ),
    inference(avatar_split_clause,[],[f3605,f3514,f1290,f23569]) ).

tff(f23569,plain,
    ( spl18_576
  <=> ! [X2: nat,X0: nat,X1: fun(int,bool)] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(int,bool,X1,sK3(X1)),X2,X0)) )
        | ord_less_eq(int,zero_zero(int),sK4(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_576])]) ).

tff(f1290,plain,
    ( spl18_107
  <=> ! [X2: nat,X0: fun(int,bool)] :
        ( ord_less_eq(int,zero_zero(int),sK4(X0))
        | ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_107])]) ).

tff(f3605,plain,
    ( ! [X2: nat,X0: nat,X1: fun(int,bool)] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(int,bool,X1,sK3(X1)),X2,X0)) )
        | ord_less_eq(int,zero_zero(int),sK4(X1)) )
    | ~ spl18_107
    | ~ spl18_241 ),
    inference(resolution,[],[f3515,f1291]) ).

tff(f1291,plain,
    ( ! [X2: nat,X0: fun(int,bool)] :
        ( ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,X2)))
        | ord_less_eq(int,zero_zero(int),sK4(X0)) )
    | ~ spl18_107 ),
    inference(avatar_component_clause,[],[f1290]) ).

tff(f23567,plain,
    ( spl18_575
    | ~ spl18_44
    | ~ spl18_244 ),
    inference(avatar_split_clause,[],[f3543,f3538,f788,f23565]) ).

tff(f23565,plain,
    ( spl18_575
  <=> ! [X0: $tType,X4: fun(X0,nat),X3: nat,X2: X0,X1: fun(X0,nat)] :
        ( ord_less_eq(nat,aa(X0,nat,X1,X2),X3)
        | ~ ord_less_eq(fun(X0,nat),X1,X4)
        | ord_less_eq(nat,X3,aa(X0,nat,X4,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_575])]) ).

tff(f788,plain,
    ( spl18_44
  <=> ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ord_less_eq(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_44])]) ).

tff(f3543,plain,
    ( ! [X0: $tType,X2: X0,X3: nat,X1: fun(X0,nat),X4: fun(X0,nat)] :
        ( ord_less_eq(nat,aa(X0,nat,X1,X2),X3)
        | ~ ord_less_eq(fun(X0,nat),X1,X4)
        | ord_less_eq(nat,X3,aa(X0,nat,X4,X2)) )
    | ~ spl18_44
    | ~ spl18_244 ),
    inference(resolution,[],[f3539,f789]) ).

tff(f789,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ord_less_eq(nat,X1,X0) )
    | ~ spl18_44 ),
    inference(avatar_component_clause,[],[f788]) ).

tff(f23563,plain,
    ( spl18_574
    | ~ spl18_31
    | ~ spl18_211 ),
    inference(avatar_split_clause,[],[f2919,f2796,f725,f23561]) ).

tff(f23561,plain,
    ( spl18_574
  <=> ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X3: nat,X1: fun(nat,fun(X0,bool))] :
        ( ( fTrue = huffma107959123e_case(X0,bool,X1,X5,huffma2021818691e_Leaf(X0,X3,X4)) )
        | ( fFalse = huffma1280178957ee_rec(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_574])]) ).

tff(f2919,plain,
    ( ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X3: nat,X1: fun(nat,fun(X0,bool)),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)))] :
        ( ( fTrue = huffma107959123e_case(X0,bool,X1,X5,huffma2021818691e_Leaf(X0,X3,X4)) )
        | ( fFalse = huffma1280178957ee_rec(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) ) )
    | ~ spl18_31
    | ~ spl18_211 ),
    inference(superposition,[],[f2797,f726]) ).

tff(f23559,plain,
    ( spl18_573
    | ~ spl18_31
    | ~ spl18_211 ),
    inference(avatar_split_clause,[],[f2910,f2796,f725,f23557]) ).

tff(f23557,plain,
    ( spl18_573
  <=> ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X3: nat,X1: fun(nat,fun(X0,bool))] :
        ( ( fTrue = huffma1280178957ee_rec(X0,bool,X1,X5,huffma2021818691e_Leaf(X0,X3,X4)) )
        | ( fFalse = huffma107959123e_case(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_573])]) ).

tff(f2910,plain,
    ( ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X3: nat,X1: fun(nat,fun(X0,bool)),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))))] :
        ( ( fTrue = huffma1280178957ee_rec(X0,bool,X1,X5,huffma2021818691e_Leaf(X0,X3,X4)) )
        | ( fFalse = huffma107959123e_case(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) ) )
    | ~ spl18_31
    | ~ spl18_211 ),
    inference(superposition,[],[f2797,f726]) ).

tff(f23555,plain,
    ( spl18_572
    | ~ spl18_31
    | ~ spl18_210 ),
    inference(avatar_split_clause,[],[f2885,f2792,f725,f23553]) ).

tff(f23553,plain,
    ( spl18_572
  <=> ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X3: nat,X1: fun(nat,fun(X0,bool))] :
        ( ( fTrue = huffma1280178957ee_rec(X0,bool,X1,X5,huffma2021818691e_Leaf(X0,X3,X4)) )
        | ( fFalse = huffma1280178957ee_rec(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_572])]) ).

tff(f2885,plain,
    ( ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X3: nat,X1: fun(nat,fun(X0,bool)),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))))] :
        ( ( fTrue = huffma1280178957ee_rec(X0,bool,X1,X5,huffma2021818691e_Leaf(X0,X3,X4)) )
        | ( fFalse = huffma1280178957ee_rec(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) ) )
    | ~ spl18_31
    | ~ spl18_210 ),
    inference(superposition,[],[f2793,f726]) ).

tff(f23551,plain,
    ( spl18_571
    | ~ spl18_31
    | ~ spl18_209 ),
    inference(avatar_split_clause,[],[f2865,f2788,f725,f23549]) ).

tff(f23549,plain,
    ( spl18_571
  <=> ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X3: nat,X1: fun(nat,fun(X0,bool))] :
        ( ( fTrue = huffma107959123e_case(X0,bool,X1,X5,huffma2021818691e_Leaf(X0,X3,X4)) )
        | ( fFalse = huffma107959123e_case(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_571])]) ).

tff(f2865,plain,
    ( ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X3: nat,X1: fun(nat,fun(X0,bool)),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)))] :
        ( ( fTrue = huffma107959123e_case(X0,bool,X1,X5,huffma2021818691e_Leaf(X0,X3,X4)) )
        | ( fFalse = huffma107959123e_case(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) ) )
    | ~ spl18_31
    | ~ spl18_209 ),
    inference(superposition,[],[f2789,f726]) ).

tff(f23547,plain,
    ( spl18_570
    | ~ spl18_135
    | ~ spl18_205 ),
    inference(avatar_split_clause,[],[f2815,f2772,f1814,f23545]) ).

tff(f23545,plain,
    ( spl18_570
  <=> ! [X2: nat,X0: nat,X1: huffma1450048681e_tree(bool)] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(bool,bool,huffma675207370phabet(bool,X1),fTrue),X0,X2)) )
        | ( fFalse = sK14(bool,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_570])]) ).

tff(f1814,plain,
    ( spl18_135
  <=> ! [X0: huffma1450048681e_tree(bool)] :
        ( member(bool,fTrue,huffma675207370phabet(bool,X0))
        | ( fFalse = sK14(bool,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_135])]) ).

tff(f2815,plain,
    ( ! [X2: nat,X0: nat,X1: huffma1450048681e_tree(bool)] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(bool,bool,huffma675207370phabet(bool,X1),fTrue),X0,X2)) )
        | ( fFalse = sK14(bool,X1) ) )
    | ~ spl18_135
    | ~ spl18_205 ),
    inference(resolution,[],[f2773,f1815]) ).

tff(f1815,plain,
    ( ! [X0: huffma1450048681e_tree(bool)] :
        ( member(bool,fTrue,huffma675207370phabet(bool,X0))
        | ( fFalse = sK14(bool,X0) ) )
    | ~ spl18_135 ),
    inference(avatar_component_clause,[],[f1814]) ).

tff(f23496,plain,
    ( spl18_569
    | ~ spl18_73
    | ~ spl18_205 ),
    inference(avatar_split_clause,[],[f2807,f2772,f942,f23494]) ).

tff(f23494,plain,
    ( spl18_569
  <=> ! [X1: $tType,X0: nat,X3: nat,X2: huffma1450048681e_tree(X1)] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(X1,bool,huffma675207370phabet(X1,X2),sK6(X1,X2)),X0,X3)) )
        | ~ huffma1518433673istent(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_569])]) ).

tff(f942,plain,
    ( spl18_73
  <=> ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
        ( member(X0,sK6(X0,X1),huffma675207370phabet(X0,X1))
        | ~ huffma1518433673istent(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_73])]) ).

tff(f2807,plain,
    ( ! [X1: $tType,X2: huffma1450048681e_tree(X1),X3: nat,X0: nat] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(X1,bool,huffma675207370phabet(X1,X2),sK6(X1,X2)),X0,X3)) )
        | ~ huffma1518433673istent(X1,X2) )
    | ~ spl18_73
    | ~ spl18_205 ),
    inference(resolution,[],[f2773,f943]) ).

tff(f943,plain,
    ( ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
        ( member(X0,sK6(X0,X1),huffma675207370phabet(X0,X1))
        | ~ huffma1518433673istent(X0,X1) )
    | ~ spl18_73 ),
    inference(avatar_component_clause,[],[f942]) ).

tff(f23492,plain,
    ( spl18_568
    | ~ spl18_162
    | ~ spl18_200 ),
    inference(avatar_split_clause,[],[f2743,f2720,f2168,f23490]) ).

tff(f23490,plain,
    ( spl18_568
  <=> ! [X0: fun(int,bool),X1: int] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ member(int,X1,X0)
        | ( zero_zero(int) = X1 )
        | ord_less(int,X1,zero_zero(int)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_568])]) ).

tff(f2168,plain,
    ( spl18_162
  <=> ! [X0: int,X1: int] :
        ( ( X0 = X1 )
        | ord_less_eq(int,X0,X1)
        | ord_less(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_162])]) ).

tff(f2743,plain,
    ( ! [X0: fun(int,bool),X1: int] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ member(int,X1,X0)
        | ( zero_zero(int) = X1 )
        | ord_less(int,X1,zero_zero(int)) )
    | ~ spl18_162
    | ~ spl18_200 ),
    inference(resolution,[],[f2721,f2169]) ).

tff(f2169,plain,
    ( ! [X0: int,X1: int] :
        ( ord_less_eq(int,X0,X1)
        | ( X0 = X1 )
        | ord_less(int,X1,X0) )
    | ~ spl18_162 ),
    inference(avatar_component_clause,[],[f2168]) ).

tff(f23488,plain,
    ( spl18_567
    | ~ spl18_76
    | ~ spl18_196 ),
    inference(avatar_split_clause,[],[f2661,f2573,f954,f23486]) ).

tff(f23486,plain,
    ( spl18_567
  <=> ! [X0: fun(int,bool),X1: int] :
        ( pp(aa(int,bool,X0,X1))
        | ~ ord_less_eq(int,zero_zero(int),X1)
        | ( zero_zero(int) = sK3(X0) )
        | ord_less(int,zero_zero(int),sK3(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_567])]) ).

tff(f954,plain,
    ( spl18_76
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,X1,X0)
        | ( X0 = X1 )
        | ~ ord_less_eq(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_76])]) ).

tff(f2661,plain,
    ( ! [X0: fun(int,bool),X1: int] :
        ( pp(aa(int,bool,X0,X1))
        | ~ ord_less_eq(int,zero_zero(int),X1)
        | ( zero_zero(int) = sK3(X0) )
        | ord_less(int,zero_zero(int),sK3(X0)) )
    | ~ spl18_76
    | ~ spl18_196 ),
    inference(resolution,[],[f2574,f955]) ).

tff(f955,plain,
    ( ! [X0: int,X1: int] :
        ( ~ ord_less_eq(int,X1,X0)
        | ( X0 = X1 )
        | ord_less(int,X1,X0) )
    | ~ spl18_76 ),
    inference(avatar_component_clause,[],[f954]) ).

tff(f23484,plain,
    ( spl18_566
    | ~ spl18_74
    | ~ spl18_193 ),
    inference(avatar_split_clause,[],[f2620,f2560,f946,f23482]) ).

tff(f23482,plain,
    ( spl18_566
  <=> ! [X0: nat,X1: fun(nat,bool)] :
        ( pp(aa(nat,bool,X1,zero_zero(nat)))
        | ~ member(nat,X0,X1)
        | ( sK7(X0,X1) = X0 )
        | ord_less(nat,sK7(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_566])]) ).

tff(f946,plain,
    ( spl18_74
  <=> ! [X0: nat,X1: nat] :
        ( ord_less(nat,X1,X0)
        | ( X0 = X1 )
        | ~ ord_less_eq(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_74])]) ).

tff(f2620,plain,
    ( ! [X0: nat,X1: fun(nat,bool)] :
        ( pp(aa(nat,bool,X1,zero_zero(nat)))
        | ~ member(nat,X0,X1)
        | ( sK7(X0,X1) = X0 )
        | ord_less(nat,sK7(X0,X1),X0) )
    | ~ spl18_74
    | ~ spl18_193 ),
    inference(resolution,[],[f2561,f947]) ).

tff(f947,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X1,X0)
        | ( X0 = X1 )
        | ord_less(nat,X1,X0) )
    | ~ spl18_74 ),
    inference(avatar_component_clause,[],[f946]) ).

tff(f23480,plain,
    ( spl18_565
    | ~ spl18_75
    | ~ spl18_193 ),
    inference(avatar_split_clause,[],[f2619,f2560,f950,f23478]) ).

tff(f23478,plain,
    ( spl18_565
  <=> ! [X0: nat,X1: fun(nat,bool)] :
        ( pp(aa(nat,bool,X1,zero_zero(nat)))
        | ~ member(nat,X0,X1)
        | ~ ord_less_eq(nat,X0,sK7(X0,X1))
        | ( sK7(X0,X1) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_565])]) ).

tff(f950,plain,
    ( spl18_75
  <=> ! [X0: nat,X1: nat] :
        ( ( X0 = X1 )
        | ~ ord_less_eq(nat,X0,X1)
        | ~ ord_less_eq(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_75])]) ).

tff(f2619,plain,
    ( ! [X0: nat,X1: fun(nat,bool)] :
        ( pp(aa(nat,bool,X1,zero_zero(nat)))
        | ~ member(nat,X0,X1)
        | ~ ord_less_eq(nat,X0,sK7(X0,X1))
        | ( sK7(X0,X1) = X0 ) )
    | ~ spl18_75
    | ~ spl18_193 ),
    inference(resolution,[],[f2561,f951]) ).

tff(f951,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X1,X0)
        | ~ ord_less_eq(nat,X0,X1)
        | ( X0 = X1 ) )
    | ~ spl18_75 ),
    inference(avatar_component_clause,[],[f950]) ).

tff(f23476,plain,
    ( spl18_564
    | ~ spl18_120
    | ~ spl18_193 ),
    inference(avatar_split_clause,[],[f2611,f2560,f1539,f23474]) ).

tff(f23474,plain,
    ( spl18_564
  <=> ! [X2: nat,X0: fun(nat,bool),X1: nat] :
        ( ord_less_eq(nat,sK7(X1,X0),X1)
        | ~ member(nat,X1,X0)
        | ord_less(nat,zero_zero(nat),sK8(X0))
        | pp(aa(nat,bool,X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_564])]) ).

tff(f1539,plain,
    ( spl18_120
  <=> ! [X0: nat,X1: fun(nat,bool)] :
        ( pp(aa(nat,bool,X1,X0))
        | ord_less(nat,zero_zero(nat),sK8(X1))
        | ~ pp(aa(nat,bool,X1,zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_120])]) ).

tff(f2611,plain,
    ( ! [X2: nat,X0: fun(nat,bool),X1: nat] :
        ( ord_less_eq(nat,sK7(X1,X0),X1)
        | ~ member(nat,X1,X0)
        | ord_less(nat,zero_zero(nat),sK8(X0))
        | pp(aa(nat,bool,X0,X2)) )
    | ~ spl18_120
    | ~ spl18_193 ),
    inference(resolution,[],[f2561,f1540]) ).

tff(f1540,plain,
    ( ! [X0: nat,X1: fun(nat,bool)] :
        ( ~ pp(aa(nat,bool,X1,zero_zero(nat)))
        | ord_less(nat,zero_zero(nat),sK8(X1))
        | pp(aa(nat,bool,X1,X0)) )
    | ~ spl18_120 ),
    inference(avatar_component_clause,[],[f1539]) ).

tff(f23472,plain,
    ( spl18_563
    | ~ spl18_187
    | ~ spl18_188 ),
    inference(avatar_split_clause,[],[f2537,f2480,f2466,f23470]) ).

tff(f23470,plain,
    ( spl18_563
  <=> ! [X0: $tType,X3: nat,X2: nat,X1: X0] :
        ( ord_less_eq(X0,X1,semiring_1_of_nat(X0,X2))
        | ~ preorder(X0)
        | ord_less_eq(X0,semiring_1_of_nat(X0,X3),X1)
        | ~ linorder(X0)
        | ~ linordered_semidom(X0)
        | ord_less_eq(nat,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_563])]) ).

tff(f2466,plain,
    ( spl18_187
  <=> ! [X2: $tType,X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ~ linordered_semidom(X2)
        | ord_less_eq(X2,semiring_1_of_nat(X2,X1),semiring_1_of_nat(X2,X0))
        | ~ linorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_187])]) ).

tff(f2480,plain,
    ( spl18_188
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ~ ord_less_eq(X0,X1,X2)
        | ord_less_eq(X0,X3,X2)
        | ~ preorder(X0)
        | ord_less_eq(X0,X1,X3)
        | ~ linorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_188])]) ).

tff(f2537,plain,
    ( ! [X0: $tType,X2: nat,X3: nat,X1: X0] :
        ( ord_less_eq(X0,X1,semiring_1_of_nat(X0,X2))
        | ~ preorder(X0)
        | ord_less_eq(X0,semiring_1_of_nat(X0,X3),X1)
        | ~ linorder(X0)
        | ~ linordered_semidom(X0)
        | ord_less_eq(nat,X2,X3) )
    | ~ spl18_187
    | ~ spl18_188 ),
    inference(duplicate_literal_removal,[],[f2534]) ).

tff(f2534,plain,
    ( ! [X0: $tType,X2: nat,X3: nat,X1: X0] :
        ( ord_less_eq(X0,X1,semiring_1_of_nat(X0,X2))
        | ~ preorder(X0)
        | ord_less_eq(X0,semiring_1_of_nat(X0,X3),X1)
        | ~ linorder(X0)
        | ~ linordered_semidom(X0)
        | ord_less_eq(nat,X2,X3)
        | ~ linorder(X0) )
    | ~ spl18_187
    | ~ spl18_188 ),
    inference(resolution,[],[f2481,f2467]) ).

tff(f2467,plain,
    ( ! [X2: $tType,X0: nat,X1: nat] :
        ( ord_less_eq(X2,semiring_1_of_nat(X2,X1),semiring_1_of_nat(X2,X0))
        | ~ linordered_semidom(X2)
        | ord_less_eq(nat,X0,X1)
        | ~ linorder(X2) )
    | ~ spl18_187 ),
    inference(avatar_component_clause,[],[f2466]) ).

tff(f2481,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( ~ ord_less_eq(X0,X1,X2)
        | ord_less_eq(X0,X3,X2)
        | ~ preorder(X0)
        | ord_less_eq(X0,X1,X3)
        | ~ linorder(X0) )
    | ~ spl18_188 ),
    inference(avatar_component_clause,[],[f2480]) ).

tff(f23468,plain,
    ( spl18_562
    | ~ spl18_103
    | ~ spl18_188 ),
    inference(avatar_split_clause,[],[f2535,f2480,f1274,f23466]) ).

tff(f23466,plain,
    ( spl18_562
  <=> ! [X0: $tType,X3: nat,X2: nat,X1: X0] :
        ( ord_less_eq(X0,X1,semiring_1_of_nat(X0,X2))
        | ~ preorder(X0)
        | ord_less_eq(X0,semiring_1_of_nat(X0,X3),X1)
        | ~ linorder(X0)
        | ~ ord_less_eq(nat,X3,X2)
        | ~ linordered_semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_562])]) ).

tff(f1274,plain,
    ( spl18_103
  <=> ! [X0: $tType,X2: nat,X1: nat] :
        ( ord_less_eq(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
        | ~ ord_less_eq(nat,X2,X1)
        | ~ linordered_semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_103])]) ).

tff(f2535,plain,
    ( ! [X0: $tType,X2: nat,X3: nat,X1: X0] :
        ( ord_less_eq(X0,X1,semiring_1_of_nat(X0,X2))
        | ~ preorder(X0)
        | ord_less_eq(X0,semiring_1_of_nat(X0,X3),X1)
        | ~ linorder(X0)
        | ~ ord_less_eq(nat,X3,X2)
        | ~ linordered_semidom(X0) )
    | ~ spl18_103
    | ~ spl18_188 ),
    inference(resolution,[],[f2481,f1275]) ).

tff(f1275,plain,
    ( ! [X0: $tType,X2: nat,X1: nat] :
        ( ord_less_eq(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
        | ~ ord_less_eq(nat,X2,X1)
        | ~ linordered_semidom(X0) )
    | ~ spl18_103 ),
    inference(avatar_component_clause,[],[f1274]) ).

tff(f23464,plain,
    ( spl18_561
    | ~ spl18_104
    | ~ spl18_187 ),
    inference(avatar_split_clause,[],[f2492,f2466,f1278,f23462]) ).

tff(f23462,plain,
    ( spl18_561
  <=> ! [X0: $tType,X3: X0,X2: nat,X1: nat] :
        ( ~ linordered_semidom(X0)
        | ord_less_eq(nat,X1,X2)
        | ~ linorder(X0)
        | ~ ord_less_eq(X0,semiring_1_of_nat(X0,X1),X3)
        | ord_less_eq(X0,semiring_1_of_nat(X0,X2),X3)
        | ~ preorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_561])]) ).

tff(f2492,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: nat] :
        ( ~ linordered_semidom(X0)
        | ord_less_eq(nat,X1,X2)
        | ~ linorder(X0)
        | ~ ord_less_eq(X0,semiring_1_of_nat(X0,X1),X3)
        | ord_less_eq(X0,semiring_1_of_nat(X0,X2),X3)
        | ~ preorder(X0) )
    | ~ spl18_104
    | ~ spl18_187 ),
    inference(resolution,[],[f2467,f1279]) ).

tff(f23460,plain,
    ( spl18_560
    | ~ spl18_94
    | ~ spl18_171 ),
    inference(avatar_split_clause,[],[f2286,f2228,f1211,f23458]) ).

tff(f23458,plain,
    ( spl18_560
  <=> ! [X2: nat,X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,sK4(X0)),X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_560])]) ).

tff(f2228,plain,
    ( spl18_171
  <=> ! [X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,sK4(X0)))
        | ord_less_eq(int,zero_zero(int),sK3(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_171])]) ).

tff(f2286,plain,
    ( ! [X2: nat,X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,sK4(X0)),X1,X2)) ) )
    | ~ spl18_94
    | ~ spl18_171 ),
    inference(resolution,[],[f2229,f1212]) ).

tff(f2229,plain,
    ( ! [X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,sK4(X0)))
        | ord_less_eq(int,zero_zero(int),sK3(X0)) )
    | ~ spl18_171 ),
    inference(avatar_component_clause,[],[f2228]) ).

tff(f23456,plain,
    ( spl18_559
    | ~ spl18_432 ),
    inference(avatar_split_clause,[],[f15989,f12524,f23454]) ).

tff(f23454,plain,
    ( spl18_559
  <=> ! [X2: bool,X0: nat,X1: bool] :
        ( ( fFalse != X2 )
        | ( fFalse = huffma1401021291ibling(bool,huffma2021818691e_Leaf(bool,X0,X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_559])]) ).

tff(f12524,plain,
    ( spl18_432
  <=> ! [X2: bool,X0: nat,X1: bool,X3: bool] :
        ( ( X2 = X3 )
        | ( fFalse = X3 )
        | ( fFalse = huffma1401021291ibling(bool,huffma2021818691e_Leaf(bool,X0,X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_432])]) ).

tff(f15989,plain,
    ( ! [X2: bool,X0: nat,X1: bool] :
        ( ( fFalse != X2 )
        | ( fFalse = huffma1401021291ibling(bool,huffma2021818691e_Leaf(bool,X0,X1),X2) ) )
    | ~ spl18_432 ),
    inference(duplicate_literal_removal,[],[f15980]) ).

tff(f15980,plain,
    ( ! [X2: bool,X0: nat,X1: bool] :
        ( ( fFalse != X2 )
        | ( fFalse = huffma1401021291ibling(bool,huffma2021818691e_Leaf(bool,X0,X1),X2) )
        | ( fFalse = huffma1401021291ibling(bool,huffma2021818691e_Leaf(bool,X0,X1),X2) ) )
    | ~ spl18_432 ),
    inference(equality_factoring,[],[f12525]) ).

tff(f12525,plain,
    ( ! [X2: bool,X3: bool,X0: nat,X1: bool] :
        ( ( X2 = X3 )
        | ( fFalse = X3 )
        | ( fFalse = huffma1401021291ibling(bool,huffma2021818691e_Leaf(bool,X0,X1),X2) ) )
    | ~ spl18_432 ),
    inference(avatar_component_clause,[],[f12524]) ).

tff(f23452,plain,
    ( spl18_558
    | ~ spl18_88
    | ~ spl18_170 ),
    inference(avatar_split_clause,[],[f2280,f2224,f1044,f23450]) ).

tff(f23450,plain,
    ( spl18_558
  <=> ! [X0: huffma1450048681e_tree(int),X1: nat] :
        ( pp(aa(int,bool,huffma675207370phabet(int,X0),semiring_1_of_nat(int,X1)))
        | ( sK3(huffma675207370phabet(int,X0)) = huffma1401021291ibling(int,X0,sK3(huffma675207370phabet(int,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_558])]) ).

tff(f2280,plain,
    ( ! [X0: huffma1450048681e_tree(int),X1: nat] :
        ( pp(aa(int,bool,huffma675207370phabet(int,X0),semiring_1_of_nat(int,X1)))
        | ( sK3(huffma675207370phabet(int,X0)) = huffma1401021291ibling(int,X0,sK3(huffma675207370phabet(int,X0))) ) )
    | ~ spl18_88
    | ~ spl18_170 ),
    inference(resolution,[],[f2225,f1045]) ).

tff(f23448,plain,
    ( spl18_557
    | ~ spl18_95
    | ~ spl18_169 ),
    inference(avatar_split_clause,[],[f2268,f2220,f1215,f23446]) ).

tff(f23446,plain,
    ( spl18_557
  <=> ! [X2: nat,X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK4(X0))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,zero_zero(int)),X2,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_557])]) ).

tff(f2268,plain,
    ( ! [X2: nat,X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK4(X0))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,zero_zero(int)),X2,X1)) ) )
    | ~ spl18_95
    | ~ spl18_169 ),
    inference(resolution,[],[f2221,f1216]) ).

tff(f23444,plain,
    ( spl18_556
    | ~ spl18_94
    | ~ spl18_168 ),
    inference(avatar_split_clause,[],[f2258,f2216,f1211,f23442]) ).

tff(f23442,plain,
    ( spl18_556
  <=> ! [X2: nat,X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,zero_zero(int)),X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_556])]) ).

tff(f2258,plain,
    ( ! [X2: nat,X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,zero_zero(int)),X1,X2)) ) )
    | ~ spl18_94
    | ~ spl18_168 ),
    inference(resolution,[],[f2217,f1212]) ).

tff(f23440,plain,
    ( spl18_555
    | ~ spl18_132
    | ~ spl18_135 ),
    inference(avatar_split_clause,[],[f1961,f1814,f1770,f23438]) ).

tff(f23438,plain,
    ( spl18_555
  <=> ! [X4: huffma1450048681e_tree(bool),X0: huffma1450048681e_tree(bool),X3: huffma1450048681e_tree(bool),X2: nat,X1: nat] :
        ( ( fFalse = sK14(bool,X0) )
        | ( huffma1401021291ibling(bool,X0,fTrue) = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X1,X0,huffma1146269203erNode(bool,X2,X3,X4)),fTrue) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_555])]) ).

tff(f1961,plain,
    ( ! [X2: nat,X3: huffma1450048681e_tree(bool),X0: huffma1450048681e_tree(bool),X1: nat,X4: huffma1450048681e_tree(bool)] :
        ( ( fFalse = sK14(bool,X0) )
        | ( huffma1401021291ibling(bool,X0,fTrue) = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X1,X0,huffma1146269203erNode(bool,X2,X3,X4)),fTrue) ) )
    | ~ spl18_132
    | ~ spl18_135 ),
    inference(resolution,[],[f1815,f1771]) ).

tff(f23436,plain,
    ( spl18_554
    | ~ spl18_81
    | ~ spl18_118 ),
    inference(avatar_split_clause,[],[f1520,f1503,f1016,f23434]) ).

tff(f23434,plain,
    ( spl18_554
  <=> ! [X3: nat,X4: bool,X0: nat,X5: bool,X2: bool,X1: nat] :
        ( ( X4 = X5 )
        | ( fFalse = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X0,huffma2021818691e_Leaf(bool,X1,X2),huffma2021818691e_Leaf(bool,X3,X4)),X2) )
        | ( fFalse = X5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_554])]) ).

tff(f1503,plain,
    ( spl18_118
  <=> ! [X0: $tType,X3: nat,X4: nat,X6: X0,X2: nat,X1: X0] : ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,huffma2021818691e_Leaf(X0,X3,X6),huffma2021818691e_Leaf(X0,X2,X1)),X6) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_118])]) ).

tff(f1520,plain,
    ( ! [X2: bool,X3: nat,X0: nat,X1: nat,X4: bool,X5: bool] :
        ( ( X4 = X5 )
        | ( fFalse = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X0,huffma2021818691e_Leaf(bool,X1,X2),huffma2021818691e_Leaf(bool,X3,X4)),X2) )
        | ( fFalse = X5 ) )
    | ~ spl18_81
    | ~ spl18_118 ),
    inference(superposition,[],[f1504,f1017]) ).

tff(f1504,plain,
    ( ! [X0: $tType,X2: nat,X3: nat,X1: X0,X6: X0,X4: nat] : ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,huffma2021818691e_Leaf(X0,X3,X6),huffma2021818691e_Leaf(X0,X2,X1)),X6) = X1 )
    | ~ spl18_118 ),
    inference(avatar_component_clause,[],[f1503]) ).

tff(f23432,plain,
    ( spl18_553
    | ~ spl18_81
    | ~ spl18_118 ),
    inference(avatar_split_clause,[],[f1518,f1503,f1016,f23430]) ).

tff(f23430,plain,
    ( spl18_553
  <=> ! [X3: nat,X4: bool,X0: nat,X5: bool,X2: bool,X1: nat] :
        ( ( fFalse = X4 )
        | ( huffma1401021291ibling(bool,huffma1146269203erNode(bool,X0,huffma2021818691e_Leaf(bool,X1,X2),huffma2021818691e_Leaf(bool,X3,X4)),X2) = X5 )
        | ( fFalse = X5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_553])]) ).

tff(f1518,plain,
    ( ! [X2: bool,X3: nat,X0: nat,X1: nat,X4: bool,X5: bool] :
        ( ( fFalse = X4 )
        | ( huffma1401021291ibling(bool,huffma1146269203erNode(bool,X0,huffma2021818691e_Leaf(bool,X1,X2),huffma2021818691e_Leaf(bool,X3,X4)),X2) = X5 )
        | ( fFalse = X5 ) )
    | ~ spl18_81
    | ~ spl18_118 ),
    inference(superposition,[],[f1504,f1017]) ).

tff(f22766,plain,
    ( spl18_552
    | ~ spl18_31
    | ~ spl18_534 ),
    inference(avatar_split_clause,[],[f22634,f22540,f725,f22764]) ).

tff(f22764,plain,
    ( spl18_552
  <=> ! [X0: nat,X1: bool] :
        ( ( fTrue = X1 )
        | ( fFalse = sK13(bool,huffma2021818691e_Leaf(bool,X0,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_552])]) ).

tff(f22540,plain,
    ( spl18_534
  <=> ! [X0: $tType,X2: X0,X1: nat] : ( sK13(X0,huffma2021818691e_Leaf(X0,X1,X2)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_534])]) ).

tff(f22634,plain,
    ( ! [X0: nat,X1: bool] :
        ( ( fTrue = X1 )
        | ( fFalse = sK13(bool,huffma2021818691e_Leaf(bool,X0,X1)) ) )
    | ~ spl18_31
    | ~ spl18_534 ),
    inference(superposition,[],[f22541,f726]) ).

tff(f22541,plain,
    ( ! [X0: $tType,X2: X0,X1: nat] : ( sK13(X0,huffma2021818691e_Leaf(X0,X1,X2)) = X2 )
    | ~ spl18_534 ),
    inference(avatar_component_clause,[],[f22540]) ).

tff(f22701,plain,
    ( spl18_551
    | ~ spl18_32
    | ~ spl18_256 ),
    inference(avatar_split_clause,[],[f4107,f4103,f729,f22699]) ).

tff(f22699,plain,
    ( spl18_551
  <=> ! [X2: $tType,X0: X2,X3: nat,X1: X2] :
        ( ( X0 = X1 )
        | ord_less_eq(nat,aa(X2,nat,huffma1352802255e_freq(X2,huffma2021818691e_Leaf(X2,X3,X0)),X1),zero_zero(nat))
        | ~ preorder(fun(X2,nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_551])]) ).

tff(f729,plain,
    ( spl18_32
  <=> ! [X0: $tType,X1: X0] :
        ( ord_less_eq(X0,X1,X1)
        | ~ preorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_32])]) ).

tff(f4103,plain,
    ( spl18_256
  <=> ! [X0: $tType,X4: fun(X0,nat),X3: X0,X2: X0,X1: nat] :
        ( ord_less_eq(nat,aa(X0,nat,X4,X3),zero_zero(nat))
        | ( X2 = X3 )
        | ~ ord_less_eq(fun(X0,nat),X4,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_256])]) ).

tff(f4107,plain,
    ( ! [X2: $tType,X3: nat,X0: X2,X1: X2] :
        ( ( X0 = X1 )
        | ord_less_eq(nat,aa(X2,nat,huffma1352802255e_freq(X2,huffma2021818691e_Leaf(X2,X3,X0)),X1),zero_zero(nat))
        | ~ preorder(fun(X2,nat)) )
    | ~ spl18_32
    | ~ spl18_256 ),
    inference(resolution,[],[f4104,f730]) ).

tff(f730,plain,
    ( ! [X0: $tType,X1: X0] :
        ( ord_less_eq(X0,X1,X1)
        | ~ preorder(X0) )
    | ~ spl18_32 ),
    inference(avatar_component_clause,[],[f729]) ).

tff(f4104,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: nat,X4: fun(X0,nat)] :
        ( ~ ord_less_eq(fun(X0,nat),X4,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)))
        | ( X2 = X3 )
        | ord_less_eq(nat,aa(X0,nat,X4,X3),zero_zero(nat)) )
    | ~ spl18_256 ),
    inference(avatar_component_clause,[],[f4103]) ).

tff(f22697,plain,
    ( spl18_550
    | ~ spl18_69
    | ~ spl18_256 ),
    inference(avatar_split_clause,[],[f4106,f4103,f926,f22695]) ).

tff(f22695,plain,
    ( spl18_550
  <=> ! [X2: $tType,X0: X2,X3: nat,X1: X2] :
        ( ( X0 = X1 )
        | ord_less_eq(nat,aa(X2,nat,huffma1352802255e_freq(X2,huffma2021818691e_Leaf(X2,X3,X0)),X1),zero_zero(nat))
        | ~ linorder(fun(X2,nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_550])]) ).

tff(f926,plain,
    ( spl18_69
  <=> ! [X0: $tType,X1: X0] :
        ( ord_less_eq(X0,X1,X1)
        | ~ linorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_69])]) ).

tff(f4106,plain,
    ( ! [X2: $tType,X3: nat,X0: X2,X1: X2] :
        ( ( X0 = X1 )
        | ord_less_eq(nat,aa(X2,nat,huffma1352802255e_freq(X2,huffma2021818691e_Leaf(X2,X3,X0)),X1),zero_zero(nat))
        | ~ linorder(fun(X2,nat)) )
    | ~ spl18_69
    | ~ spl18_256 ),
    inference(resolution,[],[f4104,f927]) ).

tff(f927,plain,
    ( ! [X0: $tType,X1: X0] :
        ( ord_less_eq(X0,X1,X1)
        | ~ linorder(X0) )
    | ~ spl18_69 ),
    inference(avatar_component_clause,[],[f926]) ).

tff(f22693,plain,
    ( spl18_549
    | ~ spl18_65
    | ~ spl18_240 ),
    inference(avatar_split_clause,[],[f3502,f3410,f896,f22691]) ).

tff(f22691,plain,
    ( spl18_549
  <=> ! [X2: fun(nat,bool),X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,sK7(X1,X2))
        | pp(aa(nat,bool,X2,zero_zero(nat)))
        | ~ member(nat,X0,X2)
        | ~ member(nat,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_549])]) ).

tff(f3502,plain,
    ( ! [X2: fun(nat,bool),X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,sK7(X1,X2))
        | pp(aa(nat,bool,X2,zero_zero(nat)))
        | ~ member(nat,X0,X2)
        | ~ member(nat,X1,X2) )
    | ~ spl18_65
    | ~ spl18_240 ),
    inference(resolution,[],[f3411,f897]) ).

tff(f22689,plain,
    ( spl18_548
    | ~ spl18_37
    | ~ spl18_215 ),
    inference(avatar_split_clause,[],[f2997,f2943,f752,f22687]) ).

tff(f22687,plain,
    ( spl18_548
  <=> ! [X0: $tType,X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X3: nat,X2: fun(nat,fun(X0,bool)),X1: X0] :
        ( member(X0,X1,aa(nat,fun(X0,bool),X2,X3))
        | ( fFalse = huffma1280178957ee_rec(X0,bool,X2,X4,huffma2021818691e_Leaf(X0,X3,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_548])]) ).

tff(f2943,plain,
    ( spl18_215
  <=> ! [X0: $tType,X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X3: X0,X2: nat,X1: fun(nat,fun(X0,bool))] :
        ( ~ pp(huffma1280178957ee_rec(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)))
        | member(X0,X3,aa(nat,fun(X0,bool),X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_215])]) ).

tff(f2997,plain,
    ( ! [X0: $tType,X2: fun(nat,fun(X0,bool)),X3: nat,X1: X0,X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))))] :
        ( member(X0,X1,aa(nat,fun(X0,bool),X2,X3))
        | ( fFalse = huffma1280178957ee_rec(X0,bool,X2,X4,huffma2021818691e_Leaf(X0,X3,X1)) ) )
    | ~ spl18_37
    | ~ spl18_215 ),
    inference(resolution,[],[f2944,f753]) ).

tff(f2944,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: fun(nat,fun(X0,bool)),X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))))] :
        ( ~ pp(huffma1280178957ee_rec(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)))
        | member(X0,X3,aa(nat,fun(X0,bool),X1,X2)) )
    | ~ spl18_215 ),
    inference(avatar_component_clause,[],[f2943]) ).

tff(f22685,plain,
    ( spl18_547
    | ~ spl18_37
    | ~ spl18_213 ),
    inference(avatar_split_clause,[],[f2982,f2935,f752,f22683]) ).

tff(f22683,plain,
    ( spl18_547
  <=> ! [X0: $tType,X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X3: nat,X2: fun(nat,fun(X0,bool)),X1: X0] :
        ( member(X0,X1,aa(nat,fun(X0,bool),X2,X3))
        | ( fFalse = huffma107959123e_case(X0,bool,X2,X4,huffma2021818691e_Leaf(X0,X3,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_547])]) ).

tff(f2935,plain,
    ( spl18_213
  <=> ! [X0: $tType,X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X3: X0,X2: nat,X1: fun(nat,fun(X0,bool))] :
        ( ~ pp(huffma107959123e_case(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)))
        | member(X0,X3,aa(nat,fun(X0,bool),X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_213])]) ).

tff(f2982,plain,
    ( ! [X0: $tType,X2: fun(nat,fun(X0,bool)),X3: nat,X1: X0,X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)))] :
        ( member(X0,X1,aa(nat,fun(X0,bool),X2,X3))
        | ( fFalse = huffma107959123e_case(X0,bool,X2,X4,huffma2021818691e_Leaf(X0,X3,X1)) ) )
    | ~ spl18_37
    | ~ spl18_213 ),
    inference(resolution,[],[f2936,f753]) ).

tff(f2936,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: fun(nat,fun(X0,bool)),X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)))] :
        ( ~ pp(huffma107959123e_case(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)))
        | member(X0,X3,aa(nat,fun(X0,bool),X1,X2)) )
    | ~ spl18_213 ),
    inference(avatar_component_clause,[],[f2935]) ).

tff(f22681,plain,
    ( spl18_546
    | ~ spl18_126
    | ~ spl18_208 ),
    inference(avatar_split_clause,[],[f2857,f2784,f1639,f22679]) ).

tff(f22679,plain,
    ( spl18_546
  <=> ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,zero_zero(nat)))
        | member(nat,sK7(sK7(X1,X0),X0),X0)
        | ~ pp(aa(nat,bool,X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_546])]) ).

tff(f2784,plain,
    ( spl18_208
  <=> ! [X0: fun(nat,bool),X1: nat] :
        ( ~ pp(aa(nat,bool,X0,X1))
        | pp(aa(nat,bool,X0,zero_zero(nat)))
        | member(nat,sK7(X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_208])]) ).

tff(f2857,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,zero_zero(nat)))
        | member(nat,sK7(sK7(X1,X0),X0),X0)
        | ~ pp(aa(nat,bool,X0,X1)) )
    | ~ spl18_126
    | ~ spl18_208 ),
    inference(duplicate_literal_removal,[],[f2843]) ).

tff(f2843,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,zero_zero(nat)))
        | member(nat,sK7(sK7(X1,X0),X0),X0)
        | ~ pp(aa(nat,bool,X0,X1))
        | pp(aa(nat,bool,X0,zero_zero(nat))) )
    | ~ spl18_126
    | ~ spl18_208 ),
    inference(resolution,[],[f2785,f1640]) ).

tff(f2785,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( ~ pp(aa(nat,bool,X0,X1))
        | pp(aa(nat,bool,X0,zero_zero(nat)))
        | member(nat,sK7(X1,X0),X0) )
    | ~ spl18_208 ),
    inference(avatar_component_clause,[],[f2784]) ).

tff(f22677,plain,
    ( spl18_545
    | ~ spl18_193
    | ~ spl18_201 ),
    inference(avatar_split_clause,[],[f2749,f2724,f2560,f22675]) ).

tff(f22675,plain,
    ( spl18_545
  <=> ! [X2: nat,X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ member(nat,sK8(X0),X0)
        | ord_less_eq(nat,sK7(X2,X0),X2)
        | ~ member(nat,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_545])]) ).

tff(f2724,plain,
    ( spl18_201
  <=> ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ pp(aa(nat,bool,X0,zero_zero(nat)))
        | ~ member(nat,sK8(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_201])]) ).

tff(f2749,plain,
    ( ! [X2: nat,X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ member(nat,sK8(X0),X0)
        | ord_less_eq(nat,sK7(X2,X0),X2)
        | ~ member(nat,X2,X0) )
    | ~ spl18_193
    | ~ spl18_201 ),
    inference(resolution,[],[f2725,f2561]) ).

tff(f2725,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( ~ pp(aa(nat,bool,X0,zero_zero(nat)))
        | pp(aa(nat,bool,X0,X1))
        | ~ member(nat,sK8(X0),X0) )
    | ~ spl18_201 ),
    inference(avatar_component_clause,[],[f2724]) ).

tff(f22673,plain,
    ( spl18_544
    | ~ spl18_162
    | ~ spl18_198 ),
    inference(avatar_split_clause,[],[f2707,f2691,f2168,f22671]) ).

tff(f22671,plain,
    ( spl18_544
  <=> ! [X2: int,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less_eq(int,semiring_1_of_nat(int,X0),X2)
        | ( semiring_1_of_nat(int,X1) = X2 )
        | ord_less(int,X2,semiring_1_of_nat(int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_544])]) ).

tff(f2691,plain,
    ( spl18_198
  <=> ! [X2: nat,X0: nat,X1: int] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X0),X1)
        | ~ ord_less_eq(nat,X2,X0)
        | ord_less_eq(int,semiring_1_of_nat(int,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_198])]) ).

tff(f2707,plain,
    ( ! [X2: int,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less_eq(int,semiring_1_of_nat(int,X0),X2)
        | ( semiring_1_of_nat(int,X1) = X2 )
        | ord_less(int,X2,semiring_1_of_nat(int,X1)) )
    | ~ spl18_162
    | ~ spl18_198 ),
    inference(resolution,[],[f2692,f2169]) ).

tff(f2692,plain,
    ( ! [X2: nat,X0: nat,X1: int] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X0),X1)
        | ~ ord_less_eq(nat,X2,X0)
        | ord_less_eq(int,semiring_1_of_nat(int,X2),X1) )
    | ~ spl18_198 ),
    inference(avatar_component_clause,[],[f2691]) ).

tff(f22669,plain,
    ( spl18_543
    | ~ spl18_142
    | ~ spl18_197 ),
    inference(avatar_split_clause,[],[f2678,f2674,f1885,f22667]) ).

tff(f22667,plain,
    ( spl18_543
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,semiring_1_of_nat(nat,X0),X1)
        | ~ ord_less_eq(nat,X0,X2)
        | ( semiring_1_of_nat(nat,X2) = X1 )
        | ord_less(nat,X1,semiring_1_of_nat(nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_543])]) ).

tff(f1885,plain,
    ( spl18_142
  <=> ! [X0: nat,X1: nat] :
        ( ord_less(nat,X1,X0)
        | ( X0 = X1 )
        | ord_less_eq(nat,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_142])]) ).

tff(f2674,plain,
    ( spl18_197
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less_eq(nat,semiring_1_of_nat(nat,X0),X2)
        | ~ ord_less_eq(nat,semiring_1_of_nat(nat,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_197])]) ).

tff(f2678,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,semiring_1_of_nat(nat,X0),X1)
        | ~ ord_less_eq(nat,X0,X2)
        | ( semiring_1_of_nat(nat,X2) = X1 )
        | ord_less(nat,X1,semiring_1_of_nat(nat,X2)) )
    | ~ spl18_142
    | ~ spl18_197 ),
    inference(resolution,[],[f2675,f1886]) ).

tff(f1886,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ( X0 = X1 )
        | ord_less(nat,X1,X0) )
    | ~ spl18_142 ),
    inference(avatar_component_clause,[],[f1885]) ).

tff(f2675,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,semiring_1_of_nat(nat,X1),X2)
        | ord_less_eq(nat,semiring_1_of_nat(nat,X0),X2)
        | ~ ord_less_eq(nat,X0,X1) )
    | ~ spl18_197 ),
    inference(avatar_component_clause,[],[f2674]) ).

tff(f22633,plain,
    ( spl18_542
    | ~ spl18_87
    | ~ spl18_193 ),
    inference(avatar_split_clause,[],[f2618,f2560,f1040,f22631]) ).

tff(f22631,plain,
    ( spl18_542
  <=> ! [X2: nat,X0: nat,X1: fun(nat,bool)] :
        ( pp(aa(nat,bool,X1,zero_zero(nat)))
        | ~ member(nat,X0,X1)
        | ~ ord_less_eq(nat,X0,X2)
        | ord_less_eq(nat,sK7(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_542])]) ).

tff(f1040,plain,
    ( spl18_87
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,X2,X0)
        | ~ ord_less_eq(nat,X1,X0)
        | ~ ord_less_eq(nat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_87])]) ).

tff(f2618,plain,
    ( ! [X2: nat,X0: nat,X1: fun(nat,bool)] :
        ( pp(aa(nat,bool,X1,zero_zero(nat)))
        | ~ member(nat,X0,X1)
        | ~ ord_less_eq(nat,X0,X2)
        | ord_less_eq(nat,sK7(X0,X1),X2) )
    | ~ spl18_87
    | ~ spl18_193 ),
    inference(resolution,[],[f2561,f1041]) ).

tff(f1041,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X2,X1)
        | ~ ord_less_eq(nat,X1,X0)
        | ord_less_eq(nat,X2,X0) )
    | ~ spl18_87 ),
    inference(avatar_component_clause,[],[f1040]) ).

tff(f22629,plain,
    ( spl18_541
    | ~ spl18_156
    | ~ spl18_193 ),
    inference(avatar_split_clause,[],[f2617,f2560,f2078,f22627]) ).

tff(f22627,plain,
    ( spl18_541
  <=> ! [X2: nat,X0: nat,X1: fun(nat,bool)] :
        ( pp(aa(nat,bool,X1,zero_zero(nat)))
        | ~ member(nat,X0,X1)
        | ord_less_eq(nat,X2,X0)
        | ord_less_eq(nat,sK7(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_541])]) ).

tff(f2617,plain,
    ( ! [X2: nat,X0: nat,X1: fun(nat,bool)] :
        ( pp(aa(nat,bool,X1,zero_zero(nat)))
        | ~ member(nat,X0,X1)
        | ord_less_eq(nat,X2,X0)
        | ord_less_eq(nat,sK7(X0,X1),X2) )
    | ~ spl18_156
    | ~ spl18_193 ),
    inference(resolution,[],[f2561,f2079]) ).

tff(f22606,plain,
    ( ~ spl18_9
    | spl18_540
    | ~ spl18_99
    | ~ spl18_184 ),
    inference(avatar_split_clause,[],[f2439,f2416,f1258,f22604,f620]) ).

tff(f620,plain,
    ( spl18_9
  <=> linordered_semidom(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_9])]) ).

tff(f22604,plain,
    ( spl18_540
  <=> ! [X0: nat] :
        ( ( semiring_1_of_nat(int,semiring_1_of_nat(nat,X0)) = semiring_1_of_nat(int,sK1(semiring_1_of_nat(int,semiring_1_of_nat(nat,X0)))) )
        | ~ ord_less(nat,zero_zero(nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_540])]) ).

tff(f1258,plain,
    ( spl18_99
  <=> ! [X0: $tType,X1: nat] :
        ( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
        | ~ ord_less(nat,zero_zero(nat),X1)
        | ~ linordered_semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_99])]) ).

tff(f2439,plain,
    ( ! [X0: nat] :
        ( ( semiring_1_of_nat(int,semiring_1_of_nat(nat,X0)) = semiring_1_of_nat(int,sK1(semiring_1_of_nat(int,semiring_1_of_nat(nat,X0)))) )
        | ~ ord_less(nat,zero_zero(nat),X0)
        | ~ linordered_semidom(nat) )
    | ~ spl18_99
    | ~ spl18_184 ),
    inference(resolution,[],[f2417,f1259]) ).

tff(f1259,plain,
    ( ! [X0: $tType,X1: nat] :
        ( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
        | ~ ord_less(nat,zero_zero(nat),X1)
        | ~ linordered_semidom(X0) )
    | ~ spl18_99 ),
    inference(avatar_component_clause,[],[f1258]) ).

tff(f22602,plain,
    ( spl18_539
    | ~ spl18_88
    | ~ spl18_172 ),
    inference(avatar_split_clause,[],[f2297,f2232,f1044,f22600]) ).

tff(f22600,plain,
    ( spl18_539
  <=> ! [X0: huffma1450048681e_tree(int),X1: nat] :
        ( pp(aa(int,bool,huffma675207370phabet(int,X0),sK4(huffma675207370phabet(int,X0))))
        | ( semiring_1_of_nat(int,X1) = huffma1401021291ibling(int,X0,semiring_1_of_nat(int,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_539])]) ).

tff(f2297,plain,
    ( ! [X0: huffma1450048681e_tree(int),X1: nat] :
        ( pp(aa(int,bool,huffma675207370phabet(int,X0),sK4(huffma675207370phabet(int,X0))))
        | ( semiring_1_of_nat(int,X1) = huffma1401021291ibling(int,X0,semiring_1_of_nat(int,X1)) ) )
    | ~ spl18_88
    | ~ spl18_172 ),
    inference(resolution,[],[f2233,f1045]) ).

tff(f22558,plain,
    ( ~ spl18_16
    | spl18_538
    | ~ spl18_92
    | ~ spl18_152 ),
    inference(avatar_split_clause,[],[f2104,f2052,f1203,f22556,f655]) ).

tff(f22556,plain,
    ( spl18_538
  <=> ! [X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,X1)
        | ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
        | ~ ord_less_eq(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_538])]) ).

tff(f2052,plain,
    ( spl18_152
  <=> ! [X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,X1)
        | ord_less_eq(int,semiring_1_of_nat(int,X0),semiring_1_of_nat(int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_152])]) ).

tff(f2104,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,X1)
        | ~ ord_less_eq(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
        | ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
        | ~ order(int) )
    | ~ spl18_92
    | ~ spl18_152 ),
    inference(resolution,[],[f2053,f1204]) ).

tff(f2053,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less_eq(int,semiring_1_of_nat(int,X0),semiring_1_of_nat(int,X1))
        | ~ ord_less(nat,X0,X1) )
    | ~ spl18_152 ),
    inference(avatar_component_clause,[],[f2052]) ).

tff(f22554,plain,
    ( spl18_537
    | ~ spl18_37
    | ~ spl18_125 ),
    inference(avatar_split_clause,[],[f1632,f1580,f752,f22552]) ).

tff(f22552,plain,
    ( spl18_537
  <=> ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ pp(aa(nat,bool,X0,zero_zero(nat)))
        | ( fFalse = aa(nat,bool,X0,sK8(X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_537])]) ).

tff(f1580,plain,
    ( spl18_125
  <=> ! [X0: nat,X1: fun(nat,bool)] :
        ( pp(aa(nat,bool,X1,X0))
        | ~ pp(aa(nat,bool,X1,sK8(X1)))
        | ~ pp(aa(nat,bool,X1,zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_125])]) ).

tff(f1632,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ pp(aa(nat,bool,X0,zero_zero(nat)))
        | ( fFalse = aa(nat,bool,X0,sK8(X0)) ) )
    | ~ spl18_37
    | ~ spl18_125 ),
    inference(resolution,[],[f1581,f753]) ).

tff(f1581,plain,
    ( ! [X0: nat,X1: fun(nat,bool)] :
        ( ~ pp(aa(nat,bool,X1,sK8(X1)))
        | pp(aa(nat,bool,X1,X0))
        | ~ pp(aa(nat,bool,X1,zero_zero(nat))) )
    | ~ spl18_125 ),
    inference(avatar_component_clause,[],[f1580]) ).

tff(f22550,plain,
    ( spl18_536
    | ~ spl18_37
    | ~ spl18_123 ),
    inference(avatar_split_clause,[],[f1604,f1572,f752,f22548]) ).

tff(f22548,plain,
    ( spl18_536
  <=> ! [X0: fun(int,bool),X1: int] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ ord_less_eq(int,zero_zero(int),X1)
        | ( fFalse = aa(int,bool,X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_536])]) ).

tff(f1572,plain,
    ( spl18_123
  <=> ! [X4: int,X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ pp(aa(int,bool,X0,X4))
        | ~ ord_less_eq(int,zero_zero(int),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_123])]) ).

tff(f1604,plain,
    ( ! [X0: fun(int,bool),X1: int] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ ord_less_eq(int,zero_zero(int),X1)
        | ( fFalse = aa(int,bool,X0,X1) ) )
    | ~ spl18_37
    | ~ spl18_123 ),
    inference(resolution,[],[f1573,f753]) ).

tff(f1573,plain,
    ( ! [X0: fun(int,bool),X4: int] :
        ( ~ pp(aa(int,bool,X0,X4))
        | pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ ord_less_eq(int,zero_zero(int),X4) )
    | ~ spl18_123 ),
    inference(avatar_component_clause,[],[f1572]) ).

tff(f22546,plain,
    ( spl18_535
    | ~ spl18_37
    | ~ spl18_122 ),
    inference(avatar_split_clause,[],[f1586,f1568,f752,f22544]) ).

tff(f22544,plain,
    ( spl18_535
  <=> ! [X0: int,X1: fun(int,bool)] :
        ( ~ ord_less_eq(int,zero_zero(int),X0)
        | pp(aa(int,bool,X1,X0))
        | ( fFalse = aa(int,bool,X1,semiring_1_of_nat(int,sK2(X1))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_535])]) ).

tff(f1568,plain,
    ( spl18_122
  <=> ! [X0: fun(int,bool),X1: int] :
        ( pp(aa(int,bool,X0,X1))
        | ~ ord_less_eq(int,zero_zero(int),X1)
        | ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,sK2(X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_122])]) ).

tff(f1586,plain,
    ( ! [X0: int,X1: fun(int,bool)] :
        ( ~ ord_less_eq(int,zero_zero(int),X0)
        | pp(aa(int,bool,X1,X0))
        | ( fFalse = aa(int,bool,X1,semiring_1_of_nat(int,sK2(X1))) ) )
    | ~ spl18_37
    | ~ spl18_122 ),
    inference(resolution,[],[f1569,f753]) ).

tff(f1569,plain,
    ( ! [X0: fun(int,bool),X1: int] :
        ( ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,sK2(X0))))
        | ~ ord_less_eq(int,zero_zero(int),X1)
        | pp(aa(int,bool,X0,X1)) )
    | ~ spl18_122 ),
    inference(avatar_component_clause,[],[f1568]) ).

tff(f22542,plain,
    ( spl18_534
    | ~ spl18_118
    | ~ spl18_530 ),
    inference(avatar_split_clause,[],[f22323,f21945,f1503,f22540]) ).

tff(f21945,plain,
    ( spl18_530
  <=> ! [X0: $tType,X2: X0,X1: nat] : ( huffma2021818691e_Leaf(X0,X1,X2) = huffma2021818691e_Leaf(X0,sK12(X0,huffma2021818691e_Leaf(X0,X1,X2)),sK13(X0,huffma2021818691e_Leaf(X0,X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_530])]) ).

tff(f22323,plain,
    ( ! [X0: $tType,X2: X0,X1: nat] : ( sK13(X0,huffma2021818691e_Leaf(X0,X1,X2)) = X2 )
    | ~ spl18_118
    | ~ spl18_530 ),
    inference(forward_demodulation,[],[f22245,f1504]) ).

tff(f22245,plain,
    ( ! [X0: $tType,X2: X0,X3: nat,X1: nat,X4: nat,X5: X0] : ( sK13(X0,huffma2021818691e_Leaf(X0,X1,X2)) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,huffma2021818691e_Leaf(X0,X4,X5),huffma2021818691e_Leaf(X0,X1,X2)),X5) )
    | ~ spl18_118
    | ~ spl18_530 ),
    inference(superposition,[],[f1504,f21946]) ).

tff(f21946,plain,
    ( ! [X0: $tType,X2: X0,X1: nat] : ( huffma2021818691e_Leaf(X0,X1,X2) = huffma2021818691e_Leaf(X0,sK12(X0,huffma2021818691e_Leaf(X0,X1,X2)),sK13(X0,huffma2021818691e_Leaf(X0,X1,X2))) )
    | ~ spl18_530 ),
    inference(avatar_component_clause,[],[f21945]) ).

tff(f21959,plain,
    ( spl18_533
    | ~ spl18_103
    | ~ spl18_212 ),
    inference(avatar_split_clause,[],[f2979,f2931,f1274,f21957]) ).

tff(f21957,plain,
    ( spl18_533
  <=> ! [X0: $tType,X3: nat,X2: nat,X1: nat] :
        ( ord_less_eq(X0,semiring_1_of_nat(X0,X1),semiring_1_of_nat(X0,X2))
        | ~ preorder(X0)
        | ~ ord_less_eq(nat,X1,X3)
        | ~ linordered_semidom(X0)
        | ~ ord_less_eq(nat,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_533])]) ).

tff(f2931,plain,
    ( spl18_212
  <=> ! [X0: $tType,X3: nat,X2: X0,X1: nat] :
        ( ~ ord_less_eq(X0,semiring_1_of_nat(X0,X1),X2)
        | ord_less_eq(X0,semiring_1_of_nat(X0,X3),X2)
        | ~ preorder(X0)
        | ~ ord_less_eq(nat,X3,X1)
        | ~ linordered_semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_212])]) ).

tff(f2979,plain,
    ( ! [X0: $tType,X2: nat,X3: nat,X1: nat] :
        ( ord_less_eq(X0,semiring_1_of_nat(X0,X1),semiring_1_of_nat(X0,X2))
        | ~ preorder(X0)
        | ~ ord_less_eq(nat,X1,X3)
        | ~ linordered_semidom(X0)
        | ~ ord_less_eq(nat,X3,X2) )
    | ~ spl18_103
    | ~ spl18_212 ),
    inference(duplicate_literal_removal,[],[f2966]) ).

tff(f2966,plain,
    ( ! [X0: $tType,X2: nat,X3: nat,X1: nat] :
        ( ord_less_eq(X0,semiring_1_of_nat(X0,X1),semiring_1_of_nat(X0,X2))
        | ~ preorder(X0)
        | ~ ord_less_eq(nat,X1,X3)
        | ~ linordered_semidom(X0)
        | ~ ord_less_eq(nat,X3,X2)
        | ~ linordered_semidom(X0) )
    | ~ spl18_103
    | ~ spl18_212 ),
    inference(resolution,[],[f2932,f1275]) ).

tff(f2932,plain,
    ( ! [X0: $tType,X2: X0,X3: nat,X1: nat] :
        ( ~ ord_less_eq(X0,semiring_1_of_nat(X0,X1),X2)
        | ord_less_eq(X0,semiring_1_of_nat(X0,X3),X2)
        | ~ preorder(X0)
        | ~ ord_less_eq(nat,X3,X1)
        | ~ linordered_semidom(X0) )
    | ~ spl18_212 ),
    inference(avatar_component_clause,[],[f2931]) ).

tff(f21955,plain,
    ( spl18_532
    | ~ spl18_37
    | ~ spl18_208 ),
    inference(avatar_split_clause,[],[f2849,f2784,f752,f21953]) ).

tff(f21953,plain,
    ( spl18_532
  <=> ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,zero_zero(nat)))
        | member(nat,sK7(X1,X0),X0)
        | ( fFalse = aa(nat,bool,X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_532])]) ).

tff(f2849,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,zero_zero(nat)))
        | member(nat,sK7(X1,X0),X0)
        | ( fFalse = aa(nat,bool,X0,X1) ) )
    | ~ spl18_37
    | ~ spl18_208 ),
    inference(resolution,[],[f2785,f753]) ).

tff(f21951,plain,
    ( spl18_531
    | spl18_48
    | ~ spl18_431 ),
    inference(avatar_split_clause,[],[f15319,f12520,f803,f21949]) ).

tff(f21949,plain,
    ( spl18_531
  <=> ! [X2: bool,X0: bool,X1: bool] :
        ( ( X0 = X1 )
        | ( X1 = X2 )
        | ( X0 = X2 )
        | ( fTrue = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_531])]) ).

tff(f803,plain,
    ( spl18_48
  <=> ( fTrue = fFalse ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_48])]) ).

tff(f12520,plain,
    ( spl18_431
  <=> ! [X0: bool,X3: bool,X2: bool,X1: bool] :
        ( ( X0 = X1 )
        | ( X1 = X2 )
        | ( X0 = X2 )
        | ( X0 = X3 )
        | ( fFalse = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_431])]) ).

tff(f15319,plain,
    ( ! [X2: bool,X0: bool,X1: bool] :
        ( ( X0 = X1 )
        | ( X1 = X2 )
        | ( X0 = X2 )
        | ( fTrue = X0 ) )
    | spl18_48
    | ~ spl18_431 ),
    inference(trivial_inequality_removal,[],[f15086]) ).

tff(f15086,plain,
    ( ! [X2: bool,X0: bool,X1: bool] :
        ( ( fFalse != fFalse )
        | ( X0 = X1 )
        | ( X1 = X2 )
        | ( X0 = X2 )
        | ( fTrue = X0 ) )
    | spl18_48
    | ~ spl18_431 ),
    inference(superposition,[],[f805,f12521]) ).

tff(f12521,plain,
    ( ! [X2: bool,X3: bool,X0: bool,X1: bool] :
        ( ( X0 = X1 )
        | ( X1 = X2 )
        | ( X0 = X2 )
        | ( X0 = X3 )
        | ( fFalse = X3 ) )
    | ~ spl18_431 ),
    inference(avatar_component_clause,[],[f12520]) ).

tff(f805,plain,
    ( ( fTrue != fFalse )
    | spl18_48 ),
    inference(avatar_component_clause,[],[f803]) ).

tff(f21947,plain,
    ( spl18_530
    | ~ spl18_202 ),
    inference(avatar_split_clause,[],[f2762,f2728,f21945]) ).

tff(f2728,plain,
    ( spl18_202
  <=> ! [X0: $tType,X3: X0,X2: nat,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma2021818691e_Leaf(X0,X2,X3) != X1 )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_202])]) ).

tff(f2762,plain,
    ( ! [X0: $tType,X2: X0,X1: nat] : ( huffma2021818691e_Leaf(X0,X1,X2) = huffma2021818691e_Leaf(X0,sK12(X0,huffma2021818691e_Leaf(X0,X1,X2)),sK13(X0,huffma2021818691e_Leaf(X0,X1,X2))) )
    | ~ spl18_202 ),
    inference(equality_resolution,[],[f2729]) ).

tff(f2729,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma2021818691e_Leaf(X0,X2,X3) != X1 )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) )
    | ~ spl18_202 ),
    inference(avatar_component_clause,[],[f2728]) ).

tff(f21943,plain,
    ( spl18_529
    | ~ spl18_158
    | ~ spl18_200 ),
    inference(avatar_split_clause,[],[f2742,f2720,f2086,f21941]) ).

tff(f21941,plain,
    ( spl18_529
  <=> ! [X0: fun(int,bool),X1: fun(int,bool)] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ member(int,sK4(X1),X0)
        | ord_less_eq(int,zero_zero(int),sK3(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_529])]) ).

tff(f2086,plain,
    ( spl18_158
  <=> ! [X0: fun(int,bool)] :
        ( ord_less_eq(int,zero_zero(int),sK4(X0))
        | ord_less_eq(int,zero_zero(int),sK3(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_158])]) ).

tff(f2742,plain,
    ( ! [X0: fun(int,bool),X1: fun(int,bool)] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ member(int,sK4(X1),X0)
        | ord_less_eq(int,zero_zero(int),sK3(X1)) )
    | ~ spl18_158
    | ~ spl18_200 ),
    inference(resolution,[],[f2721,f2087]) ).

tff(f2087,plain,
    ( ! [X0: fun(int,bool)] :
        ( ord_less_eq(int,zero_zero(int),sK4(X0))
        | ord_less_eq(int,zero_zero(int),sK3(X0)) )
    | ~ spl18_158 ),
    inference(avatar_component_clause,[],[f2086]) ).

tff(f21939,plain,
    ( spl18_528
    | ~ spl18_157
    | ~ spl18_200 ),
    inference(avatar_split_clause,[],[f2741,f2720,f2082,f21937]) ).

tff(f21937,plain,
    ( spl18_528
  <=> ! [X2: nat,X0: fun(int,bool),X1: fun(int,bool)] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ member(int,sK3(X1),X0)
        | member(int,semiring_1_of_nat(int,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_528])]) ).

tff(f2082,plain,
    ( spl18_157
  <=> ! [X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | member(int,semiring_1_of_nat(int,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_157])]) ).

tff(f2741,plain,
    ( ! [X2: nat,X0: fun(int,bool),X1: fun(int,bool)] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ member(int,sK3(X1),X0)
        | member(int,semiring_1_of_nat(int,X2),X1) )
    | ~ spl18_157
    | ~ spl18_200 ),
    inference(resolution,[],[f2721,f2083]) ).

tff(f2083,plain,
    ( ! [X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | member(int,semiring_1_of_nat(int,X1),X0) )
    | ~ spl18_157 ),
    inference(avatar_component_clause,[],[f2082]) ).

tff(f21905,plain,
    ( ~ spl18_11
    | ~ spl18_15
    | spl18_527
    | ~ spl18_155
    | ~ spl18_188 ),
    inference(avatar_split_clause,[],[f2527,f2480,f2074,f21903,f650,f630]) ).

tff(f630,plain,
    ( spl18_11
  <=> linorder(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_11])]) ).

tff(f21903,plain,
    ( spl18_527
  <=> ! [X0: int,X1: nat] :
        ( ord_less_eq(int,X0,zero_zero(int))
        | ~ ord_less_eq(nat,X1,zero_zero(nat))
        | ord_less_eq(int,semiring_1_of_nat(int,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_527])]) ).

tff(f2074,plain,
    ( spl18_155
  <=> ! [X0: nat] :
        ( ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int))
        | ~ ord_less_eq(nat,X0,zero_zero(nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_155])]) ).

tff(f2527,plain,
    ( ! [X0: int,X1: nat] :
        ( ord_less_eq(int,X0,zero_zero(int))
        | ~ preorder(int)
        | ord_less_eq(int,semiring_1_of_nat(int,X1),X0)
        | ~ linorder(int)
        | ~ ord_less_eq(nat,X1,zero_zero(nat)) )
    | ~ spl18_155
    | ~ spl18_188 ),
    inference(resolution,[],[f2481,f2075]) ).

tff(f2075,plain,
    ( ! [X0: nat] :
        ( ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int))
        | ~ ord_less_eq(nat,X0,zero_zero(nat)) )
    | ~ spl18_155 ),
    inference(avatar_component_clause,[],[f2074]) ).

tff(f21901,plain,
    ( spl18_526
    | ~ spl18_112
    | ~ spl18_159 ),
    inference(avatar_split_clause,[],[f2157,f2090,f1479,f21899]) ).

tff(f21899,plain,
    ( spl18_526
  <=> ! [X0: huffma1450048681e_tree(int),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK4(huffma675207370phabet(int,X0)))
        | ( zero_zero(nat) = aa(int,nat,huffma1352802255e_freq(int,X0),semiring_1_of_nat(int,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_526])]) ).

tff(f2090,plain,
    ( spl18_159
  <=> ! [X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK4(X0))
        | ~ member(int,semiring_1_of_nat(int,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_159])]) ).

tff(f2157,plain,
    ( ! [X0: huffma1450048681e_tree(int),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK4(huffma675207370phabet(int,X0)))
        | ( zero_zero(nat) = aa(int,nat,huffma1352802255e_freq(int,X0),semiring_1_of_nat(int,X1)) ) )
    | ~ spl18_112
    | ~ spl18_159 ),
    inference(resolution,[],[f2091,f1480]) ).

tff(f2091,plain,
    ( ! [X0: fun(int,bool),X1: nat] :
        ( ~ member(int,semiring_1_of_nat(int,X1),X0)
        | ord_less_eq(int,zero_zero(int),sK4(X0)) )
    | ~ spl18_159 ),
    inference(avatar_component_clause,[],[f2090]) ).

tff(f21897,plain,
    ( spl18_525
    | ~ spl18_37
    | ~ spl18_120 ),
    inference(avatar_split_clause,[],[f1556,f1539,f752,f21895]) ).

tff(f21895,plain,
    ( spl18_525
  <=> ! [X0: fun(nat,bool),X1: nat] :
        ( ord_less(nat,zero_zero(nat),sK8(X0))
        | pp(aa(nat,bool,X0,X1))
        | ( fFalse = aa(nat,bool,X0,zero_zero(nat)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_525])]) ).

tff(f1556,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( ord_less(nat,zero_zero(nat),sK8(X0))
        | pp(aa(nat,bool,X0,X1))
        | ( fFalse = aa(nat,bool,X0,zero_zero(nat)) ) )
    | ~ spl18_37
    | ~ spl18_120 ),
    inference(resolution,[],[f1540,f753]) ).

tff(f21893,plain,
    ( spl18_524
    | ~ spl18_37
    | ~ spl18_119 ),
    inference(avatar_split_clause,[],[f1548,f1524,f752,f21891]) ).

tff(f21891,plain,
    ( spl18_524
  <=> ! [X0: nat,X1: fun(nat,bool)] :
        ( ord_less_eq(nat,sK7(X0,X1),X0)
        | pp(aa(nat,bool,X1,zero_zero(nat)))
        | ( fFalse = aa(nat,bool,X1,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_524])]) ).

tff(f1524,plain,
    ( spl18_119
  <=> ! [X0: nat,X1: fun(nat,bool)] :
        ( ord_less_eq(nat,sK7(X0,X1),X0)
        | ~ pp(aa(nat,bool,X1,X0))
        | pp(aa(nat,bool,X1,zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_119])]) ).

tff(f1548,plain,
    ( ! [X0: nat,X1: fun(nat,bool)] :
        ( ord_less_eq(nat,sK7(X0,X1),X0)
        | pp(aa(nat,bool,X1,zero_zero(nat)))
        | ( fFalse = aa(nat,bool,X1,X0) ) )
    | ~ spl18_37
    | ~ spl18_119 ),
    inference(resolution,[],[f1525,f753]) ).

tff(f1525,plain,
    ( ! [X0: nat,X1: fun(nat,bool)] :
        ( ~ pp(aa(nat,bool,X1,X0))
        | ord_less_eq(nat,sK7(X0,X1),X0)
        | pp(aa(nat,bool,X1,zero_zero(nat))) )
    | ~ spl18_119 ),
    inference(avatar_component_clause,[],[f1524]) ).

tff(f20995,plain,
    ( spl18_523
    | ~ spl18_103
    | ~ spl18_232 ),
    inference(avatar_split_clause,[],[f3447,f3353,f1274,f20993]) ).

tff(f20993,plain,
    ( spl18_523
  <=> ! [X0: $tType,X2: nat,X1: nat] :
        ( ~ linordered_semidom(X0)
        | ~ ord_less_eq(nat,X1,X2)
        | ( semiring_1_of_nat(X0,X1) = semiring_1_of_nat(X0,X2) )
        | ~ order(X0)
        | ~ ord_less_eq(nat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_523])]) ).

tff(f3353,plain,
    ( spl18_232
  <=> ! [X2: $tType,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ~ linordered_semidom(X2)
        | ~ ord_less_eq(X2,semiring_1_of_nat(X2,X1),semiring_1_of_nat(X2,X0))
        | ( semiring_1_of_nat(X2,X0) = semiring_1_of_nat(X2,X1) )
        | ~ order(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_232])]) ).

tff(f3447,plain,
    ( ! [X0: $tType,X2: nat,X1: nat] :
        ( ~ linordered_semidom(X0)
        | ~ ord_less_eq(nat,X1,X2)
        | ( semiring_1_of_nat(X0,X1) = semiring_1_of_nat(X0,X2) )
        | ~ order(X0)
        | ~ ord_less_eq(nat,X2,X1) )
    | ~ spl18_103
    | ~ spl18_232 ),
    inference(duplicate_literal_removal,[],[f3424]) ).

tff(f3424,plain,
    ( ! [X0: $tType,X2: nat,X1: nat] :
        ( ~ linordered_semidom(X0)
        | ~ ord_less_eq(nat,X1,X2)
        | ( semiring_1_of_nat(X0,X1) = semiring_1_of_nat(X0,X2) )
        | ~ order(X0)
        | ~ ord_less_eq(nat,X2,X1)
        | ~ linordered_semidom(X0) )
    | ~ spl18_103
    | ~ spl18_232 ),
    inference(resolution,[],[f3354,f1275]) ).

tff(f3354,plain,
    ( ! [X2: $tType,X0: nat,X1: nat] :
        ( ~ ord_less_eq(X2,semiring_1_of_nat(X2,X1),semiring_1_of_nat(X2,X0))
        | ~ linordered_semidom(X2)
        | ~ ord_less_eq(nat,X0,X1)
        | ( semiring_1_of_nat(X2,X0) = semiring_1_of_nat(X2,X1) )
        | ~ order(X2) )
    | ~ spl18_232 ),
    inference(avatar_component_clause,[],[f3353]) ).

tff(f20991,plain,
    ( spl18_522
    | ~ spl18_32
    | ~ spl18_236 ),
    inference(avatar_split_clause,[],[f3381,f3377,f729,f20989]) ).

tff(f20989,plain,
    ( spl18_522
  <=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( ( fFalse = aa(X0,bool,X1,X2) )
        | ord_less_eq(bool,aa(X0,bool,X1,X2),fTrue)
        | ~ preorder(fun(X0,bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_522])]) ).

tff(f3381,plain,
    ( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( ( fFalse = aa(X0,bool,X1,X2) )
        | ord_less_eq(bool,aa(X0,bool,X1,X2),fTrue)
        | ~ preorder(fun(X0,bool)) )
    | ~ spl18_32
    | ~ spl18_236 ),
    inference(resolution,[],[f3378,f730]) ).

tff(f20987,plain,
    ( spl18_521
    | ~ spl18_69
    | ~ spl18_236 ),
    inference(avatar_split_clause,[],[f3380,f3377,f926,f20985]) ).

tff(f20985,plain,
    ( spl18_521
  <=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( ( fFalse = aa(X0,bool,X1,X2) )
        | ord_less_eq(bool,aa(X0,bool,X1,X2),fTrue)
        | ~ linorder(fun(X0,bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_521])]) ).

tff(f3380,plain,
    ( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( ( fFalse = aa(X0,bool,X1,X2) )
        | ord_less_eq(bool,aa(X0,bool,X1,X2),fTrue)
        | ~ linorder(fun(X0,bool)) )
    | ~ spl18_69
    | ~ spl18_236 ),
    inference(resolution,[],[f3378,f927]) ).

tff(f20983,plain,
    ( spl18_520
    | ~ spl18_32
    | ~ spl18_235 ),
    inference(avatar_split_clause,[],[f3369,f3365,f729,f20981]) ).

tff(f20981,plain,
    ( spl18_520
  <=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( ( fFalse = aa(X0,bool,X1,X2) )
        | ord_less_eq(bool,fTrue,aa(X0,bool,X1,X2))
        | ~ preorder(fun(X0,bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_520])]) ).

tff(f3369,plain,
    ( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( ( fFalse = aa(X0,bool,X1,X2) )
        | ord_less_eq(bool,fTrue,aa(X0,bool,X1,X2))
        | ~ preorder(fun(X0,bool)) )
    | ~ spl18_32
    | ~ spl18_235 ),
    inference(resolution,[],[f3366,f730]) ).

tff(f20979,plain,
    ( spl18_519
    | ~ spl18_69
    | ~ spl18_235 ),
    inference(avatar_split_clause,[],[f3368,f3365,f926,f20977]) ).

tff(f20977,plain,
    ( spl18_519
  <=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( ( fFalse = aa(X0,bool,X1,X2) )
        | ord_less_eq(bool,fTrue,aa(X0,bool,X1,X2))
        | ~ linorder(fun(X0,bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_519])]) ).

tff(f3368,plain,
    ( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( ( fFalse = aa(X0,bool,X1,X2) )
        | ord_less_eq(bool,fTrue,aa(X0,bool,X1,X2))
        | ~ linorder(fun(X0,bool)) )
    | ~ spl18_69
    | ~ spl18_235 ),
    inference(resolution,[],[f3366,f927]) ).

tff(f20975,plain,
    ( spl18_518
    | ~ spl18_142
    | ~ spl18_220 ),
    inference(avatar_split_clause,[],[f3060,f3038,f1885,f20973]) ).

tff(f20973,plain,
    ( spl18_518
  <=> ! [X0: nat,X1: nat] :
        ( ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) )
        | ~ ord_less_eq(nat,X0,X1)
        | ord_less(nat,semiring_1_of_nat(nat,X0),semiring_1_of_nat(nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_518])]) ).

tff(f3038,plain,
    ( spl18_220
  <=> ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) )
        | ~ ord_less_eq(nat,semiring_1_of_nat(nat,X1),semiring_1_of_nat(nat,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_220])]) ).

tff(f3060,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) )
        | ~ ord_less_eq(nat,X0,X1)
        | ord_less(nat,semiring_1_of_nat(nat,X0),semiring_1_of_nat(nat,X1)) )
    | ~ spl18_142
    | ~ spl18_220 ),
    inference(duplicate_literal_removal,[],[f3049]) ).

tff(f3049,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) )
        | ~ ord_less_eq(nat,X0,X1)
        | ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) )
        | ord_less(nat,semiring_1_of_nat(nat,X0),semiring_1_of_nat(nat,X1)) )
    | ~ spl18_142
    | ~ spl18_220 ),
    inference(resolution,[],[f3039,f1886]) ).

tff(f3039,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,semiring_1_of_nat(nat,X1),semiring_1_of_nat(nat,X0))
        | ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) )
        | ~ ord_less_eq(nat,X0,X1) )
    | ~ spl18_220 ),
    inference(avatar_component_clause,[],[f3038]) ).

tff(f20971,plain,
    ( spl18_517
    | ~ spl18_500 ),
    inference(avatar_split_clause,[],[f20808,f20747,f20969]) ).

tff(f20969,plain,
    ( spl18_517
  <=> ! [X0: nat,X1: bool] : ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X1,X0,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_517])]) ).

tff(f20747,plain,
    ( spl18_500
  <=> ! [X2: nat,X0: bool,X1: nat] :
        ( ( semiring_1_of_nat(int,X1) != semiring_1_of_nat(int,X2) )
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,X0,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_500])]) ).

tff(f20808,plain,
    ( ! [X0: nat,X1: bool] : ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X1,X0,X0)) )
    | ~ spl18_500 ),
    inference(equality_resolution,[],[f20748]) ).

tff(f20748,plain,
    ( ! [X2: nat,X0: bool,X1: nat] :
        ( ( semiring_1_of_nat(int,X1) != semiring_1_of_nat(int,X2) )
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,X0,X1,X2)) ) )
    | ~ spl18_500 ),
    inference(avatar_component_clause,[],[f20747]) ).

tff(f20967,plain,
    ( spl18_516
    | ~ spl18_45
    | ~ spl18_219 ),
    inference(avatar_split_clause,[],[f3034,f3029,f792,f20965]) ).

tff(f20965,plain,
    ( spl18_516
  <=> ! [X0: nat,X1: nat] :
        ( ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) )
        | ord_less(nat,X0,X1)
        | ord_less_eq(nat,semiring_1_of_nat(nat,X1),semiring_1_of_nat(nat,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_516])]) ).

tff(f792,plain,
    ( spl18_45
  <=> ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,X1,X0)
        | ~ ord_less(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_45])]) ).

tff(f3029,plain,
    ( spl18_219
  <=> ! [X0: nat,X1: nat] :
        ( ord_less(nat,X0,X1)
        | ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) )
        | ord_less(nat,semiring_1_of_nat(nat,X1),semiring_1_of_nat(nat,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_219])]) ).

tff(f3034,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) )
        | ord_less(nat,X0,X1)
        | ord_less_eq(nat,semiring_1_of_nat(nat,X1),semiring_1_of_nat(nat,X0)) )
    | ~ spl18_45
    | ~ spl18_219 ),
    inference(resolution,[],[f3030,f793]) ).

tff(f793,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less(nat,X1,X0)
        | ord_less_eq(nat,X1,X0) )
    | ~ spl18_45 ),
    inference(avatar_component_clause,[],[f792]) ).

tff(f3030,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less(nat,semiring_1_of_nat(nat,X1),semiring_1_of_nat(nat,X0))
        | ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) )
        | ord_less(nat,X0,X1) )
    | ~ spl18_219 ),
    inference(avatar_component_clause,[],[f3029]) ).

tff(f20963,plain,
    ( spl18_515
    | ~ spl18_49
    | ~ spl18_205 ),
    inference(avatar_split_clause,[],[f2806,f2772,f808,f20961]) ).

tff(f20961,plain,
    ( spl18_515
  <=> ! [X1: $tType,X0: nat,X3: nat,X2: huffma1450048681e_tree(X1)] : ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(X1,bool,huffma675207370phabet(X1,X2),sK14(X1,X2)),X0,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_515])]) ).

tff(f808,plain,
    ( spl18_49
  <=> ! [X0: $tType,X1: huffma1450048681e_tree(X0)] : member(X0,sK14(X0,X1),huffma675207370phabet(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_49])]) ).

tff(f2806,plain,
    ( ! [X1: $tType,X2: huffma1450048681e_tree(X1),X3: nat,X0: nat] : ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(X1,bool,huffma675207370phabet(X1,X2),sK14(X1,X2)),X0,X3)) )
    | ~ spl18_49
    | ~ spl18_205 ),
    inference(resolution,[],[f2773,f809]) ).

tff(f809,plain,
    ( ! [X0: $tType,X1: huffma1450048681e_tree(X0)] : member(X0,sK14(X0,X1),huffma675207370phabet(X0,X1))
    | ~ spl18_49 ),
    inference(avatar_component_clause,[],[f808]) ).

tff(f20959,plain,
    ( spl18_514
    | ~ spl18_37
    | ~ spl18_201 ),
    inference(avatar_split_clause,[],[f2754,f2724,f752,f20957]) ).

tff(f20957,plain,
    ( spl18_514
  <=> ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ member(nat,sK8(X0),X0)
        | ( fFalse = aa(nat,bool,X0,zero_zero(nat)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_514])]) ).

tff(f2754,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ member(nat,sK8(X0),X0)
        | ( fFalse = aa(nat,bool,X0,zero_zero(nat)) ) )
    | ~ spl18_37
    | ~ spl18_201 ),
    inference(resolution,[],[f2725,f753]) ).

tff(f20955,plain,
    ( spl18_513
    | ~ spl18_74
    | ~ spl18_176 ),
    inference(avatar_split_clause,[],[f2344,f2337,f946,f20953]) ).

tff(f20953,plain,
    ( spl18_513
  <=> ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) )
        | ord_less(nat,semiring_1_of_nat(nat,X1),semiring_1_of_nat(nat,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_513])]) ).

tff(f2337,plain,
    ( spl18_176
  <=> ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ord_less_eq(nat,semiring_1_of_nat(nat,X1),semiring_1_of_nat(nat,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_176])]) ).

tff(f2344,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) )
        | ord_less(nat,semiring_1_of_nat(nat,X1),semiring_1_of_nat(nat,X0)) )
    | ~ spl18_74
    | ~ spl18_176 ),
    inference(resolution,[],[f2338,f947]) ).

tff(f2338,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,semiring_1_of_nat(nat,X1),semiring_1_of_nat(nat,X0))
        | ord_less_eq(nat,X0,X1) )
    | ~ spl18_176 ),
    inference(avatar_component_clause,[],[f2337]) ).

tff(f20951,plain,
    ( spl18_512
    | ~ spl18_75
    | ~ spl18_176 ),
    inference(avatar_split_clause,[],[f2343,f2337,f950,f20949]) ).

tff(f20949,plain,
    ( spl18_512
  <=> ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ~ ord_less_eq(nat,semiring_1_of_nat(nat,X0),semiring_1_of_nat(nat,X1))
        | ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_512])]) ).

tff(f2343,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ~ ord_less_eq(nat,semiring_1_of_nat(nat,X0),semiring_1_of_nat(nat,X1))
        | ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) ) )
    | ~ spl18_75
    | ~ spl18_176 ),
    inference(resolution,[],[f2338,f951]) ).

tff(f20947,plain,
    ( spl18_511
    | ~ spl18_74
    | ~ spl18_175 ),
    inference(avatar_split_clause,[],[f2326,f2319,f946,f20945]) ).

tff(f20945,plain,
    ( spl18_511
  <=> ! [X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,X1)
        | ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) )
        | ord_less(nat,semiring_1_of_nat(nat,X0),semiring_1_of_nat(nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_511])]) ).

tff(f2319,plain,
    ( spl18_175
  <=> ! [X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,X1)
        | ord_less_eq(nat,semiring_1_of_nat(nat,X0),semiring_1_of_nat(nat,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_175])]) ).

tff(f2326,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,X1)
        | ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) )
        | ord_less(nat,semiring_1_of_nat(nat,X0),semiring_1_of_nat(nat,X1)) )
    | ~ spl18_74
    | ~ spl18_175 ),
    inference(resolution,[],[f2320,f947]) ).

tff(f2320,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,semiring_1_of_nat(nat,X0),semiring_1_of_nat(nat,X1))
        | ~ ord_less(nat,X0,X1) )
    | ~ spl18_175 ),
    inference(avatar_component_clause,[],[f2319]) ).

tff(f20943,plain,
    ( spl18_510
    | ~ spl18_75
    | ~ spl18_175 ),
    inference(avatar_split_clause,[],[f2325,f2319,f950,f20941]) ).

tff(f20941,plain,
    ( spl18_510
  <=> ! [X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,X1)
        | ~ ord_less_eq(nat,semiring_1_of_nat(nat,X1),semiring_1_of_nat(nat,X0))
        | ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_510])]) ).

tff(f2325,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,X1)
        | ~ ord_less_eq(nat,semiring_1_of_nat(nat,X1),semiring_1_of_nat(nat,X0))
        | ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) ) )
    | ~ spl18_75
    | ~ spl18_175 ),
    inference(resolution,[],[f2320,f951]) ).

tff(f20939,plain,
    ( spl18_509
    | ~ spl18_74
    | ~ spl18_163 ),
    inference(avatar_split_clause,[],[f2243,f2181,f946,f20937]) ).

tff(f20937,plain,
    ( spl18_509
  <=> ! [X0: $tType,X3: X0,X2: nat,X1: huffma1450048681e_tree(X0)] :
        ( ~ ord_less_eq(nat,huffma945805758height(X0,X1),X2)
        | ( huffma410068972_depth(X0,X1,X3) = X2 )
        | ord_less(nat,huffma410068972_depth(X0,X1,X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_509])]) ).

tff(f2181,plain,
    ( spl18_163
  <=> ! [X0: $tType,X3: X0,X2: nat,X1: huffma1450048681e_tree(X0)] :
        ( ~ ord_less_eq(nat,huffma945805758height(X0,X1),X2)
        | ord_less_eq(nat,huffma410068972_depth(X0,X1,X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_163])]) ).

tff(f2243,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: huffma1450048681e_tree(X0)] :
        ( ~ ord_less_eq(nat,huffma945805758height(X0,X1),X2)
        | ( huffma410068972_depth(X0,X1,X3) = X2 )
        | ord_less(nat,huffma410068972_depth(X0,X1,X3),X2) )
    | ~ spl18_74
    | ~ spl18_163 ),
    inference(resolution,[],[f2182,f947]) ).

tff(f2182,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: huffma1450048681e_tree(X0)] :
        ( ord_less_eq(nat,huffma410068972_depth(X0,X1,X3),X2)
        | ~ ord_less_eq(nat,huffma945805758height(X0,X1),X2) )
    | ~ spl18_163 ),
    inference(avatar_component_clause,[],[f2181]) ).

tff(f20935,plain,
    ( spl18_508
    | ~ spl18_75
    | ~ spl18_163 ),
    inference(avatar_split_clause,[],[f2242,f2181,f950,f20933]) ).

tff(f20933,plain,
    ( spl18_508
  <=> ! [X0: $tType,X3: X0,X2: nat,X1: huffma1450048681e_tree(X0)] :
        ( ~ ord_less_eq(nat,huffma945805758height(X0,X1),X2)
        | ~ ord_less_eq(nat,X2,huffma410068972_depth(X0,X1,X3))
        | ( huffma410068972_depth(X0,X1,X3) = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_508])]) ).

tff(f2242,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: huffma1450048681e_tree(X0)] :
        ( ~ ord_less_eq(nat,huffma945805758height(X0,X1),X2)
        | ~ ord_less_eq(nat,X2,huffma410068972_depth(X0,X1,X3))
        | ( huffma410068972_depth(X0,X1,X3) = X2 ) )
    | ~ spl18_75
    | ~ spl18_163 ),
    inference(resolution,[],[f2182,f951]) ).

tff(f20931,plain,
    ( spl18_507
    | ~ spl18_85
    | ~ spl18_162 ),
    inference(avatar_split_clause,[],[f2176,f2168,f1032,f20929]) ).

tff(f20929,plain,
    ( spl18_507
  <=> ! [X0: nat,X1: nat] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
        | ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
        | ord_less_eq(nat,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_507])]) ).

tff(f1032,plain,
    ( spl18_85
  <=> ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,X1,X0)
        | ~ ord_less_eq(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_85])]) ).

tff(f2176,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
        | ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
        | ord_less_eq(nat,X0,X1) )
    | ~ spl18_85
    | ~ spl18_162 ),
    inference(resolution,[],[f2169,f1033]) ).

tff(f1033,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
        | ord_less_eq(nat,X1,X0) )
    | ~ spl18_85 ),
    inference(avatar_component_clause,[],[f1032]) ).

tff(f20927,plain,
    ( spl18_506
    | ~ spl18_28
    | ~ spl18_499 ),
    inference(avatar_split_clause,[],[f20771,f20743,f711,f20925]) ).

tff(f20925,plain,
    ( spl18_506
  <=> ! [X0: nat] :
        ( ( zero_zero(nat) = semiring_1_of_nat(nat,X0) )
        | ~ ord_less_eq(nat,X0,zero_zero(nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_506])]) ).

tff(f711,plain,
    ( spl18_28
  <=> ! [X0: nat] : ord_less_eq(nat,zero_zero(nat),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_28])]) ).

tff(f20743,plain,
    ( spl18_499
  <=> ! [X0: nat] :
        ( ~ ord_less_eq(nat,zero_zero(nat),semiring_1_of_nat(nat,X0))
        | ( zero_zero(nat) = semiring_1_of_nat(nat,X0) )
        | ~ ord_less_eq(nat,X0,zero_zero(nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_499])]) ).

tff(f20771,plain,
    ( ! [X0: nat] :
        ( ( zero_zero(nat) = semiring_1_of_nat(nat,X0) )
        | ~ ord_less_eq(nat,X0,zero_zero(nat)) )
    | ~ spl18_28
    | ~ spl18_499 ),
    inference(resolution,[],[f20744,f712]) ).

tff(f712,plain,
    ( ! [X0: nat] : ord_less_eq(nat,zero_zero(nat),X0)
    | ~ spl18_28 ),
    inference(avatar_component_clause,[],[f711]) ).

tff(f20744,plain,
    ( ! [X0: nat] :
        ( ~ ord_less_eq(nat,zero_zero(nat),semiring_1_of_nat(nat,X0))
        | ( zero_zero(nat) = semiring_1_of_nat(nat,X0) )
        | ~ ord_less_eq(nat,X0,zero_zero(nat)) )
    | ~ spl18_499 ),
    inference(avatar_component_clause,[],[f20743]) ).

tff(f20915,plain,
    ( ~ spl18_16
    | spl18_505
    | ~ spl18_92
    | ~ spl18_158 ),
    inference(avatar_split_clause,[],[f2154,f2086,f1203,f20913,f655]) ).

tff(f20913,plain,
    ( spl18_505
  <=> ! [X0: fun(int,bool)] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | ( zero_zero(int) = sK4(X0) )
        | ~ ord_less_eq(int,sK4(X0),zero_zero(int)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_505])]) ).

tff(f2154,plain,
    ( ! [X0: fun(int,bool)] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | ~ ord_less_eq(int,sK4(X0),zero_zero(int))
        | ( zero_zero(int) = sK4(X0) )
        | ~ order(int) )
    | ~ spl18_92
    | ~ spl18_158 ),
    inference(resolution,[],[f2087,f1204]) ).

tff(f20903,plain,
    ( ~ spl18_16
    | spl18_504
    | ~ spl18_92
    | ~ spl18_157 ),
    inference(avatar_split_clause,[],[f2146,f2082,f1203,f20901,f655]) ).

tff(f20901,plain,
    ( spl18_504
  <=> ! [X0: fun(int,bool),X1: nat] :
        ( member(int,semiring_1_of_nat(int,X1),X0)
        | ( zero_zero(int) = sK3(X0) )
        | ~ ord_less_eq(int,sK3(X0),zero_zero(int)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_504])]) ).

tff(f2146,plain,
    ( ! [X0: fun(int,bool),X1: nat] :
        ( member(int,semiring_1_of_nat(int,X1),X0)
        | ~ ord_less_eq(int,sK3(X0),zero_zero(int))
        | ( zero_zero(int) = sK3(X0) )
        | ~ order(int) )
    | ~ spl18_92
    | ~ spl18_157 ),
    inference(resolution,[],[f2083,f1204]) ).

tff(f20761,plain,
    ( spl18_503
    | ~ spl18_25
    | ~ spl18_244 ),
    inference(avatar_split_clause,[],[f3541,f3538,f699,f20759]) ).

tff(f20759,plain,
    ( spl18_503
  <=> ! [X0: $tType,X3: fun(X0,nat),X2: X0,X1: fun(X0,nat)] :
        ( ord_less_eq(nat,aa(X0,nat,X1,X2),aa(X0,nat,X3,X2))
        | ~ ord_less_eq(fun(X0,nat),X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_503])]) ).

tff(f699,plain,
    ( spl18_25
  <=> ! [X0: nat] : ord_less_eq(nat,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_25])]) ).

tff(f3541,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,nat),X1: fun(X0,nat)] :
        ( ord_less_eq(nat,aa(X0,nat,X1,X2),aa(X0,nat,X3,X2))
        | ~ ord_less_eq(fun(X0,nat),X1,X3) )
    | ~ spl18_25
    | ~ spl18_244 ),
    inference(resolution,[],[f3539,f700]) ).

tff(f700,plain,
    ( ! [X0: nat] : ord_less_eq(nat,X0,X0)
    | ~ spl18_25 ),
    inference(avatar_component_clause,[],[f699]) ).

tff(f20757,plain,
    ( spl18_502
    | ~ spl18_431 ),
    inference(avatar_split_clause,[],[f15318,f12520,f20755]) ).

tff(f20755,plain,
    ( spl18_502
  <=> ! [X2: bool,X0: bool,X1: bool] :
        ( ( X0 != X1 )
        | ( X0 = X2 )
        | ( fFalse = X2 )
        | ( fFalse = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_502])]) ).

tff(f15318,plain,
    ( ! [X2: bool,X0: bool,X1: bool] :
        ( ( X0 != X1 )
        | ( X0 = X2 )
        | ( fFalse = X2 )
        | ( fFalse = X1 ) )
    | ~ spl18_431 ),
    inference(duplicate_literal_removal,[],[f15248]) ).

tff(f15248,plain,
    ( ! [X2: bool,X0: bool,X1: bool] :
        ( ( X0 != X1 )
        | ( X0 = X2 )
        | ( fFalse = X2 )
        | ( fFalse = X1 )
        | ( fFalse = X1 ) )
    | ~ spl18_431 ),
    inference(equality_factoring,[],[f12521]) ).

tff(f20753,plain,
    ( spl18_501
    | ~ spl18_228 ),
    inference(avatar_split_clause,[],[f3292,f3165,f20751]) ).

tff(f20751,plain,
    ( spl18_501
  <=> ! [X2: nat,X0: bool,X1: nat] :
        ( ( semiring_1_of_nat(int,X1) != semiring_1_of_nat(int,X2) )
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,X0,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_501])]) ).

tff(f3292,plain,
    ( ! [X2: nat,X0: bool,X1: nat] :
        ( ( semiring_1_of_nat(int,X1) != semiring_1_of_nat(int,X2) )
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,X0,X1,X2)) ) )
    | ~ spl18_228 ),
    inference(equality_factoring,[],[f3166]) ).

tff(f20749,plain,
    ( spl18_500
    | ~ spl18_228 ),
    inference(avatar_split_clause,[],[f3291,f3165,f20747]) ).

tff(f3291,plain,
    ( ! [X2: nat,X0: bool,X1: nat] :
        ( ( semiring_1_of_nat(int,X1) != semiring_1_of_nat(int,X2) )
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,X0,X1,X2)) ) )
    | ~ spl18_228 ),
    inference(equality_factoring,[],[f3166]) ).

tff(f20745,plain,
    ( spl18_499
    | ~ spl18_60
    | ~ spl18_220 ),
    inference(avatar_split_clause,[],[f3058,f3038,f867,f20743]) ).

tff(f867,plain,
    ( spl18_60
  <=> ( zero_zero(nat) = semiring_1_of_nat(nat,zero_zero(nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_60])]) ).

tff(f3058,plain,
    ( ! [X0: nat] :
        ( ~ ord_less_eq(nat,zero_zero(nat),semiring_1_of_nat(nat,X0))
        | ( zero_zero(nat) = semiring_1_of_nat(nat,X0) )
        | ~ ord_less_eq(nat,X0,zero_zero(nat)) )
    | ~ spl18_60
    | ~ spl18_220 ),
    inference(superposition,[],[f3039,f869]) ).

tff(f869,plain,
    ( ( zero_zero(nat) = semiring_1_of_nat(nat,zero_zero(nat)) )
    | ~ spl18_60 ),
    inference(avatar_component_clause,[],[f867]) ).

tff(f20688,plain,
    ( ~ spl18_11
    | spl18_498
    | ~ spl18_61
    | ~ spl18_198 ),
    inference(avatar_split_clause,[],[f2712,f2691,f880,f20686,f630]) ).

tff(f20686,plain,
    ( spl18_498
  <=> ! [X2: int,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less_eq(int,X2,semiring_1_of_nat(int,X1))
        | ord_less_eq(int,semiring_1_of_nat(int,X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_498])]) ).

tff(f2712,plain,
    ( ! [X2: int,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less_eq(int,semiring_1_of_nat(int,X0),X2)
        | ord_less_eq(int,X2,semiring_1_of_nat(int,X1))
        | ~ linorder(int) )
    | ~ spl18_61
    | ~ spl18_198 ),
    inference(resolution,[],[f2692,f881]) ).

tff(f20657,plain,
    ( ~ spl18_15
    | spl18_497
    | ~ spl18_104
    | ~ spl18_174 ),
    inference(avatar_split_clause,[],[f2314,f2307,f1278,f20655,f650]) ).

tff(f20655,plain,
    ( spl18_497
  <=> ! [X2: int,X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ord_less_eq(int,semiring_1_of_nat(int,X1),X2)
        | ~ ord_less_eq(int,semiring_1_of_nat(int,X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_497])]) ).

tff(f2307,plain,
    ( spl18_174
  <=> ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ord_less_eq(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_174])]) ).

tff(f2314,plain,
    ( ! [X2: int,X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ~ ord_less_eq(int,semiring_1_of_nat(int,X0),X2)
        | ord_less_eq(int,semiring_1_of_nat(int,X1),X2)
        | ~ preorder(int) )
    | ~ spl18_104
    | ~ spl18_174 ),
    inference(resolution,[],[f2308,f1279]) ).

tff(f2308,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less_eq(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
        | ord_less_eq(nat,X0,X1) )
    | ~ spl18_174 ),
    inference(avatar_component_clause,[],[f2307]) ).

tff(f20653,plain,
    ( spl18_496
    | ~ spl18_88
    | ~ spl18_159 ),
    inference(avatar_split_clause,[],[f2158,f2090,f1044,f20651]) ).

tff(f20651,plain,
    ( spl18_496
  <=> ! [X0: huffma1450048681e_tree(int),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK4(huffma675207370phabet(int,X0)))
        | ( semiring_1_of_nat(int,X1) = huffma1401021291ibling(int,X0,semiring_1_of_nat(int,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_496])]) ).

tff(f2158,plain,
    ( ! [X0: huffma1450048681e_tree(int),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK4(huffma675207370phabet(int,X0)))
        | ( semiring_1_of_nat(int,X1) = huffma1401021291ibling(int,X0,semiring_1_of_nat(int,X1)) ) )
    | ~ spl18_88
    | ~ spl18_159 ),
    inference(resolution,[],[f2091,f1045]) ).

tff(f20638,plain,
    ( ~ spl18_15
    | spl18_495
    | ~ spl18_104
    | ~ spl18_158 ),
    inference(avatar_split_clause,[],[f2153,f2086,f1278,f20636,f650]) ).

tff(f20636,plain,
    ( spl18_495
  <=> ! [X0: fun(int,bool),X1: int] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | ord_less_eq(int,zero_zero(int),X1)
        | ~ ord_less_eq(int,sK4(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_495])]) ).

tff(f2153,plain,
    ( ! [X0: fun(int,bool),X1: int] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | ~ ord_less_eq(int,sK4(X0),X1)
        | ord_less_eq(int,zero_zero(int),X1)
        | ~ preorder(int) )
    | ~ spl18_104
    | ~ spl18_158 ),
    inference(resolution,[],[f2087,f1279]) ).

tff(f20634,plain,
    ( spl18_494
    | ~ spl18_431 ),
    inference(avatar_split_clause,[],[f15317,f12520,f20632]) ).

tff(f20632,plain,
    ( spl18_494
  <=> ! [X2: bool,X0: bool,X1: bool] :
        ( ( X0 = X2 )
        | ( X1 = X2 )
        | ( X0 = X1 )
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_494])]) ).

tff(f15317,plain,
    ( ! [X2: bool,X0: bool,X1: bool] :
        ( ( X0 = X2 )
        | ( X1 = X2 )
        | ( X0 = X1 )
        | ( fFalse = X0 ) )
    | ~ spl18_431 ),
    inference(trivial_inequality_removal,[],[f15252]) ).

tff(f15252,plain,
    ( ! [X2: bool,X0: bool,X1: bool] :
        ( ( X1 != X1 )
        | ( X0 = X2 )
        | ( X1 = X2 )
        | ( X0 = X1 )
        | ( fFalse = X0 ) )
    | ~ spl18_431 ),
    inference(equality_factoring,[],[f12521]) ).

tff(f20619,plain,
    ( ~ spl18_15
    | spl18_493
    | ~ spl18_104
    | ~ spl18_157 ),
    inference(avatar_split_clause,[],[f2145,f2082,f1278,f20617,f650]) ).

tff(f20617,plain,
    ( spl18_493
  <=> ! [X2: int,X0: fun(int,bool),X1: nat] :
        ( member(int,semiring_1_of_nat(int,X1),X0)
        | ord_less_eq(int,zero_zero(int),X2)
        | ~ ord_less_eq(int,sK3(X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_493])]) ).

tff(f2145,plain,
    ( ! [X2: int,X0: fun(int,bool),X1: nat] :
        ( member(int,semiring_1_of_nat(int,X1),X0)
        | ~ ord_less_eq(int,sK3(X0),X2)
        | ord_less_eq(int,zero_zero(int),X2)
        | ~ preorder(int) )
    | ~ spl18_104
    | ~ spl18_157 ),
    inference(resolution,[],[f2083,f1279]) ).

tff(f20588,plain,
    ( ~ spl18_15
    | spl18_492
    | ~ spl18_104
    | ~ spl18_152 ),
    inference(avatar_split_clause,[],[f2103,f2052,f1278,f20586,f650]) ).

tff(f20586,plain,
    ( spl18_492
  <=> ! [X2: int,X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,X1)
        | ord_less_eq(int,semiring_1_of_nat(int,X0),X2)
        | ~ ord_less_eq(int,semiring_1_of_nat(int,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_492])]) ).

tff(f2103,plain,
    ( ! [X2: int,X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,X1)
        | ~ ord_less_eq(int,semiring_1_of_nat(int,X1),X2)
        | ord_less_eq(int,semiring_1_of_nat(int,X0),X2)
        | ~ preorder(int) )
    | ~ spl18_104
    | ~ spl18_152 ),
    inference(resolution,[],[f2053,f1279]) ).

tff(f20353,plain,
    ( spl18_491
    | ~ spl18_431 ),
    inference(avatar_split_clause,[],[f15315,f12520,f20351]) ).

tff(f20351,plain,
    ( spl18_491
  <=> ! [X2: bool,X0: bool,X1: bool] :
        ( ( fFalse != X1 )
        | ( X0 = X2 )
        | ( X1 = X2 )
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_491])]) ).

tff(f15315,plain,
    ( ! [X2: bool,X0: bool,X1: bool] :
        ( ( fFalse != X1 )
        | ( X0 = X2 )
        | ( X1 = X2 )
        | ( fFalse = X0 ) )
    | ~ spl18_431 ),
    inference(duplicate_literal_removal,[],[f15260]) ).

tff(f15260,plain,
    ( ! [X2: bool,X0: bool,X1: bool] :
        ( ( fFalse != X1 )
        | ( X0 = X2 )
        | ( X1 = X2 )
        | ( X0 = X2 )
        | ( fFalse = X0 ) )
    | ~ spl18_431 ),
    inference(equality_factoring,[],[f12521]) ).

tff(f20245,plain,
    ( ~ spl18_9
    | spl18_490
    | ~ spl18_101
    | ~ spl18_219 ),
    inference(avatar_split_clause,[],[f3032,f3029,f1266,f20243,f620]) ).

tff(f20243,plain,
    ( spl18_490
  <=> ! [X0: nat,X1: nat] :
        ( ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) )
        | ord_less(nat,X1,X0)
        | ord_less(nat,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_490])]) ).

tff(f1266,plain,
    ( spl18_101
  <=> ! [X0: $tType,X2: nat,X1: nat] :
        ( ord_less(nat,X2,X1)
        | ~ ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
        | ~ linordered_semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_101])]) ).

tff(f3032,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) )
        | ord_less(nat,X0,X1)
        | ord_less(nat,X1,X0)
        | ~ linordered_semidom(nat) )
    | ~ spl18_101
    | ~ spl18_219 ),
    inference(resolution,[],[f3030,f1267]) ).

tff(f1267,plain,
    ( ! [X0: $tType,X2: nat,X1: nat] :
        ( ~ ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
        | ord_less(nat,X2,X1)
        | ~ linordered_semidom(X0) )
    | ~ spl18_101 ),
    inference(avatar_component_clause,[],[f1266]) ).

tff(f20241,plain,
    ( spl18_489
    | ~ spl18_65
    | ~ spl18_208 ),
    inference(avatar_split_clause,[],[f2847,f2784,f896,f20239]) ).

tff(f20239,plain,
    ( spl18_489
  <=> ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,zero_zero(nat)))
        | member(nat,sK7(X1,X0),X0)
        | ~ member(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_489])]) ).

tff(f2847,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,zero_zero(nat)))
        | member(nat,sK7(X1,X0),X0)
        | ~ member(nat,X1,X0) )
    | ~ spl18_65
    | ~ spl18_208 ),
    inference(resolution,[],[f2785,f897]) ).

tff(f20237,plain,
    ( spl18_488
    | ~ spl18_61
    | ~ spl18_186 ),
    inference(avatar_split_clause,[],[f2454,f2430,f880,f20235]) ).

tff(f20235,plain,
    ( spl18_488
  <=> ! [X0: $tType,X2: nat,X1: X0] :
        ( ord_less_eq(X0,zero_zero(X0),X1)
        | ~ preorder(X0)
        | ~ linordered_semidom(X0)
        | ord_less_eq(X0,X1,semiring_1_of_nat(X0,X2))
        | ~ linorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_488])]) ).

tff(f2430,plain,
    ( spl18_186
  <=> ! [X0: $tType,X2: X0,X1: nat] :
        ( ~ ord_less_eq(X0,semiring_1_of_nat(X0,X1),X2)
        | ord_less_eq(X0,zero_zero(X0),X2)
        | ~ preorder(X0)
        | ~ linordered_semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_186])]) ).

tff(f2454,plain,
    ( ! [X0: $tType,X2: nat,X1: X0] :
        ( ord_less_eq(X0,zero_zero(X0),X1)
        | ~ preorder(X0)
        | ~ linordered_semidom(X0)
        | ord_less_eq(X0,X1,semiring_1_of_nat(X0,X2))
        | ~ linorder(X0) )
    | ~ spl18_61
    | ~ spl18_186 ),
    inference(resolution,[],[f2431,f881]) ).

tff(f2431,plain,
    ( ! [X0: $tType,X2: X0,X1: nat] :
        ( ~ ord_less_eq(X0,semiring_1_of_nat(X0,X1),X2)
        | ord_less_eq(X0,zero_zero(X0),X2)
        | ~ preorder(X0)
        | ~ linordered_semidom(X0) )
    | ~ spl18_186 ),
    inference(avatar_component_clause,[],[f2430]) ).

tff(f20233,plain,
    ( spl18_487
    | ~ spl18_68
    | ~ spl18_184 ),
    inference(avatar_split_clause,[],[f2436,f2416,f922,f20231]) ).

tff(f20231,plain,
    ( spl18_487
  <=> ! [X0: int] :
        ( ( semiring_1_of_nat(int,sK1(X0)) = semiring_1_of_nat(int,sK1(semiring_1_of_nat(int,sK1(X0)))) )
        | ~ ord_less(int,zero_zero(int),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_487])]) ).

tff(f922,plain,
    ( spl18_68
  <=> ! [X0: int] :
        ( ord_less(nat,zero_zero(nat),sK1(X0))
        | ~ ord_less(int,zero_zero(int),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_68])]) ).

tff(f2436,plain,
    ( ! [X0: int] :
        ( ( semiring_1_of_nat(int,sK1(X0)) = semiring_1_of_nat(int,sK1(semiring_1_of_nat(int,sK1(X0)))) )
        | ~ ord_less(int,zero_zero(int),X0) )
    | ~ spl18_68
    | ~ spl18_184 ),
    inference(resolution,[],[f2417,f923]) ).

tff(f923,plain,
    ( ! [X0: int] :
        ( ord_less(nat,zero_zero(nat),sK1(X0))
        | ~ ord_less(int,zero_zero(int),X0) )
    | ~ spl18_68 ),
    inference(avatar_component_clause,[],[f922]) ).

tff(f20229,plain,
    ( spl18_486
    | ~ spl18_87
    | ~ spl18_163 ),
    inference(avatar_split_clause,[],[f2241,f2181,f1040,f20227]) ).

tff(f20227,plain,
    ( spl18_486
  <=> ! [X0: $tType,X4: X0,X3: nat,X2: nat,X1: huffma1450048681e_tree(X0)] :
        ( ~ ord_less_eq(nat,huffma945805758height(X0,X1),X2)
        | ~ ord_less_eq(nat,X2,X3)
        | ord_less_eq(nat,huffma410068972_depth(X0,X1,X4),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_486])]) ).

tff(f2241,plain,
    ( ! [X0: $tType,X2: nat,X3: nat,X1: huffma1450048681e_tree(X0),X4: X0] :
        ( ~ ord_less_eq(nat,huffma945805758height(X0,X1),X2)
        | ~ ord_less_eq(nat,X2,X3)
        | ord_less_eq(nat,huffma410068972_depth(X0,X1,X4),X3) )
    | ~ spl18_87
    | ~ spl18_163 ),
    inference(resolution,[],[f2182,f1041]) ).

tff(f20225,plain,
    ( spl18_485
    | ~ spl18_431 ),
    inference(avatar_split_clause,[],[f15304,f12520,f20223]) ).

tff(f20223,plain,
    ( spl18_485
  <=> ! [X2: bool,X0: bool,X1: bool] :
        ( ( fFalse != X1 )
        | ( X0 = X1 )
        | ( X0 = X2 )
        | ( X1 = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_485])]) ).

tff(f15304,plain,
    ( ! [X2: bool,X0: bool,X1: bool] :
        ( ( fFalse != X1 )
        | ( X0 = X1 )
        | ( X0 = X2 )
        | ( X1 = X2 ) )
    | ~ spl18_431 ),
    inference(duplicate_literal_removal,[],[f15295]) ).

tff(f15295,plain,
    ( ! [X2: bool,X0: bool,X1: bool] :
        ( ( fFalse != X1 )
        | ( X0 = X1 )
        | ( X0 = X2 )
        | ( X1 = X2 )
        | ( X0 = X1 ) )
    | ~ spl18_431 ),
    inference(equality_factoring,[],[f12521]) ).

tff(f20221,plain,
    ( spl18_484
    | ~ spl18_156
    | ~ spl18_163 ),
    inference(avatar_split_clause,[],[f2240,f2181,f2078,f20219]) ).

tff(f20219,plain,
    ( spl18_484
  <=> ! [X0: $tType,X4: X0,X3: nat,X2: nat,X1: huffma1450048681e_tree(X0)] :
        ( ~ ord_less_eq(nat,huffma945805758height(X0,X1),X2)
        | ord_less_eq(nat,X3,X2)
        | ord_less_eq(nat,huffma410068972_depth(X0,X1,X4),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_484])]) ).

tff(f2240,plain,
    ( ! [X0: $tType,X2: nat,X3: nat,X1: huffma1450048681e_tree(X0),X4: X0] :
        ( ~ ord_less_eq(nat,huffma945805758height(X0,X1),X2)
        | ord_less_eq(nat,X3,X2)
        | ord_less_eq(nat,huffma410068972_depth(X0,X1,X4),X3) )
    | ~ spl18_156
    | ~ spl18_163 ),
    inference(resolution,[],[f2182,f2079]) ).

tff(f20179,plain,
    ( ~ spl18_15
    | spl18_483
    | ~ spl18_104
    | ~ spl18_162 ),
    inference(avatar_split_clause,[],[f2172,f2168,f1278,f20177,f650]) ).

tff(f20177,plain,
    ( spl18_483
  <=> ! [X2: int,X0: int,X1: int] :
        ( ( X0 = X1 )
        | ord_less_eq(int,X0,X2)
        | ~ ord_less_eq(int,X1,X2)
        | ord_less(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_483])]) ).

tff(f2172,plain,
    ( ! [X2: int,X0: int,X1: int] :
        ( ( X0 = X1 )
        | ord_less(int,X1,X0)
        | ~ ord_less_eq(int,X1,X2)
        | ord_less_eq(int,X0,X2)
        | ~ preorder(int) )
    | ~ spl18_104
    | ~ spl18_162 ),
    inference(resolution,[],[f2169,f1279]) ).

tff(f20175,plain,
    ( spl18_482
    | ~ spl18_76
    | ~ spl18_158 ),
    inference(avatar_split_clause,[],[f2152,f2086,f954,f20173]) ).

tff(f20173,plain,
    ( spl18_482
  <=> ! [X0: fun(int,bool)] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | ( zero_zero(int) = sK4(X0) )
        | ord_less(int,zero_zero(int),sK4(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_482])]) ).

tff(f2152,plain,
    ( ! [X0: fun(int,bool)] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | ( zero_zero(int) = sK4(X0) )
        | ord_less(int,zero_zero(int),sK4(X0)) )
    | ~ spl18_76
    | ~ spl18_158 ),
    inference(resolution,[],[f2087,f955]) ).

tff(f20171,plain,
    ( spl18_481
    | ~ spl18_76
    | ~ spl18_157 ),
    inference(avatar_split_clause,[],[f2144,f2082,f954,f20169]) ).

tff(f20169,plain,
    ( spl18_481
  <=> ! [X0: fun(int,bool),X1: nat] :
        ( member(int,semiring_1_of_nat(int,X1),X0)
        | ( zero_zero(int) = sK3(X0) )
        | ord_less(int,zero_zero(int),sK3(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_481])]) ).

tff(f2144,plain,
    ( ! [X0: fun(int,bool),X1: nat] :
        ( member(int,semiring_1_of_nat(int,X1),X0)
        | ( zero_zero(int) = sK3(X0) )
        | ord_less(int,zero_zero(int),sK3(X0)) )
    | ~ spl18_76
    | ~ spl18_157 ),
    inference(resolution,[],[f2083,f955]) ).

tff(f20167,plain,
    ( spl18_480
    | ~ spl18_37
    | ~ spl18_113 ),
    inference(avatar_split_clause,[],[f1508,f1483,f752,f20165]) ).

tff(f20165,plain,
    ( spl18_480
  <=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( ~ sP0(X0,X1,X2)
        | ( fFalse = aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_480])]) ).

tff(f1483,plain,
    ( spl18_113
  <=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
        | ~ sP0(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_113])]) ).

tff(f1508,plain,
    ( ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( ~ sP0(X0,X1,X2)
        | ( fFalse = aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0) ) )
    | ~ spl18_37
    | ~ spl18_113 ),
    inference(resolution,[],[f1484,f753]) ).

tff(f1484,plain,
    ( ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
        | ~ sP0(X0,X1,X2) )
    | ~ spl18_113 ),
    inference(avatar_component_clause,[],[f1483]) ).

tff(f20163,plain,
    ( spl18_479
    | ~ spl18_73
    | ~ spl18_81 ),
    inference(avatar_split_clause,[],[f1125,f1016,f942,f20161]) ).

tff(f20161,plain,
    ( spl18_479
  <=> ! [X0: huffma1450048681e_tree(bool),X1: bool] :
        ( member(bool,fFalse,huffma675207370phabet(bool,X0))
        | ~ huffma1518433673istent(bool,X0)
        | ( sK6(bool,X0) = X1 )
        | ( fFalse = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_479])]) ).

tff(f1125,plain,
    ( ! [X0: huffma1450048681e_tree(bool),X1: bool] :
        ( member(bool,fFalse,huffma675207370phabet(bool,X0))
        | ~ huffma1518433673istent(bool,X0)
        | ( sK6(bool,X0) = X1 )
        | ( fFalse = X1 ) )
    | ~ spl18_73
    | ~ spl18_81 ),
    inference(superposition,[],[f943,f1017]) ).

tff(f20159,plain,
    ( spl18_478
    | ~ spl18_73
    | ~ spl18_81 ),
    inference(avatar_split_clause,[],[f1087,f1016,f942,f20157]) ).

tff(f20157,plain,
    ( spl18_478
  <=> ! [X0: huffma1450048681e_tree(bool),X1: bool] :
        ( member(bool,X1,huffma675207370phabet(bool,X0))
        | ~ huffma1518433673istent(bool,X0)
        | ( fFalse = X1 )
        | ( fFalse = sK6(bool,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_478])]) ).

tff(f1087,plain,
    ( ! [X0: huffma1450048681e_tree(bool),X1: bool] :
        ( member(bool,X1,huffma675207370phabet(bool,X0))
        | ~ huffma1518433673istent(bool,X0)
        | ( fFalse = X1 )
        | ( fFalse = sK6(bool,X0) ) )
    | ~ spl18_73
    | ~ spl18_81 ),
    inference(superposition,[],[f943,f1017]) ).

tff(f20038,plain,
    ( spl18_477
    | ~ spl18_29
    | ~ spl18_205 ),
    inference(avatar_split_clause,[],[f2805,f2772,f715,f20036]) ).

tff(f20036,plain,
    ( spl18_477
  <=> ! [X0: nat,X1: nat] : ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(a1,bool,huffma675207370phabet(a1,t_1),a),X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_477])]) ).

tff(f2805,plain,
    ( ! [X0: nat,X1: nat] : ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(a1,bool,huffma675207370phabet(a1,t_1),a),X0,X1)) )
    | ~ spl18_29
    | ~ spl18_205 ),
    inference(resolution,[],[f2773,f717]) ).

tff(f20034,plain,
    ( spl18_476
    | ~ spl18_66
    | ~ spl18_429 ),
    inference(avatar_split_clause,[],[f12486,f12295,f902,f20032]) ).

tff(f20032,plain,
    ( spl18_476
  <=> ! [X0: fun(int,bool)] :
        ( ~ member(int,zero_zero(int),X0)
        | member(int,semiring_1_of_nat(int,sK5(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_476])]) ).

tff(f12295,plain,
    ( spl18_429
  <=> ! [X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ member(int,zero_zero(int),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_429])]) ).

tff(f12486,plain,
    ( ! [X0: fun(int,bool)] :
        ( ~ member(int,zero_zero(int),X0)
        | member(int,semiring_1_of_nat(int,sK5(X0)),X0) )
    | ~ spl18_66
    | ~ spl18_429 ),
    inference(resolution,[],[f12296,f903]) ).

tff(f12296,plain,
    ( ! [X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ member(int,zero_zero(int),X0) )
    | ~ spl18_429 ),
    inference(avatar_component_clause,[],[f12295]) ).

tff(f19593,plain,
    ( spl18_475
    | spl18_1
    | ~ spl18_413 ),
    inference(avatar_split_clause,[],[f11072,f9319,f580,f19591]) ).

tff(f9319,plain,
    ( spl18_413
  <=> ! [X1: $tType,X4: bool,X0: bool,X3: X1,X2: X1] :
        ( ( if(X1,X0,X2,X3) = X3 )
        | ( X0 = X4 )
        | ( fFalse = X4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_413])]) ).

tff(f11072,plain,
    ( ! [X1: $tType,X2: bool,X3: X1,X0: bool,X4: X1] :
        ( ~ pp(X0)
        | ( if(X1,X2,X3,X4) = X4 )
        | ( X0 = X2 ) )
    | spl18_1
    | ~ spl18_413 ),
    inference(superposition,[],[f582,f9320]) ).

tff(f9320,plain,
    ( ! [X1: $tType,X2: X1,X3: X1,X0: bool,X4: bool] :
        ( ( if(X1,X0,X2,X3) = X3 )
        | ( X0 = X4 )
        | ( fFalse = X4 ) )
    | ~ spl18_413 ),
    inference(avatar_component_clause,[],[f9319]) ).

tff(f582,plain,
    ( ~ pp(fFalse)
    | spl18_1 ),
    inference(avatar_component_clause,[],[f580]) ).

tff(f18334,plain,
    ( spl18_474
    | ~ spl18_60
    | ~ spl18_409 ),
    inference(avatar_split_clause,[],[f9305,f9189,f867,f18332]) ).

tff(f18332,plain,
    ( spl18_474
  <=> ! [X0: nat] :
        ( ord_less_eq(nat,semiring_1_of_nat(nat,X0),zero_zero(nat))
        | ~ ord_less_eq(nat,X0,zero_zero(nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_474])]) ).

tff(f9189,plain,
    ( spl18_409
  <=> ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,semiring_1_of_nat(nat,X0),semiring_1_of_nat(nat,X1))
        | ~ ord_less_eq(nat,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_409])]) ).

tff(f9305,plain,
    ( ! [X0: nat] :
        ( ord_less_eq(nat,semiring_1_of_nat(nat,X0),zero_zero(nat))
        | ~ ord_less_eq(nat,X0,zero_zero(nat)) )
    | ~ spl18_60
    | ~ spl18_409 ),
    inference(superposition,[],[f9190,f869]) ).

tff(f9190,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,semiring_1_of_nat(nat,X0),semiring_1_of_nat(nat,X1))
        | ~ ord_less_eq(nat,X0,X1) )
    | ~ spl18_409 ),
    inference(avatar_component_clause,[],[f9189]) ).

tff(f17187,plain,
    ( spl18_473
    | ~ spl18_230 ),
    inference(avatar_split_clause,[],[f3337,f3173,f17185]) ).

tff(f17185,plain,
    ( spl18_473
  <=> ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ ord_less(nat,X1,sK8(X0))
        | ~ member(nat,zero_zero(nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_473])]) ).

tff(f3173,plain,
    ( spl18_230
  <=> ! [X2: nat,X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ ord_less(nat,X1,sK8(X0))
        | pp(aa(nat,bool,X0,X2))
        | ~ member(nat,zero_zero(nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_230])]) ).

tff(f3337,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ ord_less(nat,X1,sK8(X0))
        | ~ member(nat,zero_zero(nat),X0) )
    | ~ spl18_230 ),
    inference(factoring,[],[f3174]) ).

tff(f3174,plain,
    ( ! [X2: nat,X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X2))
        | pp(aa(nat,bool,X0,X1))
        | ~ ord_less(nat,X1,sK8(X0))
        | ~ member(nat,zero_zero(nat),X0) )
    | ~ spl18_230 ),
    inference(avatar_component_clause,[],[f3173]) ).

tff(f17183,plain,
    ( spl18_472
    | ~ spl18_65
    | ~ spl18_201 ),
    inference(avatar_split_clause,[],[f2752,f2724,f896,f17181]) ).

tff(f17181,plain,
    ( spl18_472
  <=> ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ member(nat,sK8(X0),X0)
        | ~ member(nat,zero_zero(nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_472])]) ).

tff(f2752,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ member(nat,sK8(X0),X0)
        | ~ member(nat,zero_zero(nat),X0) )
    | ~ spl18_65
    | ~ spl18_201 ),
    inference(resolution,[],[f2725,f897]) ).

tff(f17179,plain,
    ( spl18_471
    | ~ spl18_39
    | ~ spl18_198 ),
    inference(avatar_split_clause,[],[f2714,f2691,f761,f17177]) ).

tff(f17177,plain,
    ( spl18_471
  <=> ! [X0: int,X1: nat] :
        ( ~ ord_less_eq(int,zero_zero(int),X0)
        | ~ ord_less_eq(nat,X1,zero_zero(nat))
        | ord_less_eq(int,semiring_1_of_nat(int,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_471])]) ).

tff(f2714,plain,
    ( ! [X0: int,X1: nat] :
        ( ~ ord_less_eq(int,zero_zero(int),X0)
        | ~ ord_less_eq(nat,X1,zero_zero(nat))
        | ord_less_eq(int,semiring_1_of_nat(int,X1),X0) )
    | ~ spl18_39
    | ~ spl18_198 ),
    inference(superposition,[],[f2692,f763]) ).

tff(f17175,plain,
    ( spl18_470
    | ~ spl18_155
    | ~ spl18_198 ),
    inference(avatar_split_clause,[],[f2706,f2691,f2074,f17173]) ).

tff(f17173,plain,
    ( spl18_470
  <=> ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int))
        | ~ ord_less_eq(nat,X1,zero_zero(nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_470])]) ).

tff(f2706,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int))
        | ~ ord_less_eq(nat,X1,zero_zero(nat)) )
    | ~ spl18_155
    | ~ spl18_198 ),
    inference(resolution,[],[f2692,f2075]) ).

tff(f17171,plain,
    ( spl18_469
    | ~ spl18_86
    | ~ spl18_198 ),
    inference(avatar_split_clause,[],[f2705,f2691,f1036,f17169]) ).

tff(f17169,plain,
    ( spl18_469
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less_eq(int,semiring_1_of_nat(int,X0),semiring_1_of_nat(int,X2))
        | ~ ord_less_eq(nat,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_469])]) ).

tff(f1036,plain,
    ( spl18_86
  <=> ! [X0: nat,X1: nat] :
        ( ord_less_eq(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
        | ~ ord_less_eq(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_86])]) ).

tff(f2705,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less_eq(int,semiring_1_of_nat(int,X0),semiring_1_of_nat(int,X2))
        | ~ ord_less_eq(nat,X1,X2) )
    | ~ spl18_86
    | ~ spl18_198 ),
    inference(resolution,[],[f2692,f1037]) ).

tff(f1037,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less_eq(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
        | ~ ord_less_eq(nat,X1,X0) )
    | ~ spl18_86 ),
    inference(avatar_component_clause,[],[f1036]) ).

tff(f17167,plain,
    ( spl18_468
    | ~ spl18_152
    | ~ spl18_198 ),
    inference(avatar_split_clause,[],[f2704,f2691,f2052,f17165]) ).

tff(f17165,plain,
    ( spl18_468
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less_eq(int,semiring_1_of_nat(int,X0),semiring_1_of_nat(int,X2))
        | ~ ord_less(nat,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_468])]) ).

tff(f2704,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less_eq(int,semiring_1_of_nat(int,X0),semiring_1_of_nat(int,X2))
        | ~ ord_less(nat,X1,X2) )
    | ~ spl18_152
    | ~ spl18_198 ),
    inference(resolution,[],[f2692,f2053]) ).

tff(f17109,plain,
    ( spl18_467
    | ~ spl18_174
    | ~ spl18_198 ),
    inference(avatar_split_clause,[],[f2703,f2691,f2307,f17107]) ).

tff(f17107,plain,
    ( spl18_467
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less_eq(int,semiring_1_of_nat(int,X0),semiring_1_of_nat(int,X2))
        | ord_less_eq(nat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_467])]) ).

tff(f2703,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less_eq(int,semiring_1_of_nat(int,X0),semiring_1_of_nat(int,X2))
        | ord_less_eq(nat,X2,X1) )
    | ~ spl18_174
    | ~ spl18_198 ),
    inference(resolution,[],[f2692,f2308]) ).

tff(f17105,plain,
    ( spl18_466
    | ~ spl18_60
    | ~ spl18_197 ),
    inference(avatar_split_clause,[],[f2689,f2674,f867,f17103]) ).

tff(f17103,plain,
    ( spl18_466
  <=> ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,zero_zero(nat),X0)
        | ord_less_eq(nat,semiring_1_of_nat(nat,X1),X0)
        | ~ ord_less_eq(nat,X1,zero_zero(nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_466])]) ).

tff(f2689,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,zero_zero(nat),X0)
        | ord_less_eq(nat,semiring_1_of_nat(nat,X1),X0)
        | ~ ord_less_eq(nat,X1,zero_zero(nat)) )
    | ~ spl18_60
    | ~ spl18_197 ),
    inference(superposition,[],[f2675,f869]) ).

tff(f17101,plain,
    ( spl18_465
    | ~ spl18_175
    | ~ spl18_197 ),
    inference(avatar_split_clause,[],[f2682,f2674,f2319,f17099]) ).

tff(f17099,plain,
    ( spl18_465
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,semiring_1_of_nat(nat,X0),semiring_1_of_nat(nat,X1))
        | ~ ord_less_eq(nat,X0,X2)
        | ~ ord_less(nat,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_465])]) ).

tff(f2682,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,semiring_1_of_nat(nat,X0),semiring_1_of_nat(nat,X1))
        | ~ ord_less_eq(nat,X0,X2)
        | ~ ord_less(nat,X2,X1) )
    | ~ spl18_175
    | ~ spl18_197 ),
    inference(resolution,[],[f2675,f2320]) ).

tff(f17097,plain,
    ( spl18_464
    | ~ spl18_176
    | ~ spl18_197 ),
    inference(avatar_split_clause,[],[f2681,f2674,f2337,f17095]) ).

tff(f17095,plain,
    ( spl18_464
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,semiring_1_of_nat(nat,X0),semiring_1_of_nat(nat,X1))
        | ~ ord_less_eq(nat,X0,X2)
        | ord_less_eq(nat,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_464])]) ).

tff(f2681,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,semiring_1_of_nat(nat,X0),semiring_1_of_nat(nat,X1))
        | ~ ord_less_eq(nat,X0,X2)
        | ord_less_eq(nat,X1,X2) )
    | ~ spl18_176
    | ~ spl18_197 ),
    inference(resolution,[],[f2675,f2338]) ).

tff(f17093,plain,
    ( spl18_463
    | ~ spl18_44
    | ~ spl18_197 ),
    inference(avatar_split_clause,[],[f2679,f2674,f788,f17091]) ).

tff(f17091,plain,
    ( spl18_463
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,semiring_1_of_nat(nat,X0),X1)
        | ~ ord_less_eq(nat,X0,X2)
        | ord_less_eq(nat,X1,semiring_1_of_nat(nat,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_463])]) ).

tff(f2679,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,semiring_1_of_nat(nat,X0),X1)
        | ~ ord_less_eq(nat,X0,X2)
        | ord_less_eq(nat,X1,semiring_1_of_nat(nat,X2)) )
    | ~ spl18_44
    | ~ spl18_197 ),
    inference(resolution,[],[f2675,f789]) ).

tff(f17089,plain,
    ( spl18_462
    | ~ spl18_61
    | ~ spl18_188 ),
    inference(avatar_split_clause,[],[f2539,f2480,f880,f17087]) ).

tff(f17087,plain,
    ( spl18_462
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ord_less_eq(X0,X1,X2)
        | ~ preorder(X0)
        | ord_less_eq(X0,X3,X1)
        | ~ linorder(X0)
        | ord_less_eq(X0,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_462])]) ).

tff(f2539,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( ord_less_eq(X0,X1,X2)
        | ~ preorder(X0)
        | ord_less_eq(X0,X3,X1)
        | ~ linorder(X0)
        | ord_less_eq(X0,X2,X3) )
    | ~ spl18_61
    | ~ spl18_188 ),
    inference(duplicate_literal_removal,[],[f2531]) ).

tff(f2531,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( ord_less_eq(X0,X1,X2)
        | ~ preorder(X0)
        | ord_less_eq(X0,X3,X1)
        | ~ linorder(X0)
        | ord_less_eq(X0,X2,X3)
        | ~ linorder(X0) )
    | ~ spl18_61
    | ~ spl18_188 ),
    inference(resolution,[],[f2481,f881]) ).

tff(f17085,plain,
    ( spl18_461
    | ~ spl18_164
    | ~ spl18_184 ),
    inference(avatar_split_clause,[],[f2434,f2416,f2185,f17083]) ).

tff(f17083,plain,
    ( spl18_461
  <=> ! [X0: nat] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,sK1(semiring_1_of_nat(int,X0))) )
        | ( zero_zero(nat) = semiring_1_of_nat(nat,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_461])]) ).

tff(f2185,plain,
    ( spl18_164
  <=> ! [X0: nat] :
        ( ord_less(nat,zero_zero(nat),X0)
        | ( zero_zero(nat) = semiring_1_of_nat(nat,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_164])]) ).

tff(f2434,plain,
    ( ! [X0: nat] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,sK1(semiring_1_of_nat(int,X0))) )
        | ( zero_zero(nat) = semiring_1_of_nat(nat,X0) ) )
    | ~ spl18_164
    | ~ spl18_184 ),
    inference(resolution,[],[f2417,f2186]) ).

tff(f2186,plain,
    ( ! [X0: nat] :
        ( ord_less(nat,zero_zero(nat),X0)
        | ( zero_zero(nat) = semiring_1_of_nat(nat,X0) ) )
    | ~ spl18_164 ),
    inference(avatar_component_clause,[],[f2185]) ).

tff(f17081,plain,
    ( spl18_460
    | ~ spl18_87
    | ~ spl18_176 ),
    inference(avatar_split_clause,[],[f2342,f2337,f1040,f17079]) ).

tff(f17079,plain,
    ( spl18_460
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ~ ord_less_eq(nat,semiring_1_of_nat(nat,X0),X2)
        | ord_less_eq(nat,semiring_1_of_nat(nat,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_460])]) ).

tff(f2342,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ~ ord_less_eq(nat,semiring_1_of_nat(nat,X0),X2)
        | ord_less_eq(nat,semiring_1_of_nat(nat,X1),X2) )
    | ~ spl18_87
    | ~ spl18_176 ),
    inference(resolution,[],[f2338,f1041]) ).

tff(f17077,plain,
    ( spl18_459
    | ~ spl18_156
    | ~ spl18_176 ),
    inference(avatar_split_clause,[],[f2341,f2337,f2078,f17075]) ).

tff(f17075,plain,
    ( spl18_459
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ord_less_eq(nat,X2,semiring_1_of_nat(nat,X0))
        | ord_less_eq(nat,semiring_1_of_nat(nat,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_459])]) ).

tff(f2341,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ord_less_eq(nat,X2,semiring_1_of_nat(nat,X0))
        | ord_less_eq(nat,semiring_1_of_nat(nat,X1),X2) )
    | ~ spl18_156
    | ~ spl18_176 ),
    inference(resolution,[],[f2338,f2079]) ).

tff(f17073,plain,
    ( spl18_458
    | ~ spl18_87
    | ~ spl18_175 ),
    inference(avatar_split_clause,[],[f2324,f2319,f1040,f17071]) ).

tff(f17071,plain,
    ( spl18_458
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,X1)
        | ~ ord_less_eq(nat,semiring_1_of_nat(nat,X1),X2)
        | ord_less_eq(nat,semiring_1_of_nat(nat,X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_458])]) ).

tff(f2324,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,X1)
        | ~ ord_less_eq(nat,semiring_1_of_nat(nat,X1),X2)
        | ord_less_eq(nat,semiring_1_of_nat(nat,X0),X2) )
    | ~ spl18_87
    | ~ spl18_175 ),
    inference(resolution,[],[f2320,f1041]) ).

tff(f17012,plain,
    ( spl18_457
    | ~ spl18_156
    | ~ spl18_175 ),
    inference(avatar_split_clause,[],[f2323,f2319,f2078,f17010]) ).

tff(f17010,plain,
    ( spl18_457
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,X1)
        | ord_less_eq(nat,X2,semiring_1_of_nat(nat,X1))
        | ord_less_eq(nat,semiring_1_of_nat(nat,X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_457])]) ).

tff(f2323,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,X1)
        | ord_less_eq(nat,X2,semiring_1_of_nat(nat,X1))
        | ord_less_eq(nat,semiring_1_of_nat(nat,X0),X2) )
    | ~ spl18_156
    | ~ spl18_175 ),
    inference(resolution,[],[f2320,f2079]) ).

tff(f17008,plain,
    ( spl18_456
    | ~ spl18_70
    | ~ spl18_161 ),
    inference(avatar_split_clause,[],[f2236,f2164,f930,f17006]) ).

tff(f17006,plain,
    ( spl18_456
  <=> ! [X0: nat] :
        ( ( zero_zero(int) = semiring_1_of_nat(int,X0) )
        | ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,sK1(semiring_1_of_nat(int,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_456])]) ).

tff(f930,plain,
    ( spl18_70
  <=> ! [X0: int] :
        ( ( semiring_1_of_nat(int,sK1(X0)) = X0 )
        | ~ ord_less(int,zero_zero(int),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_70])]) ).

tff(f2164,plain,
    ( spl18_161
  <=> ! [X0: nat] :
        ( ( zero_zero(int) = semiring_1_of_nat(int,X0) )
        | ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_161])]) ).

tff(f2236,plain,
    ( ! [X0: nat] :
        ( ( zero_zero(int) = semiring_1_of_nat(int,X0) )
        | ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,sK1(semiring_1_of_nat(int,X0))) ) )
    | ~ spl18_70
    | ~ spl18_161 ),
    inference(resolution,[],[f2165,f931]) ).

tff(f931,plain,
    ( ! [X0: int] :
        ( ~ ord_less(int,zero_zero(int),X0)
        | ( semiring_1_of_nat(int,sK1(X0)) = X0 ) )
    | ~ spl18_70 ),
    inference(avatar_component_clause,[],[f930]) ).

tff(f2165,plain,
    ( ! [X0: nat] :
        ( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0))
        | ( zero_zero(int) = semiring_1_of_nat(int,X0) ) )
    | ~ spl18_161 ),
    inference(avatar_component_clause,[],[f2164]) ).

tff(f17004,plain,
    ( spl18_455
    | ~ spl18_162
    | ~ spl18_167 ),
    inference(avatar_split_clause,[],[f2208,f2202,f2168,f17002]) ).

tff(f17002,plain,
    ( spl18_455
  <=> ! [X0: int,X1: nat] :
        ( ord_less_eq(int,zero_zero(int),X0)
        | ( semiring_1_of_nat(int,X1) = X0 )
        | ord_less(int,X0,semiring_1_of_nat(int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_455])]) ).

tff(f2202,plain,
    ( spl18_167
  <=> ! [X0: nat,X1: int] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X0),X1)
        | ord_less_eq(int,zero_zero(int),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_167])]) ).

tff(f2208,plain,
    ( ! [X0: int,X1: nat] :
        ( ord_less_eq(int,zero_zero(int),X0)
        | ( semiring_1_of_nat(int,X1) = X0 )
        | ord_less(int,X0,semiring_1_of_nat(int,X1)) )
    | ~ spl18_162
    | ~ spl18_167 ),
    inference(resolution,[],[f2203,f2169]) ).

tff(f2203,plain,
    ( ! [X0: nat,X1: int] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X0),X1)
        | ord_less_eq(int,zero_zero(int),X1) )
    | ~ spl18_167 ),
    inference(avatar_component_clause,[],[f2202]) ).

tff(f17000,plain,
    ( spl18_454
    | ~ spl18_81
    | ~ spl18_108 ),
    inference(avatar_split_clause,[],[f1596,f1434,f1016,f16998]) ).

tff(f16998,plain,
    ( spl18_454
  <=> ! [X0: bool,X3: bool,X2: bool,X1: bool] :
        ( ( X1 = X3 )
        | ( fFalse = X0 )
        | ( fFalse = if(bool,X0,X1,X2) )
        | ( fFalse = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_454])]) ).

tff(f1434,plain,
    ( spl18_108
  <=> ! [X1: $tType,X0: bool,X3: X1,X2: X1] :
        ( ( if(X1,X0,X2,X3) = X2 )
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_108])]) ).

tff(f1596,plain,
    ( ! [X2: bool,X3: bool,X0: bool,X1: bool] :
        ( ( X1 = X3 )
        | ( fFalse = X0 )
        | ( fFalse = if(bool,X0,X1,X2) )
        | ( fFalse = X3 ) )
    | ~ spl18_81
    | ~ spl18_108 ),
    inference(superposition,[],[f1435,f1017]) ).

tff(f1435,plain,
    ( ! [X1: $tType,X2: X1,X3: X1,X0: bool] :
        ( ( if(X1,X0,X2,X3) = X2 )
        | ( fFalse = X0 ) )
    | ~ spl18_108 ),
    inference(avatar_component_clause,[],[f1434]) ).

tff(f16996,plain,
    ( spl18_453
    | ~ spl18_81
    | ~ spl18_108 ),
    inference(avatar_split_clause,[],[f1594,f1434,f1016,f16994]) ).

tff(f16994,plain,
    ( spl18_453
  <=> ! [X0: bool,X3: bool,X2: bool,X1: bool] :
        ( ( fFalse = X1 )
        | ( fFalse = X0 )
        | ( if(bool,X0,X1,X2) = X3 )
        | ( fFalse = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_453])]) ).

tff(f1594,plain,
    ( ! [X2: bool,X3: bool,X0: bool,X1: bool] :
        ( ( fFalse = X1 )
        | ( fFalse = X0 )
        | ( if(bool,X0,X1,X2) = X3 )
        | ( fFalse = X3 ) )
    | ~ spl18_81
    | ~ spl18_108 ),
    inference(superposition,[],[f1435,f1017]) ).

tff(f16992,plain,
    ( spl18_452
    | ~ spl18_81
    | ~ spl18_105 ),
    inference(avatar_split_clause,[],[f1527,f1282,f1016,f16990]) ).

tff(f16990,plain,
    ( spl18_452
  <=> ! [X0: bool,X3: bool,X2: bool,X1: bool] :
        ( ( if(bool,X0,X1,X2) = X0 )
        | ( fTrue = X2 )
        | ( X0 = X3 )
        | ( fFalse = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_452])]) ).

tff(f1282,plain,
    ( spl18_105
  <=> ! [X0: bool,X1: bool] :
        ( ( fTrue = X1 )
        | ( fFalse = if(bool,fFalse,X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_105])]) ).

tff(f1527,plain,
    ( ! [X2: bool,X3: bool,X0: bool,X1: bool] :
        ( ( if(bool,X0,X1,X2) = X0 )
        | ( fTrue = X2 )
        | ( X0 = X3 )
        | ( fFalse = X3 ) )
    | ~ spl18_81
    | ~ spl18_105 ),
    inference(superposition,[],[f1283,f1017]) ).

tff(f1283,plain,
    ( ! [X0: bool,X1: bool] :
        ( ( fFalse = if(bool,fFalse,X0,X1) )
        | ( fTrue = X1 ) )
    | ~ spl18_105 ),
    inference(avatar_component_clause,[],[f1282]) ).

tff(f16988,plain,
    ( spl18_451
    | ~ spl18_37
    | ~ spl18_110 ),
    inference(avatar_split_clause,[],[f1470,f1452,f752,f16986]) ).

tff(f16986,plain,
    ( spl18_451
  <=> ! [X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,sK4(X0)))
        | ( fFalse = aa(int,bool,X0,semiring_1_of_nat(int,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_451])]) ).

tff(f1470,plain,
    ( ! [X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,sK4(X0)))
        | ( fFalse = aa(int,bool,X0,semiring_1_of_nat(int,X1)) ) )
    | ~ spl18_37
    | ~ spl18_110 ),
    inference(resolution,[],[f1453,f753]) ).

tff(f16984,plain,
    ( spl18_450
    | ~ spl18_37
    | ~ spl18_109 ),
    inference(avatar_split_clause,[],[f1461,f1448,f752,f16982]) ).

tff(f16982,plain,
    ( spl18_450
  <=> ! [X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,X1)))
        | ( fFalse = aa(int,bool,X0,sK3(X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_450])]) ).

tff(f1448,plain,
    ( spl18_109
  <=> ! [X0: fun(int,bool),X3: nat] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,X3)))
        | ~ pp(aa(int,bool,X0,sK3(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_109])]) ).

tff(f1461,plain,
    ( ! [X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,X1)))
        | ( fFalse = aa(int,bool,X0,sK3(X0)) ) )
    | ~ spl18_37
    | ~ spl18_109 ),
    inference(resolution,[],[f1449,f753]) ).

tff(f1449,plain,
    ( ! [X3: nat,X0: fun(int,bool)] :
        ( ~ pp(aa(int,bool,X0,sK3(X0)))
        | pp(aa(int,bool,X0,semiring_1_of_nat(int,X3))) )
    | ~ spl18_109 ),
    inference(avatar_component_clause,[],[f1448]) ).

tff(f12623,plain,
    ( spl18_449
    | ~ spl18_175
    | ~ spl18_220 ),
    inference(avatar_split_clause,[],[f3047,f3038,f2319,f12621]) ).

tff(f12621,plain,
    ( spl18_449
  <=> ! [X0: nat,X1: nat] :
        ( ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) )
        | ~ ord_less_eq(nat,X0,X1)
        | ~ ord_less(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_449])]) ).

tff(f3047,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) )
        | ~ ord_less_eq(nat,X0,X1)
        | ~ ord_less(nat,X1,X0) )
    | ~ spl18_175
    | ~ spl18_220 ),
    inference(resolution,[],[f3039,f2320]) ).

tff(f12619,plain,
    ( spl18_448
    | ~ spl18_86
    | ~ spl18_218 ),
    inference(avatar_split_clause,[],[f3017,f3012,f1036,f12617]) ).

tff(f12617,plain,
    ( spl18_448
  <=> ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
        | ~ ord_less_eq(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_448])]) ).

tff(f3012,plain,
    ( spl18_218
  <=> ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X0),semiring_1_of_nat(int,X1))
        | ~ ord_less_eq(nat,X1,X0)
        | ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_218])]) ).

tff(f3017,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
        | ~ ord_less_eq(nat,X1,X0) )
    | ~ spl18_86
    | ~ spl18_218 ),
    inference(resolution,[],[f3013,f1037]) ).

tff(f3013,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X0),semiring_1_of_nat(int,X1))
        | ~ ord_less_eq(nat,X1,X0)
        | ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) ) )
    | ~ spl18_218 ),
    inference(avatar_component_clause,[],[f3012]) ).

tff(f12615,plain,
    ( spl18_447
    | ~ spl18_152
    | ~ spl18_218 ),
    inference(avatar_split_clause,[],[f3016,f3012,f2052,f12613]) ).

tff(f12613,plain,
    ( spl18_447
  <=> ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
        | ~ ord_less(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_447])]) ).

tff(f3016,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
        | ~ ord_less(nat,X1,X0) )
    | ~ spl18_152
    | ~ spl18_218 ),
    inference(resolution,[],[f3013,f2053]) ).

tff(f12611,plain,
    ( spl18_446
    | ~ spl18_83
    | ~ spl18_203 ),
    inference(avatar_split_clause,[],[f2799,f2764,f1024,f12609]) ).

tff(f12609,plain,
    ( spl18_446
  <=> ! [X0: nat,X1: nat] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
        | ~ ord_less_eq(nat,X0,X1)
        | ord_less(nat,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_446])]) ).

tff(f1024,plain,
    ( spl18_83
  <=> ! [X0: nat,X1: nat] :
        ( ord_less(nat,X1,X0)
        | ~ ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_83])]) ).

tff(f2764,plain,
    ( spl18_203
  <=> ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
        | ord_less(int,semiring_1_of_nat(int,X0),semiring_1_of_nat(int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_203])]) ).

tff(f2799,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
        | ~ ord_less_eq(nat,X0,X1)
        | ord_less(nat,X0,X1) )
    | ~ spl18_83
    | ~ spl18_203 ),
    inference(resolution,[],[f2765,f1025]) ).

tff(f1025,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
        | ord_less(nat,X1,X0) )
    | ~ spl18_83 ),
    inference(avatar_component_clause,[],[f1024]) ).

tff(f2765,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less(int,semiring_1_of_nat(int,X0),semiring_1_of_nat(int,X1))
        | ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
        | ~ ord_less_eq(nat,X0,X1) )
    | ~ spl18_203 ),
    inference(avatar_component_clause,[],[f2764]) ).

tff(f12607,plain,
    ( spl18_445
    | ~ spl18_41
    | ~ spl18_200 ),
    inference(avatar_split_clause,[],[f2739,f2720,f770,f12605]) ).

tff(f12605,plain,
    ( spl18_445
  <=> ! [X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ member(int,semiring_1_of_nat(int,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_445])]) ).

tff(f2739,plain,
    ( ! [X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ member(int,semiring_1_of_nat(int,X1),X0) )
    | ~ spl18_41
    | ~ spl18_200 ),
    inference(resolution,[],[f2721,f771]) ).

tff(f12581,plain,
    ( spl18_444
    | ~ spl18_66
    | ~ spl18_196 ),
    inference(avatar_split_clause,[],[f2658,f2573,f902,f12579]) ).

tff(f12579,plain,
    ( spl18_444
  <=> ! [X0: fun(int,bool),X1: int] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | ~ ord_less_eq(int,zero_zero(int),X1)
        | member(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_444])]) ).

tff(f2658,plain,
    ( ! [X0: fun(int,bool),X1: int] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | ~ ord_less_eq(int,zero_zero(int),X1)
        | member(int,X1,X0) )
    | ~ spl18_66
    | ~ spl18_196 ),
    inference(resolution,[],[f2574,f903]) ).

tff(f12577,plain,
    ( spl18_443
    | ~ spl18_66
    | ~ spl18_194 ),
    inference(avatar_split_clause,[],[f2638,f2564,f902,f12575]) ).

tff(f12575,plain,
    ( spl18_443
  <=> ! [X0: fun(nat,bool),X1: nat] :
        ( ord_less(nat,zero_zero(nat),sK8(X0))
        | ~ member(nat,zero_zero(nat),X0)
        | member(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_443])]) ).

tff(f2638,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( ord_less(nat,zero_zero(nat),sK8(X0))
        | ~ member(nat,zero_zero(nat),X0)
        | member(nat,X1,X0) )
    | ~ spl18_66
    | ~ spl18_194 ),
    inference(resolution,[],[f2565,f903]) ).

tff(f12573,plain,
    ( spl18_442
    | ~ spl18_66
    | ~ spl18_193 ),
    inference(avatar_split_clause,[],[f2614,f2560,f902,f12571]) ).

tff(f12571,plain,
    ( spl18_442
  <=> ! [X0: fun(nat,bool),X1: nat] :
        ( ord_less_eq(nat,sK7(X1,X0),X1)
        | ~ member(nat,X1,X0)
        | member(nat,zero_zero(nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_442])]) ).

tff(f2614,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( ord_less_eq(nat,sK7(X1,X0),X1)
        | ~ member(nat,X1,X0)
        | member(nat,zero_zero(nat),X0) )
    | ~ spl18_66
    | ~ spl18_193 ),
    inference(resolution,[],[f2561,f903]) ).

tff(f12569,plain,
    ( spl18_441
    | ~ spl18_37
    | ~ spl18_180 ),
    inference(avatar_split_clause,[],[f2400,f2362,f752,f12567]) ).

tff(f12567,plain,
    ( spl18_441
  <=> ! [X0: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X2: fun(nat,fun(nat,bool)),X1: nat] :
        ( ~ sP0(X0,X1,X2)
        | ( fFalse = huffma1280178957ee_rec(nat,bool,X2,X3,huffma2021818691e_Leaf(nat,X1,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_441])]) ).

tff(f2400,plain,
    ( ! [X2: fun(nat,fun(nat,bool)),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X0: nat,X1: nat] :
        ( ~ sP0(X0,X1,X2)
        | ( fFalse = huffma1280178957ee_rec(nat,bool,X2,X3,huffma2021818691e_Leaf(nat,X1,X0)) ) )
    | ~ spl18_37
    | ~ spl18_180 ),
    inference(resolution,[],[f2363,f753]) ).

tff(f12565,plain,
    ( spl18_440
    | ~ spl18_37
    | ~ spl18_179 ),
    inference(avatar_split_clause,[],[f2388,f2358,f752,f12563]) ).

tff(f12563,plain,
    ( spl18_440
  <=> ! [X0: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X2: fun(nat,fun(nat,bool)),X1: nat] :
        ( ~ sP0(X0,X1,X2)
        | ( fFalse = huffma107959123e_case(nat,bool,X2,X3,huffma2021818691e_Leaf(nat,X1,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_440])]) ).

tff(f2388,plain,
    ( ! [X2: fun(nat,fun(nat,bool)),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X0: nat,X1: nat] :
        ( ~ sP0(X0,X1,X2)
        | ( fFalse = huffma107959123e_case(nat,bool,X2,X3,huffma2021818691e_Leaf(nat,X1,X0)) ) )
    | ~ spl18_37
    | ~ spl18_179 ),
    inference(resolution,[],[f2359,f753]) ).

tff(f12561,plain,
    ( spl18_439
    | ~ spl18_37
    | ~ spl18_177 ),
    inference(avatar_split_clause,[],[f2377,f2350,f752,f12559]) ).

tff(f12559,plain,
    ( spl18_439
  <=> ! [X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,sK4(X0)))
        | ( fFalse = aa(int,bool,X0,zero_zero(int)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_439])]) ).

tff(f2377,plain,
    ( ! [X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,sK4(X0)))
        | ( fFalse = aa(int,bool,X0,zero_zero(int)) ) )
    | ~ spl18_37
    | ~ spl18_177 ),
    inference(resolution,[],[f2351,f753]) ).

tff(f12550,plain,
    ( ~ spl18_9
    | spl18_438
    | ~ spl18_98
    | ~ spl18_164 ),
    inference(avatar_split_clause,[],[f2197,f2185,f1254,f12548,f620]) ).

tff(f12548,plain,
    ( spl18_438
  <=> ! [X0: nat] :
        ( ( zero_zero(nat) = semiring_1_of_nat(nat,semiring_1_of_nat(nat,X0)) )
        | ord_less(nat,zero_zero(nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_438])]) ).

tff(f1254,plain,
    ( spl18_98
  <=> ! [X0: $tType,X1: nat] :
        ( ord_less(nat,zero_zero(nat),X1)
        | ~ ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
        | ~ linordered_semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_98])]) ).

tff(f2197,plain,
    ( ! [X0: nat] :
        ( ( zero_zero(nat) = semiring_1_of_nat(nat,semiring_1_of_nat(nat,X0)) )
        | ord_less(nat,zero_zero(nat),X0)
        | ~ linordered_semidom(nat) )
    | ~ spl18_98
    | ~ spl18_164 ),
    inference(resolution,[],[f2186,f1255]) ).

tff(f1255,plain,
    ( ! [X0: $tType,X1: nat] :
        ( ~ ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
        | ord_less(nat,zero_zero(nat),X1)
        | ~ linordered_semidom(X0) )
    | ~ spl18_98 ),
    inference(avatar_component_clause,[],[f1254]) ).

tff(f12546,plain,
    ( spl18_437
    | ~ spl18_142
    | ~ spl18_156 ),
    inference(avatar_split_clause,[],[f2132,f2078,f1885,f12544]) ).

tff(f12544,plain,
    ( spl18_437
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ord_less_eq(nat,X2,X0)
        | ( X1 = X2 )
        | ord_less(nat,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_437])]) ).

tff(f2132,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ord_less_eq(nat,X2,X0)
        | ( X1 = X2 )
        | ord_less(nat,X1,X2) )
    | ~ spl18_142
    | ~ spl18_156 ),
    inference(resolution,[],[f2079,f1886]) ).

tff(f12542,plain,
    ( spl18_436
    | ~ spl18_87
    | ~ spl18_142 ),
    inference(avatar_split_clause,[],[f2014,f1885,f1040,f12540]) ).

tff(f12540,plain,
    ( spl18_436
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( X0 = X1 )
        | ord_less(nat,X1,X0)
        | ~ ord_less_eq(nat,X1,X2)
        | ord_less_eq(nat,X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_436])]) ).

tff(f2014,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( X0 = X1 )
        | ord_less(nat,X1,X0)
        | ~ ord_less_eq(nat,X1,X2)
        | ord_less_eq(nat,X0,X2) )
    | ~ spl18_87
    | ~ spl18_142 ),
    inference(resolution,[],[f1886,f1041]) ).

tff(f12538,plain,
    ( spl18_435
    | ~ spl18_412 ),
    inference(avatar_split_clause,[],[f10649,f9315,f12536]) ).

tff(f12536,plain,
    ( spl18_435
  <=> ! [X0: bool,X1: bool] :
        ( ( fFalse != X0 )
        | ( fFalse = if(bool,fTrue,X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_435])]) ).

tff(f9315,plain,
    ( spl18_412
  <=> ! [X2: bool,X0: bool,X1: bool] :
        ( ( X0 = X2 )
        | ( fFalse = X2 )
        | ( fFalse = if(bool,fTrue,X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_412])]) ).

tff(f10649,plain,
    ( ! [X0: bool,X1: bool] :
        ( ( fFalse != X0 )
        | ( fFalse = if(bool,fTrue,X0,X1) ) )
    | ~ spl18_412 ),
    inference(duplicate_literal_removal,[],[f10640]) ).

tff(f10640,plain,
    ( ! [X0: bool,X1: bool] :
        ( ( fFalse != X0 )
        | ( fFalse = if(bool,fTrue,X0,X1) )
        | ( fFalse = if(bool,fTrue,X0,X1) ) )
    | ~ spl18_412 ),
    inference(equality_factoring,[],[f9316]) ).

tff(f9316,plain,
    ( ! [X2: bool,X0: bool,X1: bool] :
        ( ( X0 = X2 )
        | ( fFalse = X2 )
        | ( fFalse = if(bool,fTrue,X0,X1) ) )
    | ~ spl18_412 ),
    inference(avatar_component_clause,[],[f9315]) ).

tff(f12534,plain,
    ( spl18_434
    | ~ spl18_37
    | ~ spl18_107 ),
    inference(avatar_split_clause,[],[f1440,f1290,f752,f12532]) ).

tff(f12532,plain,
    ( spl18_434
  <=> ! [X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK4(X0))
        | ( fFalse = aa(int,bool,X0,semiring_1_of_nat(int,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_434])]) ).

tff(f1440,plain,
    ( ! [X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK4(X0))
        | ( fFalse = aa(int,bool,X0,semiring_1_of_nat(int,X1)) ) )
    | ~ spl18_37
    | ~ spl18_107 ),
    inference(resolution,[],[f1291,f753]) ).

tff(f12530,plain,
    ( spl18_433
    | ~ spl18_59
    | ~ spl18_81 ),
    inference(avatar_split_clause,[],[f1118,f1016,f852,f12528]) ).

tff(f12528,plain,
    ( spl18_433
  <=> ! [X0: nat,X3: bool,X2: bool,X1: bool] :
        ( ( fFalse = X2 )
        | ( huffma1401021291ibling(bool,huffma2021818691e_Leaf(bool,X0,X1),X2) = X3 )
        | ( fFalse = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_433])]) ).

tff(f1118,plain,
    ( ! [X2: bool,X3: bool,X0: nat,X1: bool] :
        ( ( fFalse = X2 )
        | ( huffma1401021291ibling(bool,huffma2021818691e_Leaf(bool,X0,X1),X2) = X3 )
        | ( fFalse = X3 ) )
    | ~ spl18_59
    | ~ spl18_81 ),
    inference(superposition,[],[f853,f1017]) ).

tff(f12526,plain,
    ( spl18_432
    | ~ spl18_59
    | ~ spl18_81 ),
    inference(avatar_split_clause,[],[f1080,f1016,f852,f12524]) ).

tff(f1080,plain,
    ( ! [X2: bool,X3: bool,X0: nat,X1: bool] :
        ( ( X2 = X3 )
        | ( fFalse = X3 )
        | ( fFalse = huffma1401021291ibling(bool,huffma2021818691e_Leaf(bool,X0,X1),X2) ) )
    | ~ spl18_59
    | ~ spl18_81 ),
    inference(superposition,[],[f853,f1017]) ).

tff(f12522,plain,
    ( spl18_431
    | ~ spl18_81 ),
    inference(avatar_split_clause,[],[f1062,f1016,f12520]) ).

tff(f1062,plain,
    ( ! [X2: bool,X3: bool,X0: bool,X1: bool] :
        ( ( X0 = X1 )
        | ( X1 = X2 )
        | ( X0 = X2 )
        | ( X0 = X3 )
        | ( fFalse = X3 ) )
    | ~ spl18_81 ),
    inference(superposition,[],[f1017,f1017]) ).

tff(f12308,plain,
    ( spl18_430
    | ~ spl18_411 ),
    inference(avatar_split_clause,[],[f9962,f9311,f12306]) ).

tff(f12306,plain,
    ( spl18_430
  <=> ! [X0: bool,X1: bool] :
        ( ( fFalse != X1 )
        | ( fFalse = if(bool,fFalse,X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_430])]) ).

tff(f9311,plain,
    ( spl18_411
  <=> ! [X2: bool,X0: bool,X1: bool] :
        ( ( X1 = X2 )
        | ( fFalse = X2 )
        | ( fFalse = if(bool,fFalse,X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_411])]) ).

tff(f9962,plain,
    ( ! [X0: bool,X1: bool] :
        ( ( fFalse != X1 )
        | ( fFalse = if(bool,fFalse,X0,X1) ) )
    | ~ spl18_411 ),
    inference(duplicate_literal_removal,[],[f9953]) ).

tff(f9953,plain,
    ( ! [X0: bool,X1: bool] :
        ( ( fFalse != X1 )
        | ( fFalse = if(bool,fFalse,X0,X1) )
        | ( fFalse = if(bool,fFalse,X0,X1) ) )
    | ~ spl18_411 ),
    inference(equality_factoring,[],[f9312]) ).

tff(f9312,plain,
    ( ! [X2: bool,X0: bool,X1: bool] :
        ( ( X1 = X2 )
        | ( fFalse = X2 )
        | ( fFalse = if(bool,fFalse,X0,X1) ) )
    | ~ spl18_411 ),
    inference(avatar_component_clause,[],[f9311]) ).

tff(f12297,plain,
    ( spl18_429
    | ~ spl18_30
    | ~ spl18_200 ),
    inference(avatar_split_clause,[],[f2738,f2720,f720,f12295]) ).

tff(f2738,plain,
    ( ! [X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ member(int,zero_zero(int),X0) )
    | ~ spl18_30
    | ~ spl18_200 ),
    inference(resolution,[],[f2721,f722]) ).

tff(f12293,plain,
    ( spl18_428
    | ~ spl18_54
    | ~ spl18_184 ),
    inference(avatar_split_clause,[],[f2435,f2416,f832,f12291]) ).

tff(f12291,plain,
    ( spl18_428
  <=> ! [X0: nat] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,sK1(semiring_1_of_nat(int,X0))) )
        | ( zero_zero(nat) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_428])]) ).

tff(f832,plain,
    ( spl18_54
  <=> ! [X0: nat] :
        ( ord_less(nat,zero_zero(nat),X0)
        | ( zero_zero(nat) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_54])]) ).

tff(f2435,plain,
    ( ! [X0: nat] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,sK1(semiring_1_of_nat(int,X0))) )
        | ( zero_zero(nat) = X0 ) )
    | ~ spl18_54
    | ~ spl18_184 ),
    inference(resolution,[],[f2417,f833]) ).

tff(f833,plain,
    ( ! [X0: nat] :
        ( ord_less(nat,zero_zero(nat),X0)
        | ( zero_zero(nat) = X0 ) )
    | ~ spl18_54 ),
    inference(avatar_component_clause,[],[f832]) ).

tff(f12289,plain,
    ( spl18_427
    | ~ spl18_37
    | ~ spl18_169 ),
    inference(avatar_split_clause,[],[f2269,f2220,f752,f12287]) ).

tff(f12287,plain,
    ( spl18_427
  <=> ! [X0: fun(int,bool)] :
        ( ord_less_eq(int,zero_zero(int),sK4(X0))
        | ( fFalse = aa(int,bool,X0,zero_zero(int)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_427])]) ).

tff(f2269,plain,
    ( ! [X0: fun(int,bool)] :
        ( ord_less_eq(int,zero_zero(int),sK4(X0))
        | ( fFalse = aa(int,bool,X0,zero_zero(int)) ) )
    | ~ spl18_37
    | ~ spl18_169 ),
    inference(resolution,[],[f2221,f753]) ).

tff(f12285,plain,
    ( spl18_426
    | ~ spl18_55
    | ~ spl18_163 ),
    inference(avatar_split_clause,[],[f2246,f2181,f836,f12283]) ).

tff(f12283,plain,
    ( spl18_426
  <=> ! [X0: $tType,X2: X0,X1: huffma1450048681e_tree(X0)] :
        ( ~ ord_less_eq(nat,huffma945805758height(X0,X1),zero_zero(nat))
        | ( zero_zero(nat) = huffma410068972_depth(X0,X1,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_426])]) ).

tff(f836,plain,
    ( spl18_55
  <=> ! [X0: nat] :
        ( ( zero_zero(nat) = X0 )
        | ~ ord_less_eq(nat,X0,zero_zero(nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_55])]) ).

tff(f2246,plain,
    ( ! [X0: $tType,X2: X0,X1: huffma1450048681e_tree(X0)] :
        ( ~ ord_less_eq(nat,huffma945805758height(X0,X1),zero_zero(nat))
        | ( zero_zero(nat) = huffma410068972_depth(X0,X1,X2) ) )
    | ~ spl18_55
    | ~ spl18_163 ),
    inference(resolution,[],[f2182,f837]) ).

tff(f837,plain,
    ( ! [X0: nat] :
        ( ~ ord_less_eq(nat,X0,zero_zero(nat))
        | ( zero_zero(nat) = X0 ) )
    | ~ spl18_55 ),
    inference(avatar_component_clause,[],[f836]) ).

tff(f12272,plain,
    ( ~ spl18_9
    | spl18_425
    | ~ spl18_60
    | ~ spl18_102 ),
    inference(avatar_split_clause,[],[f1386,f1270,f867,f12270,f620]) ).

tff(f12270,plain,
    ( spl18_425
  <=> ! [X0: nat] :
        ( ~ ord_less_eq(nat,semiring_1_of_nat(nat,X0),zero_zero(nat))
        | ord_less_eq(nat,X0,zero_zero(nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_425])]) ).

tff(f1270,plain,
    ( spl18_102
  <=> ! [X0: $tType,X2: nat,X1: nat] :
        ( ord_less_eq(nat,X2,X1)
        | ~ ord_less_eq(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
        | ~ linordered_semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_102])]) ).

tff(f1386,plain,
    ( ! [X0: nat] :
        ( ~ ord_less_eq(nat,semiring_1_of_nat(nat,X0),zero_zero(nat))
        | ord_less_eq(nat,X0,zero_zero(nat))
        | ~ linordered_semidom(nat) )
    | ~ spl18_60
    | ~ spl18_102 ),
    inference(superposition,[],[f1271,f869]) ).

tff(f1271,plain,
    ( ! [X0: $tType,X2: nat,X1: nat] :
        ( ~ ord_less_eq(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
        | ord_less_eq(nat,X2,X1)
        | ~ linordered_semidom(X0) )
    | ~ spl18_102 ),
    inference(avatar_component_clause,[],[f1270]) ).

tff(f12268,plain,
    ( spl18_424
    | ~ spl18_37
    | ~ spl18_94 ),
    inference(avatar_split_clause,[],[f1242,f1211,f752,f12266]) ).

tff(f12266,plain,
    ( spl18_424
  <=> ! [X2: nat,X0: nat,X1: bool] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X1,X0,X2)) )
        | ( fFalse = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_424])]) ).

tff(f1242,plain,
    ( ! [X2: nat,X0: nat,X1: bool] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X1,X0,X2)) )
        | ( fFalse = X1 ) )
    | ~ spl18_37
    | ~ spl18_94 ),
    inference(resolution,[],[f1212,f753]) ).

tff(f12264,plain,
    ( spl18_423
    | ~ spl18_49
    | ~ spl18_81 ),
    inference(avatar_split_clause,[],[f1126,f1016,f808,f12262]) ).

tff(f12262,plain,
    ( spl18_423
  <=> ! [X0: huffma1450048681e_tree(bool),X1: bool] :
        ( member(bool,fFalse,huffma675207370phabet(bool,X0))
        | ( sK14(bool,X0) = X1 )
        | ( fFalse = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_423])]) ).

tff(f1126,plain,
    ( ! [X0: huffma1450048681e_tree(bool),X1: bool] :
        ( member(bool,fFalse,huffma675207370phabet(bool,X0))
        | ( sK14(bool,X0) = X1 )
        | ( fFalse = X1 ) )
    | ~ spl18_49
    | ~ spl18_81 ),
    inference(superposition,[],[f809,f1017]) ).

tff(f12260,plain,
    ( spl18_422
    | ~ spl18_49
    | ~ spl18_81 ),
    inference(avatar_split_clause,[],[f1088,f1016,f808,f12258]) ).

tff(f12258,plain,
    ( spl18_422
  <=> ! [X0: huffma1450048681e_tree(bool),X1: bool] :
        ( member(bool,X1,huffma675207370phabet(bool,X0))
        | ( fFalse = X1 )
        | ( fFalse = sK14(bool,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_422])]) ).

tff(f1088,plain,
    ( ! [X0: huffma1450048681e_tree(bool),X1: bool] :
        ( member(bool,X1,huffma675207370phabet(bool,X0))
        | ( fFalse = X1 )
        | ( fFalse = sK14(bool,X0) ) )
    | ~ spl18_49
    | ~ spl18_81 ),
    inference(superposition,[],[f809,f1017]) ).

tff(f12256,plain,
    ( spl18_421
    | ~ spl18_39
    | ~ spl18_419 ),
    inference(avatar_split_clause,[],[f9361,f9343,f761,f12254]) ).

tff(f12254,plain,
    ( spl18_421
  <=> ! [X0: int] :
        ( ord_less_eq(int,X0,zero_zero(int))
        | ord_less_eq(int,zero_zero(int),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_421])]) ).

tff(f9343,plain,
    ( spl18_419
  <=> ! [X0: int,X1: nat] :
        ( ord_less_eq(int,zero_zero(int),X0)
        | ord_less_eq(int,X0,semiring_1_of_nat(int,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_419])]) ).

tff(f9361,plain,
    ( ! [X0: int] :
        ( ord_less_eq(int,X0,zero_zero(int))
        | ord_less_eq(int,zero_zero(int),X0) )
    | ~ spl18_39
    | ~ spl18_419 ),
    inference(superposition,[],[f9344,f763]) ).

tff(f9344,plain,
    ( ! [X0: int,X1: nat] :
        ( ord_less_eq(int,X0,semiring_1_of_nat(int,X1))
        | ord_less_eq(int,zero_zero(int),X0) )
    | ~ spl18_419 ),
    inference(avatar_component_clause,[],[f9343]) ).

tff(f12186,plain,
    ( spl18_420
    | ~ spl18_38
    | ~ spl18_184 ),
    inference(avatar_split_clause,[],[f2433,f2416,f756,f12183]) ).

tff(f12183,plain,
    ( spl18_420
  <=> ( semiring_1_of_nat(int,huffma945805758height(a1,t_1)) = semiring_1_of_nat(int,sK1(semiring_1_of_nat(int,huffma945805758height(a1,t_1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_420])]) ).

tff(f2433,plain,
    ( ( semiring_1_of_nat(int,huffma945805758height(a1,t_1)) = semiring_1_of_nat(int,sK1(semiring_1_of_nat(int,huffma945805758height(a1,t_1)))) )
    | ~ spl18_38
    | ~ spl18_184 ),
    inference(resolution,[],[f2417,f758]) ).

tff(f9345,plain,
    ( ~ spl18_11
    | spl18_419
    | ~ spl18_61
    | ~ spl18_167 ),
    inference(avatar_split_clause,[],[f2212,f2202,f880,f9343,f630]) ).

tff(f2212,plain,
    ( ! [X0: int,X1: nat] :
        ( ord_less_eq(int,zero_zero(int),X0)
        | ord_less_eq(int,X0,semiring_1_of_nat(int,X1))
        | ~ linorder(int) )
    | ~ spl18_61
    | ~ spl18_167 ),
    inference(resolution,[],[f2203,f881]) ).

tff(f9341,plain,
    ( spl18_418
    | ~ spl18_58
    | ~ spl18_156 ),
    inference(avatar_split_clause,[],[f2135,f2078,f848,f9339]) ).

tff(f9339,plain,
    ( spl18_418
  <=> ! [X1: $tType,X0: nat,X3: X1,X2: huffma1450048681e_tree(X1)] :
        ( ord_less_eq(nat,X0,huffma945805758height(X1,X2))
        | ord_less_eq(nat,huffma410068972_depth(X1,X2,X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_418])]) ).

tff(f848,plain,
    ( spl18_58
  <=> ! [X0: $tType,X2: huffma1450048681e_tree(X0),X1: X0] : ord_less_eq(nat,huffma410068972_depth(X0,X2,X1),huffma945805758height(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_58])]) ).

tff(f2135,plain,
    ( ! [X1: $tType,X2: huffma1450048681e_tree(X1),X3: X1,X0: nat] :
        ( ord_less_eq(nat,X0,huffma945805758height(X1,X2))
        | ord_less_eq(nat,huffma410068972_depth(X1,X2,X3),X0) )
    | ~ spl18_58
    | ~ spl18_156 ),
    inference(resolution,[],[f2079,f849]) ).

tff(f849,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X1: X0] : ord_less_eq(nat,huffma410068972_depth(X0,X2,X1),huffma945805758height(X0,X2))
    | ~ spl18_58 ),
    inference(avatar_component_clause,[],[f848]) ).

tff(f9337,plain,
    ( spl18_417
    | ~ spl18_31
    | ~ spl18_115 ),
    inference(avatar_split_clause,[],[f1725,f1491,f725,f9335]) ).

tff(f9335,plain,
    ( spl18_417
  <=> ! [X2: bool,X0: bool,X1: bool] :
        ( ( fFalse = if(bool,X0,X1,X2) )
        | ( X0 = X1 )
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_417])]) ).

tff(f1491,plain,
    ( spl18_115
  <=> ! [X0: bool,X1: bool] :
        ( ( fTrue = X0 )
        | ( fFalse = if(bool,fTrue,X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_115])]) ).

tff(f1725,plain,
    ( ! [X2: bool,X0: bool,X1: bool] :
        ( ( fFalse = if(bool,X0,X1,X2) )
        | ( X0 = X1 )
        | ( fFalse = X0 ) )
    | ~ spl18_31
    | ~ spl18_115 ),
    inference(superposition,[],[f1492,f726]) ).

tff(f1492,plain,
    ( ! [X0: bool,X1: bool] :
        ( ( fFalse = if(bool,fTrue,X0,X1) )
        | ( fTrue = X0 ) )
    | ~ spl18_115 ),
    inference(avatar_component_clause,[],[f1491]) ).

tff(f9333,plain,
    ( spl18_416
    | ~ spl18_31
    | ~ spl18_108 ),
    inference(avatar_split_clause,[],[f1598,f1434,f725,f9331]) ).

tff(f9331,plain,
    ( spl18_416
  <=> ! [X2: bool,X0: bool,X1: bool] :
        ( ( fTrue = X1 )
        | ( fFalse = X0 )
        | ( fFalse = if(bool,X0,X1,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_416])]) ).

tff(f1598,plain,
    ( ! [X2: bool,X0: bool,X1: bool] :
        ( ( fTrue = X1 )
        | ( fFalse = X0 )
        | ( fFalse = if(bool,X0,X1,X2) ) )
    | ~ spl18_31
    | ~ spl18_108 ),
    inference(superposition,[],[f1435,f726]) ).

tff(f9329,plain,
    ( spl18_415
    | ~ spl18_43
    | ~ spl18_81 ),
    inference(avatar_split_clause,[],[f1120,f1016,f779,f9327]) ).

tff(f9327,plain,
    ( spl18_415
  <=> ! [X2: bool,X0: bool,X1: bool] :
        ( ( fFalse = X0 )
        | ( if(bool,fTrue,X0,X1) = X2 )
        | ( fFalse = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_415])]) ).

tff(f779,plain,
    ( spl18_43
  <=> ! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fTrue,X2,X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_43])]) ).

tff(f1120,plain,
    ( ! [X2: bool,X0: bool,X1: bool] :
        ( ( fFalse = X0 )
        | ( if(bool,fTrue,X0,X1) = X2 )
        | ( fFalse = X2 ) )
    | ~ spl18_43
    | ~ spl18_81 ),
    inference(superposition,[],[f780,f1017]) ).

tff(f780,plain,
    ( ! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fTrue,X2,X1) = X2 )
    | ~ spl18_43 ),
    inference(avatar_component_clause,[],[f779]) ).

tff(f9325,plain,
    ( spl18_414
    | ~ spl18_42
    | ~ spl18_81 ),
    inference(avatar_split_clause,[],[f1119,f1016,f775,f9323]) ).

tff(f9323,plain,
    ( spl18_414
  <=> ! [X2: bool,X0: bool,X1: bool] :
        ( ( fFalse = X1 )
        | ( if(bool,fFalse,X0,X1) = X2 )
        | ( fFalse = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_414])]) ).

tff(f775,plain,
    ( spl18_42
  <=> ! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fFalse,X2,X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_42])]) ).

tff(f1119,plain,
    ( ! [X2: bool,X0: bool,X1: bool] :
        ( ( fFalse = X1 )
        | ( if(bool,fFalse,X0,X1) = X2 )
        | ( fFalse = X2 ) )
    | ~ spl18_42
    | ~ spl18_81 ),
    inference(superposition,[],[f776,f1017]) ).

tff(f776,plain,
    ( ! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fFalse,X2,X1) = X1 )
    | ~ spl18_42 ),
    inference(avatar_component_clause,[],[f775]) ).

tff(f9321,plain,
    ( spl18_413
    | ~ spl18_42
    | ~ spl18_81 ),
    inference(avatar_split_clause,[],[f1108,f1016,f775,f9319]) ).

tff(f1108,plain,
    ( ! [X1: $tType,X2: X1,X3: X1,X0: bool,X4: bool] :
        ( ( if(X1,X0,X2,X3) = X3 )
        | ( X0 = X4 )
        | ( fFalse = X4 ) )
    | ~ spl18_42
    | ~ spl18_81 ),
    inference(superposition,[],[f776,f1017]) ).

tff(f9317,plain,
    ( spl18_412
    | ~ spl18_43
    | ~ spl18_81 ),
    inference(avatar_split_clause,[],[f1082,f1016,f779,f9315]) ).

tff(f1082,plain,
    ( ! [X2: bool,X0: bool,X1: bool] :
        ( ( X0 = X2 )
        | ( fFalse = X2 )
        | ( fFalse = if(bool,fTrue,X0,X1) ) )
    | ~ spl18_43
    | ~ spl18_81 ),
    inference(superposition,[],[f780,f1017]) ).

tff(f9313,plain,
    ( spl18_411
    | ~ spl18_42
    | ~ spl18_81 ),
    inference(avatar_split_clause,[],[f1081,f1016,f775,f9311]) ).

tff(f1081,plain,
    ( ! [X2: bool,X0: bool,X1: bool] :
        ( ( X1 = X2 )
        | ( fFalse = X2 )
        | ( fFalse = if(bool,fFalse,X0,X1) ) )
    | ~ spl18_42
    | ~ spl18_81 ),
    inference(superposition,[],[f776,f1017]) ).

tff(f9309,plain,
    ( spl18_410
    | ~ spl18_66
    | ~ spl18_408 ),
    inference(avatar_split_clause,[],[f9271,f9185,f902,f9307]) ).

tff(f9307,plain,
    ( spl18_410
  <=> ! [X0: fun(int,bool)] :
        ( ~ member(int,zero_zero(int),X0)
        | member(int,sK4(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_410])]) ).

tff(f9185,plain,
    ( spl18_408
  <=> ! [X0: fun(int,bool)] :
        ( ~ member(int,zero_zero(int),X0)
        | pp(aa(int,bool,X0,sK4(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_408])]) ).

tff(f9271,plain,
    ( ! [X0: fun(int,bool)] :
        ( ~ member(int,zero_zero(int),X0)
        | member(int,sK4(X0),X0) )
    | ~ spl18_66
    | ~ spl18_408 ),
    inference(resolution,[],[f9186,f903]) ).

tff(f9186,plain,
    ( ! [X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,sK4(X0)))
        | ~ member(int,zero_zero(int),X0) )
    | ~ spl18_408 ),
    inference(avatar_component_clause,[],[f9185]) ).

tff(f9191,plain,
    ( spl18_409
    | ~ spl18_25
    | ~ spl18_197 ),
    inference(avatar_split_clause,[],[f2677,f2674,f699,f9189]) ).

tff(f2677,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,semiring_1_of_nat(nat,X0),semiring_1_of_nat(nat,X1))
        | ~ ord_less_eq(nat,X0,X1) )
    | ~ spl18_25
    | ~ spl18_197 ),
    inference(resolution,[],[f2675,f700]) ).

tff(f9187,plain,
    ( spl18_408
    | ~ spl18_39
    | ~ spl18_172 ),
    inference(avatar_split_clause,[],[f2301,f2232,f761,f9185]) ).

tff(f2301,plain,
    ( ! [X0: fun(int,bool)] :
        ( ~ member(int,zero_zero(int),X0)
        | pp(aa(int,bool,X0,sK4(X0))) )
    | ~ spl18_39
    | ~ spl18_172 ),
    inference(superposition,[],[f2233,f763]) ).

tff(f9183,plain,
    ( spl18_407
    | ~ spl18_44
    | ~ spl18_156 ),
    inference(avatar_split_clause,[],[f2133,f2078,f788,f9181]) ).

tff(f9181,plain,
    ( spl18_407
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ord_less_eq(nat,X2,X0)
        | ord_less_eq(nat,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_407])]) ).

tff(f2133,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ord_less_eq(nat,X2,X0)
        | ord_less_eq(nat,X1,X2) )
    | ~ spl18_44
    | ~ spl18_156 ),
    inference(resolution,[],[f2079,f789]) ).

tff(f9178,plain,
    ( ~ spl18_5
    | spl18_406
    | ~ spl18_60
    | ~ spl18_78 ),
    inference(avatar_split_clause,[],[f1057,f1004,f867,f9176,f600]) ).

tff(f600,plain,
    ( spl18_5
  <=> semiring_char_0(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_5])]) ).

tff(f9176,plain,
    ( spl18_406
  <=> ! [X0: nat] :
        ( ( zero_zero(nat) != semiring_1_of_nat(nat,X0) )
        | ( zero_zero(nat) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_406])]) ).

tff(f1004,plain,
    ( spl18_78
  <=> ! [X0: $tType,X2: nat,X1: nat] :
        ( ( X1 = X2 )
        | ( semiring_1_of_nat(X0,X1) != semiring_1_of_nat(X0,X2) )
        | ~ semiring_char_0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_78])]) ).

tff(f1057,plain,
    ( ! [X0: nat] :
        ( ( zero_zero(nat) != semiring_1_of_nat(nat,X0) )
        | ( zero_zero(nat) = X0 )
        | ~ semiring_char_0(nat) )
    | ~ spl18_60
    | ~ spl18_78 ),
    inference(superposition,[],[f1005,f869]) ).

tff(f1005,plain,
    ( ! [X0: $tType,X2: nat,X1: nat] :
        ( ( semiring_1_of_nat(X0,X1) != semiring_1_of_nat(X0,X2) )
        | ( X1 = X2 )
        | ~ semiring_char_0(X0) )
    | ~ spl18_78 ),
    inference(avatar_component_clause,[],[f1004]) ).

tff(f9074,plain,
    ( spl18_405
    | ~ spl18_43
    | ~ spl18_181 ),
    inference(avatar_split_clause,[],[f3862,f2396,f779,f9072]) ).

tff(f9072,plain,
    ( spl18_405
  <=> ! [X0: bool,X1: bool] :
        ( ( zero_zero(bool) = X0 )
        | ( fFalse = if(bool,fTrue,X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_405])]) ).

tff(f2396,plain,
    ( spl18_181
  <=> ! [X0: bool] :
        ( ( zero_zero(bool) = X0 )
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_181])]) ).

tff(f3862,plain,
    ( ! [X0: bool,X1: bool] :
        ( ( zero_zero(bool) = X0 )
        | ( fFalse = if(bool,fTrue,X0,X1) ) )
    | ~ spl18_43
    | ~ spl18_181 ),
    inference(superposition,[],[f780,f2397]) ).

tff(f2397,plain,
    ( ! [X0: bool] :
        ( ( zero_zero(bool) = X0 )
        | ( fFalse = X0 ) )
    | ~ spl18_181 ),
    inference(avatar_component_clause,[],[f2396]) ).

tff(f9070,plain,
    ( spl18_404
    | ~ spl18_129
    | ~ spl18_147 ),
    inference(avatar_split_clause,[],[f2013,f1979,f1722,f9068]) ).

tff(f9068,plain,
    ( spl18_404
  <=> ! [X0: $tType,X5: fun(nat,fun(X0,nat)),X3: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X2: nat,X6: nat,X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))))] :
        ( ord_less_eq(nat,huffma1280178957ee_rec(X0,nat,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)),aa(nat,nat,aa(nat,fun(nat,nat),aa(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))),X1,X2),X3),X4),huffma1280178957ee_rec(X0,nat,X5,X1,X3)),X6))
        | ~ ord_less_eq(nat,huffma1280178957ee_rec(X0,nat,X5,X1,X4),X6)
        | ord_less(nat,sK15(aa(nat,fun(nat,nat),aa(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))),X1,X2),X3),X4),huffma1280178957ee_rec(X0,nat,X5,X1,X3))),sK16(aa(nat,fun(nat,nat),aa(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))),X1,X2),X3),X4),huffma1280178957ee_rec(X0,nat,X5,X1,X3)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_404])]) ).

tff(f1979,plain,
    ( spl18_147
  <=> ! [X1: $tType,X0: $tType,X5: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))))),X3: huffma1450048681e_tree(X1),X4: nat,X6: fun(nat,fun(X1,X0)),X2: huffma1450048681e_tree(X1)] : ( huffma1280178957ee_rec(X1,X0,X6,X5,huffma1146269203erNode(X1,X4,X3,X2)) = aa(X0,X0,aa(X0,fun(X0,X0),aa(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0)),aa(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))),aa(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0)))),X5,X4),X3),X2),huffma1280178957ee_rec(X1,X0,X6,X5,X3)),huffma1280178957ee_rec(X1,X0,X6,X5,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_147])]) ).

tff(f2013,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))))),X6: nat,X4: huffma1450048681e_tree(X0),X5: fun(nat,fun(X0,nat))] :
        ( ord_less_eq(nat,huffma1280178957ee_rec(X0,nat,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)),aa(nat,nat,aa(nat,fun(nat,nat),aa(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))),X1,X2),X3),X4),huffma1280178957ee_rec(X0,nat,X5,X1,X3)),X6))
        | ~ ord_less_eq(nat,huffma1280178957ee_rec(X0,nat,X5,X1,X4),X6)
        | ord_less(nat,sK15(aa(nat,fun(nat,nat),aa(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))),X1,X2),X3),X4),huffma1280178957ee_rec(X0,nat,X5,X1,X3))),sK16(aa(nat,fun(nat,nat),aa(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))),X1,X2),X3),X4),huffma1280178957ee_rec(X0,nat,X5,X1,X3)))) )
    | ~ spl18_129
    | ~ spl18_147 ),
    inference(superposition,[],[f1723,f1980]) ).

tff(f1980,plain,
    ( ! [X1: $tType,X0: $tType,X2: huffma1450048681e_tree(X1),X3: huffma1450048681e_tree(X1),X6: fun(nat,fun(X1,X0)),X4: nat,X5: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0)))))] : ( huffma1280178957ee_rec(X1,X0,X6,X5,huffma1146269203erNode(X1,X4,X3,X2)) = aa(X0,X0,aa(X0,fun(X0,X0),aa(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0)),aa(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))),aa(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0)))),X5,X4),X3),X2),huffma1280178957ee_rec(X1,X0,X6,X5,X3)),huffma1280178957ee_rec(X1,X0,X6,X5,X2)) )
    | ~ spl18_147 ),
    inference(avatar_component_clause,[],[f1979]) ).

tff(f9066,plain,
    ( spl18_403
    | ~ spl18_129
    | ~ spl18_147 ),
    inference(avatar_split_clause,[],[f2012,f1979,f1722,f9064]) ).

tff(f9064,plain,
    ( spl18_403
  <=> ! [X0: $tType,X5: fun(nat,fun(X0,nat)),X6: nat,X4: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X2: nat,X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))))] :
        ( ord_less_eq(nat,aa(nat,nat,aa(nat,fun(nat,nat),aa(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))),X1,X2),X3),X4),huffma1280178957ee_rec(X0,nat,X5,X1,X3)),X6),huffma1280178957ee_rec(X0,nat,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)))
        | ~ ord_less_eq(nat,X6,huffma1280178957ee_rec(X0,nat,X5,X1,X4))
        | ord_less(nat,sK15(aa(nat,fun(nat,nat),aa(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))),X1,X2),X3),X4),huffma1280178957ee_rec(X0,nat,X5,X1,X3))),sK16(aa(nat,fun(nat,nat),aa(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))),X1,X2),X3),X4),huffma1280178957ee_rec(X0,nat,X5,X1,X3)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_403])]) ).

tff(f2012,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))))),X6: nat,X4: huffma1450048681e_tree(X0),X5: fun(nat,fun(X0,nat))] :
        ( ord_less_eq(nat,aa(nat,nat,aa(nat,fun(nat,nat),aa(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))),X1,X2),X3),X4),huffma1280178957ee_rec(X0,nat,X5,X1,X3)),X6),huffma1280178957ee_rec(X0,nat,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)))
        | ~ ord_less_eq(nat,X6,huffma1280178957ee_rec(X0,nat,X5,X1,X4))
        | ord_less(nat,sK15(aa(nat,fun(nat,nat),aa(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))),X1,X2),X3),X4),huffma1280178957ee_rec(X0,nat,X5,X1,X3))),sK16(aa(nat,fun(nat,nat),aa(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))),X1,X2),X3),X4),huffma1280178957ee_rec(X0,nat,X5,X1,X3)))) )
    | ~ spl18_129
    | ~ spl18_147 ),
    inference(superposition,[],[f1723,f1980]) ).

tff(f8893,plain,
    ( spl18_402
    | ~ spl18_127
    | ~ spl18_147 ),
    inference(avatar_split_clause,[],[f1983,f1979,f1643,f8891]) ).

tff(f8891,plain,
    ( spl18_402
  <=> ! [X1: $tType,X0: $tType,X2: fun(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))))),X3: nat,X8: huffma1450048681e_tree(X0),X6: fun(nat,fun(X0,X1)),X7: huffma1450048681e_tree(X0),X4: nat,X5: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))))))] : ( huffma1280178957ee_rec(X0,X1,X6,aa(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X2,X3),huffma1146269203erNode(X0,X4,X7,X8)) = aa(X1,X1,aa(X1,fun(X1,X1),aa(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))),huffma107959123e_case(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))),X2,X5,huffma2021818691e_Leaf(nat,X3,X4)),X7),X8),huffma1280178957ee_rec(X0,X1,X6,aa(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X2,X3),X7)),huffma1280178957ee_rec(X0,X1,X6,aa(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X2,X3),X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_402])]) ).

tff(f1983,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))))),X3: nat,X8: huffma1450048681e_tree(X0),X6: fun(nat,fun(X0,X1)),X7: huffma1450048681e_tree(X0),X4: nat,X5: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))))))] : ( huffma1280178957ee_rec(X0,X1,X6,aa(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X2,X3),huffma1146269203erNode(X0,X4,X7,X8)) = aa(X1,X1,aa(X1,fun(X1,X1),aa(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))),huffma107959123e_case(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))),X2,X5,huffma2021818691e_Leaf(nat,X3,X4)),X7),X8),huffma1280178957ee_rec(X0,X1,X6,aa(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X2,X3),X7)),huffma1280178957ee_rec(X0,X1,X6,aa(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X2,X3),X8)) )
    | ~ spl18_127
    | ~ spl18_147 ),
    inference(superposition,[],[f1980,f1644]) ).

tff(f8889,plain,
    ( spl18_401
    | ~ spl18_128
    | ~ spl18_147 ),
    inference(avatar_split_clause,[],[f1982,f1979,f1647,f8887]) ).

tff(f8887,plain,
    ( spl18_401
  <=> ! [X1: $tType,X0: $tType,X2: fun(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))))),X3: nat,X8: huffma1450048681e_tree(X0),X6: fun(nat,fun(X0,X1)),X7: huffma1450048681e_tree(X0),X4: nat,X5: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))),fun(fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))),fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))))))))] : ( huffma1280178957ee_rec(X0,X1,X6,aa(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X2,X3),huffma1146269203erNode(X0,X4,X7,X8)) = aa(X1,X1,aa(X1,fun(X1,X1),aa(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))),huffma1280178957ee_rec(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))),X2,X5,huffma2021818691e_Leaf(nat,X3,X4)),X7),X8),huffma1280178957ee_rec(X0,X1,X6,aa(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X2,X3),X7)),huffma1280178957ee_rec(X0,X1,X6,aa(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X2,X3),X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_401])]) ).

tff(f1982,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))))),X3: nat,X8: huffma1450048681e_tree(X0),X6: fun(nat,fun(X0,X1)),X7: huffma1450048681e_tree(X0),X4: nat,X5: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))),fun(fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))),fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))))))))] : ( huffma1280178957ee_rec(X0,X1,X6,aa(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X2,X3),huffma1146269203erNode(X0,X4,X7,X8)) = aa(X1,X1,aa(X1,fun(X1,X1),aa(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))),huffma1280178957ee_rec(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))),X2,X5,huffma2021818691e_Leaf(nat,X3,X4)),X7),X8),huffma1280178957ee_rec(X0,X1,X6,aa(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X2,X3),X7)),huffma1280178957ee_rec(X0,X1,X6,aa(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X2,X3),X8)) )
    | ~ spl18_128
    | ~ spl18_147 ),
    inference(superposition,[],[f1980,f1648]) ).

tff(f8789,plain,
    ( spl18_400
    | ~ spl18_134
    | ~ spl18_145 ),
    inference(avatar_split_clause,[],[f1953,f1931,f1799,f8787]) ).

tff(f8787,plain,
    ( spl18_400
  <=> ! [X1: $tType,X0: $tType,X3: nat,X4: huffma1450048681e_tree(X0),X6: fun(nat,fun(X0,X1)),X5: fun(huffma1450048681e_tree(X0),X1),X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)))] :
        ( ( huffma107959123e_case(X0,X1,X6,X2,huffma1146269203erNode(X0,X3,X4,sK17(X1,huffma1450048681e_tree(X0),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X3),X4),X5))) != aa(huffma1450048681e_tree(X0),X1,X5,sK17(X1,huffma1450048681e_tree(X0),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X3),X4),X5)) )
        | ( aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X3),X4) = X5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_400])]) ).

tff(f1931,plain,
    ( spl18_145
  <=> ! [X1: $tType,X0: $tType,X3: huffma1450048681e_tree(X1),X4: nat,X6: fun(nat,fun(X1,X0)),X5: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),X0))),X2: huffma1450048681e_tree(X1)] : ( huffma107959123e_case(X1,X0,X6,X5,huffma1146269203erNode(X1,X4,X3,X2)) = aa(huffma1450048681e_tree(X1),X0,aa(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),X0),aa(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),X0)),X5,X4),X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_145])]) ).

tff(f1953,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X3: nat,X6: fun(nat,fun(X0,X1)),X4: huffma1450048681e_tree(X0),X5: fun(huffma1450048681e_tree(X0),X1)] :
        ( ( huffma107959123e_case(X0,X1,X6,X2,huffma1146269203erNode(X0,X3,X4,sK17(X1,huffma1450048681e_tree(X0),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X3),X4),X5))) != aa(huffma1450048681e_tree(X0),X1,X5,sK17(X1,huffma1450048681e_tree(X0),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X3),X4),X5)) )
        | ( aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X3),X4) = X5 ) )
    | ~ spl18_134
    | ~ spl18_145 ),
    inference(superposition,[],[f1800,f1932]) ).

tff(f1932,plain,
    ( ! [X1: $tType,X0: $tType,X2: huffma1450048681e_tree(X1),X3: huffma1450048681e_tree(X1),X6: fun(nat,fun(X1,X0)),X4: nat,X5: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),X0)))] : ( huffma107959123e_case(X1,X0,X6,X5,huffma1146269203erNode(X1,X4,X3,X2)) = aa(huffma1450048681e_tree(X1),X0,aa(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),X0),aa(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),X0)),X5,X4),X3),X2) )
    | ~ spl18_145 ),
    inference(avatar_component_clause,[],[f1931]) ).

tff(f8785,plain,
    ( spl18_399
    | ~ spl18_134
    | ~ spl18_145 ),
    inference(avatar_split_clause,[],[f1952,f1931,f1799,f8783]) ).

tff(f8783,plain,
    ( spl18_399
  <=> ! [X1: $tType,X0: $tType,X5: fun(huffma1450048681e_tree(X0),X1),X6: fun(nat,fun(X0,X1)),X4: huffma1450048681e_tree(X0),X3: nat,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)))] :
        ( ( huffma107959123e_case(X0,X1,X6,X2,huffma1146269203erNode(X0,X3,X4,sK17(X1,huffma1450048681e_tree(X0),X5,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X3),X4)))) != aa(huffma1450048681e_tree(X0),X1,X5,sK17(X1,huffma1450048681e_tree(X0),X5,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X3),X4))) )
        | ( aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X3),X4) = X5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_399])]) ).

tff(f1952,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X3: nat,X6: fun(nat,fun(X0,X1)),X4: huffma1450048681e_tree(X0),X5: fun(huffma1450048681e_tree(X0),X1)] :
        ( ( huffma107959123e_case(X0,X1,X6,X2,huffma1146269203erNode(X0,X3,X4,sK17(X1,huffma1450048681e_tree(X0),X5,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X3),X4)))) != aa(huffma1450048681e_tree(X0),X1,X5,sK17(X1,huffma1450048681e_tree(X0),X5,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X3),X4))) )
        | ( aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X3),X4) = X5 ) )
    | ~ spl18_134
    | ~ spl18_145 ),
    inference(superposition,[],[f1800,f1932]) ).

tff(f8781,plain,
    ( spl18_398
    | ~ spl18_42
    | ~ spl18_181 ),
    inference(avatar_split_clause,[],[f3861,f2396,f775,f8779]) ).

tff(f8779,plain,
    ( spl18_398
  <=> ! [X0: bool,X1: bool] :
        ( ( zero_zero(bool) = X1 )
        | ( fFalse = if(bool,fFalse,X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_398])]) ).

tff(f3861,plain,
    ( ! [X0: bool,X1: bool] :
        ( ( zero_zero(bool) = X1 )
        | ( fFalse = if(bool,fFalse,X0,X1) ) )
    | ~ spl18_42
    | ~ spl18_181 ),
    inference(superposition,[],[f776,f2397]) ).

tff(f8607,plain,
    ( spl18_397
    | ~ spl18_128
    | ~ spl18_147 ),
    inference(avatar_split_clause,[],[f1993,f1979,f1647,f8605]) ).

tff(f8605,plain,
    ( spl18_397
  <=> ! [X1: $tType,X0: $tType,X3: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X4: nat,X7: huffma1450048681e_tree(X0),X6: nat,X5: X0,X2: fun(nat,fun(X0,X1))] : ( huffma1280178957ee_rec(X0,X1,X2,X3,huffma1146269203erNode(X0,X6,X7,huffma2021818691e_Leaf(X0,X4,X5))) = aa(X1,X1,aa(X1,fun(X1,X1),aa(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))),X3,X6),X7),huffma2021818691e_Leaf(X0,X4,X5)),huffma1280178957ee_rec(X0,X1,X2,X3,X7)),aa(X0,X1,aa(nat,fun(X0,X1),X2,X4),X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_397])]) ).

tff(f1993,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X6: nat,X7: huffma1450048681e_tree(X0),X4: nat,X5: X0] : ( huffma1280178957ee_rec(X0,X1,X2,X3,huffma1146269203erNode(X0,X6,X7,huffma2021818691e_Leaf(X0,X4,X5))) = aa(X1,X1,aa(X1,fun(X1,X1),aa(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))),X3,X6),X7),huffma2021818691e_Leaf(X0,X4,X5)),huffma1280178957ee_rec(X0,X1,X2,X3,X7)),aa(X0,X1,aa(nat,fun(X0,X1),X2,X4),X5)) )
    | ~ spl18_128
    | ~ spl18_147 ),
    inference(superposition,[],[f1980,f1648]) ).

tff(f8603,plain,
    ( spl18_396
    | ~ spl18_128
    | ~ spl18_147 ),
    inference(avatar_split_clause,[],[f1987,f1979,f1647,f8601]) ).

tff(f8601,plain,
    ( spl18_396
  <=> ! [X1: $tType,X0: $tType,X5: X0,X6: nat,X4: nat,X7: huffma1450048681e_tree(X0),X3: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X2: fun(nat,fun(X0,X1))] : ( huffma1280178957ee_rec(X0,X1,X2,X3,huffma1146269203erNode(X0,X6,huffma2021818691e_Leaf(X0,X4,X5),X7)) = aa(X1,X1,aa(X1,fun(X1,X1),aa(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))),X3,X6),huffma2021818691e_Leaf(X0,X4,X5)),X7),aa(X0,X1,aa(nat,fun(X0,X1),X2,X4),X5)),huffma1280178957ee_rec(X0,X1,X2,X3,X7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_396])]) ).

tff(f1987,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X6: nat,X7: huffma1450048681e_tree(X0),X4: nat,X5: X0] : ( huffma1280178957ee_rec(X0,X1,X2,X3,huffma1146269203erNode(X0,X6,huffma2021818691e_Leaf(X0,X4,X5),X7)) = aa(X1,X1,aa(X1,fun(X1,X1),aa(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))),X3,X6),huffma2021818691e_Leaf(X0,X4,X5)),X7),aa(X0,X1,aa(nat,fun(X0,X1),X2,X4),X5)),huffma1280178957ee_rec(X0,X1,X2,X3,X7)) )
    | ~ spl18_128
    | ~ spl18_147 ),
    inference(superposition,[],[f1980,f1648]) ).

tff(f8531,plain,
    ( spl18_395
    | ~ spl18_124
    | ~ spl18_147 ),
    inference(avatar_split_clause,[],[f2009,f1979,f1576,f8529]) ).

tff(f8529,plain,
    ( spl18_395
  <=> ! [X1: $tType,X0: $tType,X5: huffma1450048681e_tree(X1),X3: nat,X4: huffma1450048681e_tree(X1),X7: fun(X0,X0),X6: fun(nat,fun(X1,X0)),X2: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0)))))] :
        ( ord_less_eq(X0,huffma1280178957ee_rec(X1,X0,X6,X2,huffma1146269203erNode(X1,X3,X4,X5)),aa(X0,X0,X7,huffma1280178957ee_rec(X1,X0,X6,X2,X5)))
        | ~ ord_less_eq(fun(X0,X0),aa(X0,fun(X0,X0),aa(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0)),aa(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))),aa(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0)))),X2,X3),X4),X5),huffma1280178957ee_rec(X1,X0,X6,X2,X4)),X7)
        | ~ ord(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_395])]) ).

tff(f2009,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))))),X3: nat,X6: fun(nat,fun(X1,X0)),X7: fun(X0,X0),X4: huffma1450048681e_tree(X1),X5: huffma1450048681e_tree(X1)] :
        ( ord_less_eq(X0,huffma1280178957ee_rec(X1,X0,X6,X2,huffma1146269203erNode(X1,X3,X4,X5)),aa(X0,X0,X7,huffma1280178957ee_rec(X1,X0,X6,X2,X5)))
        | ~ ord_less_eq(fun(X0,X0),aa(X0,fun(X0,X0),aa(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0)),aa(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))),aa(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0)))),X2,X3),X4),X5),huffma1280178957ee_rec(X1,X0,X6,X2,X4)),X7)
        | ~ ord(X0) )
    | ~ spl18_124
    | ~ spl18_147 ),
    inference(superposition,[],[f1577,f1980]) ).

tff(f8527,plain,
    ( spl18_394
    | ~ spl18_124
    | ~ spl18_147 ),
    inference(avatar_split_clause,[],[f2008,f1979,f1576,f8525]) ).

tff(f8525,plain,
    ( spl18_394
  <=> ! [X1: $tType,X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))))),X3: nat,X4: huffma1450048681e_tree(X1),X6: fun(nat,fun(X1,X0)),X5: huffma1450048681e_tree(X1),X7: fun(X0,X0)] :
        ( ord_less_eq(X0,aa(X0,X0,X7,huffma1280178957ee_rec(X1,X0,X6,X2,X5)),huffma1280178957ee_rec(X1,X0,X6,X2,huffma1146269203erNode(X1,X3,X4,X5)))
        | ~ ord_less_eq(fun(X0,X0),X7,aa(X0,fun(X0,X0),aa(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0)),aa(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))),aa(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0)))),X2,X3),X4),X5),huffma1280178957ee_rec(X1,X0,X6,X2,X4)))
        | ~ ord(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_394])]) ).

tff(f2008,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))))),X3: nat,X6: fun(nat,fun(X1,X0)),X7: fun(X0,X0),X4: huffma1450048681e_tree(X1),X5: huffma1450048681e_tree(X1)] :
        ( ord_less_eq(X0,aa(X0,X0,X7,huffma1280178957ee_rec(X1,X0,X6,X2,X5)),huffma1280178957ee_rec(X1,X0,X6,X2,huffma1146269203erNode(X1,X3,X4,X5)))
        | ~ ord_less_eq(fun(X0,X0),X7,aa(X0,fun(X0,X0),aa(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0)),aa(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))),aa(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0)))),X2,X3),X4),X5),huffma1280178957ee_rec(X1,X0,X6,X2,X4)))
        | ~ ord(X0) )
    | ~ spl18_124
    | ~ spl18_147 ),
    inference(superposition,[],[f1577,f1980]) ).

tff(f8367,plain,
    ( spl18_393
    | ~ spl18_31
    | ~ spl18_147 ),
    inference(avatar_split_clause,[],[f2005,f1979,f725,f8365]) ).

tff(f8365,plain,
    ( spl18_393
  <=> ! [X0: $tType,X5: fun(nat,fun(X0,bool)),X4: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X2: nat,X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))))] :
        ( ( fTrue = huffma1280178957ee_rec(X0,bool,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)) )
        | ( fFalse = aa(bool,bool,aa(bool,fun(bool,bool),aa(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))),X1,X2),X3),X4),huffma1280178957ee_rec(X0,bool,X5,X1,X3)),huffma1280178957ee_rec(X0,bool,X5,X1,X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_393])]) ).

tff(f2005,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X4: huffma1450048681e_tree(X0),X5: fun(nat,fun(X0,bool))] :
        ( ( fTrue = huffma1280178957ee_rec(X0,bool,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)) )
        | ( fFalse = aa(bool,bool,aa(bool,fun(bool,bool),aa(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))),X1,X2),X3),X4),huffma1280178957ee_rec(X0,bool,X5,X1,X3)),huffma1280178957ee_rec(X0,bool,X5,X1,X4)) ) )
    | ~ spl18_31
    | ~ spl18_147 ),
    inference(superposition,[],[f1980,f726]) ).

tff(f8363,plain,
    ( spl18_392
    | ~ spl18_31
    | ~ spl18_147 ),
    inference(avatar_split_clause,[],[f1998,f1979,f725,f8361]) ).

tff(f8361,plain,
    ( spl18_392
  <=> ! [X0: $tType,X3: huffma1450048681e_tree(X0),X4: nat,X5: huffma1450048681e_tree(X0),X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X1: fun(nat,fun(X0,bool))] :
        ( ( huffma1280178957ee_rec(X0,bool,X1,X2,huffma1146269203erNode(X0,X4,X5,X3)) = aa(bool,bool,aa(bool,fun(bool,bool),aa(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))),X2,X4),X5),X3),huffma1280178957ee_rec(X0,bool,X1,X2,X5)),fTrue) )
        | ( fFalse = huffma1280178957ee_rec(X0,bool,X1,X2,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_392])]) ).

tff(f1998,plain,
    ( ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X3: huffma1450048681e_tree(X0),X1: fun(nat,fun(X0,bool)),X4: nat,X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1280178957ee_rec(X0,bool,X1,X2,huffma1146269203erNode(X0,X4,X5,X3)) = aa(bool,bool,aa(bool,fun(bool,bool),aa(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))),X2,X4),X5),X3),huffma1280178957ee_rec(X0,bool,X1,X2,X5)),fTrue) )
        | ( fFalse = huffma1280178957ee_rec(X0,bool,X1,X2,X3) ) )
    | ~ spl18_31
    | ~ spl18_147 ),
    inference(superposition,[],[f1980,f726]) ).

tff(f8359,plain,
    ( spl18_391
    | ~ spl18_31
    | ~ spl18_147 ),
    inference(avatar_split_clause,[],[f1992,f1979,f725,f8357]) ).

tff(f8357,plain,
    ( spl18_391
  <=> ! [X0: $tType,X3: huffma1450048681e_tree(X0),X4: nat,X5: huffma1450048681e_tree(X0),X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X1: fun(nat,fun(X0,bool))] :
        ( ( huffma1280178957ee_rec(X0,bool,X1,X2,huffma1146269203erNode(X0,X4,X3,X5)) = aa(bool,bool,aa(bool,fun(bool,bool),aa(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))),X2,X4),X3),X5),fTrue),huffma1280178957ee_rec(X0,bool,X1,X2,X5)) )
        | ( fFalse = huffma1280178957ee_rec(X0,bool,X1,X2,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_391])]) ).

tff(f1992,plain,
    ( ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X3: huffma1450048681e_tree(X0),X1: fun(nat,fun(X0,bool)),X4: nat,X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1280178957ee_rec(X0,bool,X1,X2,huffma1146269203erNode(X0,X4,X3,X5)) = aa(bool,bool,aa(bool,fun(bool,bool),aa(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))),X2,X4),X3),X5),fTrue),huffma1280178957ee_rec(X0,bool,X1,X2,X5)) )
        | ( fFalse = huffma1280178957ee_rec(X0,bool,X1,X2,X3) ) )
    | ~ spl18_31
    | ~ spl18_147 ),
    inference(superposition,[],[f1980,f726]) ).

tff(f8272,plain,
    ( spl18_390
    | ~ spl18_65
    | ~ spl18_147 ),
    inference(avatar_split_clause,[],[f2011,f1979,f896,f8270]) ).

tff(f8270,plain,
    ( spl18_390
  <=> ! [X0: $tType,X5: fun(nat,fun(X0,bool)),X4: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X2: nat,X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))))] :
        ( pp(huffma1280178957ee_rec(X0,bool,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)))
        | ~ member(bool,huffma1280178957ee_rec(X0,bool,X5,X1,X4),aa(bool,fun(bool,bool),aa(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))),X1,X2),X3),X4),huffma1280178957ee_rec(X0,bool,X5,X1,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_390])]) ).

tff(f2011,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X4: huffma1450048681e_tree(X0),X5: fun(nat,fun(X0,bool))] :
        ( pp(huffma1280178957ee_rec(X0,bool,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)))
        | ~ member(bool,huffma1280178957ee_rec(X0,bool,X5,X1,X4),aa(bool,fun(bool,bool),aa(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))),X1,X2),X3),X4),huffma1280178957ee_rec(X0,bool,X5,X1,X3))) )
    | ~ spl18_65
    | ~ spl18_147 ),
    inference(superposition,[],[f897,f1980]) ).

tff(f8268,plain,
    ( spl18_389
    | ~ spl18_66
    | ~ spl18_147 ),
    inference(avatar_split_clause,[],[f2010,f1979,f902,f8266]) ).

tff(f8266,plain,
    ( spl18_389
  <=> ! [X0: $tType,X5: fun(nat,fun(X0,bool)),X4: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X2: nat,X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))))] :
        ( ~ pp(huffma1280178957ee_rec(X0,bool,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)))
        | member(bool,huffma1280178957ee_rec(X0,bool,X5,X1,X4),aa(bool,fun(bool,bool),aa(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))),X1,X2),X3),X4),huffma1280178957ee_rec(X0,bool,X5,X1,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_389])]) ).

tff(f2010,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X4: huffma1450048681e_tree(X0),X5: fun(nat,fun(X0,bool))] :
        ( ~ pp(huffma1280178957ee_rec(X0,bool,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)))
        | member(bool,huffma1280178957ee_rec(X0,bool,X5,X1,X4),aa(bool,fun(bool,bool),aa(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))),X1,X2),X3),X4),huffma1280178957ee_rec(X0,bool,X5,X1,X3))) )
    | ~ spl18_66
    | ~ spl18_147 ),
    inference(superposition,[],[f903,f1980]) ).

tff(f8182,plain,
    ( spl18_165
    | spl18_388
    | ~ spl18_31
    | ~ spl18_154 ),
    inference(avatar_split_clause,[],[f4723,f2060,f725,f8180,f2189]) ).

tff(f2189,plain,
    ( spl18_165
  <=> ( fFalse = zero_zero(bool) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_165])]) ).

tff(f8180,plain,
    ( spl18_388
  <=> ! [X0: bool] :
        ( ~ ord_less(bool,X0,fTrue)
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_388])]) ).

tff(f2060,plain,
    ( spl18_154
  <=> ! [X0: bool] :
        ( ~ ord_less(bool,X0,zero_zero(bool))
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_154])]) ).

tff(f4723,plain,
    ( ! [X0: bool] :
        ( ~ ord_less(bool,X0,fTrue)
        | ( fFalse = X0 )
        | ( fFalse = zero_zero(bool) ) )
    | ~ spl18_31
    | ~ spl18_154 ),
    inference(superposition,[],[f2061,f726]) ).

tff(f2061,plain,
    ( ! [X0: bool] :
        ( ~ ord_less(bool,X0,zero_zero(bool))
        | ( fFalse = X0 ) )
    | ~ spl18_154 ),
    inference(avatar_component_clause,[],[f2060]) ).

tff(f8178,plain,
    ( spl18_387
    | ~ spl18_127
    | ~ spl18_147 ),
    inference(avatar_split_clause,[],[f2000,f1979,f1643,f8176]) ).

tff(f8176,plain,
    ( spl18_387
  <=> ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X6: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),nat))),X5: fun(nat,fun(X0,nat)),X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))))] : ( huffma1280178957ee_rec(X0,nat,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)) = huffma107959123e_case(nat,nat,aa(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))),X1,X2),X3),X4),X6,huffma2021818691e_Leaf(nat,huffma1280178957ee_rec(X0,nat,X5,X1,X3),huffma1280178957ee_rec(X0,nat,X5,X1,X4))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_387])]) ).

tff(f2000,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))))),X6: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),nat))),X4: huffma1450048681e_tree(X0),X5: fun(nat,fun(X0,nat))] : ( huffma1280178957ee_rec(X0,nat,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)) = huffma107959123e_case(nat,nat,aa(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))),X1,X2),X3),X4),X6,huffma2021818691e_Leaf(nat,huffma1280178957ee_rec(X0,nat,X5,X1,X3),huffma1280178957ee_rec(X0,nat,X5,X1,X4))) )
    | ~ spl18_127
    | ~ spl18_147 ),
    inference(superposition,[],[f1980,f1644]) ).

tff(f8174,plain,
    ( spl18_386
    | ~ spl18_128
    | ~ spl18_147 ),
    inference(avatar_split_clause,[],[f1999,f1979,f1647,f8172]) ).

tff(f8172,plain,
    ( spl18_386
  <=> ! [X0: $tType,X5: fun(nat,fun(X0,nat)),X6: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(nat,fun(nat,nat))))),X4: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X2: nat,X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))))] : ( huffma1280178957ee_rec(nat,nat,aa(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))),X1,X2),X3),X4),X6,huffma2021818691e_Leaf(nat,huffma1280178957ee_rec(X0,nat,X5,X1,X3),huffma1280178957ee_rec(X0,nat,X5,X1,X4))) = huffma1280178957ee_rec(X0,nat,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_386])]) ).

tff(f1999,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))))),X6: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(nat,fun(nat,nat))))),X4: huffma1450048681e_tree(X0),X5: fun(nat,fun(X0,nat))] : ( huffma1280178957ee_rec(nat,nat,aa(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat))),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(nat,fun(nat,nat)))),X1,X2),X3),X4),X6,huffma2021818691e_Leaf(nat,huffma1280178957ee_rec(X0,nat,X5,X1,X3),huffma1280178957ee_rec(X0,nat,X5,X1,X4))) = huffma1280178957ee_rec(X0,nat,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)) )
    | ~ spl18_128
    | ~ spl18_147 ),
    inference(superposition,[],[f1980,f1648]) ).

tff(f8102,plain,
    ( spl18_385
    | ~ spl18_127
    | ~ spl18_139 ),
    inference(avatar_split_clause,[],[f1895,f1873,f1643,f8100]) ).

tff(f8100,plain,
    ( spl18_385
  <=> ! [X4: nat,X0: fun(nat,fun(nat,nat)),X3: nat,X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),nat))),X1: nat] :
        ( ~ ord_less(nat,aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),sK15(aa(nat,fun(nat,nat),X0,X1))),huffma107959123e_case(nat,nat,X0,X2,huffma2021818691e_Leaf(nat,X1,sK16(aa(nat,fun(nat,nat),X0,X1)))))
        | ~ ord_less_eq(nat,X3,X4)
        | ord_less_eq(nat,aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X3),aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_385])]) ).

tff(f1873,plain,
    ( spl18_139
  <=> ! [X2: fun(nat,nat),X0: nat,X1: nat] :
        ( ord_less_eq(nat,aa(nat,nat,X2,X1),aa(nat,nat,X2,X0))
        | ~ ord_less_eq(nat,X1,X0)
        | ~ ord_less(nat,aa(nat,nat,X2,sK15(X2)),aa(nat,nat,X2,sK16(X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_139])]) ).

tff(f1895,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),nat))),X3: nat,X0: fun(nat,fun(nat,nat)),X1: nat,X4: nat] :
        ( ~ ord_less(nat,aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),sK15(aa(nat,fun(nat,nat),X0,X1))),huffma107959123e_case(nat,nat,X0,X2,huffma2021818691e_Leaf(nat,X1,sK16(aa(nat,fun(nat,nat),X0,X1)))))
        | ~ ord_less_eq(nat,X3,X4)
        | ord_less_eq(nat,aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X3),aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X4)) )
    | ~ spl18_127
    | ~ spl18_139 ),
    inference(superposition,[],[f1874,f1644]) ).

tff(f1874,plain,
    ( ! [X2: fun(nat,nat),X0: nat,X1: nat] :
        ( ~ ord_less(nat,aa(nat,nat,X2,sK15(X2)),aa(nat,nat,X2,sK16(X2)))
        | ~ ord_less_eq(nat,X1,X0)
        | ord_less_eq(nat,aa(nat,nat,X2,X1),aa(nat,nat,X2,X0)) )
    | ~ spl18_139 ),
    inference(avatar_component_clause,[],[f1873]) ).

tff(f8098,plain,
    ( spl18_384
    | ~ spl18_128
    | ~ spl18_139 ),
    inference(avatar_split_clause,[],[f1894,f1873,f1647,f8096]) ).

tff(f8096,plain,
    ( spl18_384
  <=> ! [X4: nat,X0: fun(nat,fun(nat,nat)),X3: nat,X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(nat,fun(nat,nat))))),X1: nat] :
        ( ~ ord_less(nat,aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),sK15(aa(nat,fun(nat,nat),X0,X1))),huffma1280178957ee_rec(nat,nat,X0,X2,huffma2021818691e_Leaf(nat,X1,sK16(aa(nat,fun(nat,nat),X0,X1)))))
        | ~ ord_less_eq(nat,X3,X4)
        | ord_less_eq(nat,aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X3),aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_384])]) ).

tff(f1894,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(nat,fun(nat,nat))))),X3: nat,X0: fun(nat,fun(nat,nat)),X1: nat,X4: nat] :
        ( ~ ord_less(nat,aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),sK15(aa(nat,fun(nat,nat),X0,X1))),huffma1280178957ee_rec(nat,nat,X0,X2,huffma2021818691e_Leaf(nat,X1,sK16(aa(nat,fun(nat,nat),X0,X1)))))
        | ~ ord_less_eq(nat,X3,X4)
        | ord_less_eq(nat,aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X3),aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X4)) )
    | ~ spl18_128
    | ~ spl18_139 ),
    inference(superposition,[],[f1874,f1648]) ).

tff(f8094,plain,
    ( spl18_383
    | ~ spl18_127
    | ~ spl18_139 ),
    inference(avatar_split_clause,[],[f1892,f1873,f1643,f8092]) ).

tff(f8092,plain,
    ( spl18_383
  <=> ! [X4: nat,X0: fun(nat,fun(nat,nat)),X3: nat,X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),nat))),X1: nat] :
        ( ~ ord_less(nat,huffma107959123e_case(nat,nat,X0,X2,huffma2021818691e_Leaf(nat,X1,sK15(aa(nat,fun(nat,nat),X0,X1)))),aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),sK16(aa(nat,fun(nat,nat),X0,X1))))
        | ~ ord_less_eq(nat,X3,X4)
        | ord_less_eq(nat,aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X3),aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_383])]) ).

tff(f1892,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),nat))),X3: nat,X0: fun(nat,fun(nat,nat)),X1: nat,X4: nat] :
        ( ~ ord_less(nat,huffma107959123e_case(nat,nat,X0,X2,huffma2021818691e_Leaf(nat,X1,sK15(aa(nat,fun(nat,nat),X0,X1)))),aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),sK16(aa(nat,fun(nat,nat),X0,X1))))
        | ~ ord_less_eq(nat,X3,X4)
        | ord_less_eq(nat,aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X3),aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X4)) )
    | ~ spl18_127
    | ~ spl18_139 ),
    inference(superposition,[],[f1874,f1644]) ).

tff(f8090,plain,
    ( spl18_382
    | ~ spl18_128
    | ~ spl18_139 ),
    inference(avatar_split_clause,[],[f1891,f1873,f1647,f8088]) ).

tff(f8088,plain,
    ( spl18_382
  <=> ! [X4: nat,X0: fun(nat,fun(nat,nat)),X3: nat,X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(nat,fun(nat,nat))))),X1: nat] :
        ( ~ ord_less(nat,huffma1280178957ee_rec(nat,nat,X0,X2,huffma2021818691e_Leaf(nat,X1,sK15(aa(nat,fun(nat,nat),X0,X1)))),aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),sK16(aa(nat,fun(nat,nat),X0,X1))))
        | ~ ord_less_eq(nat,X3,X4)
        | ord_less_eq(nat,aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X3),aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_382])]) ).

tff(f1891,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(nat,fun(nat,nat))))),X3: nat,X0: fun(nat,fun(nat,nat)),X1: nat,X4: nat] :
        ( ~ ord_less(nat,huffma1280178957ee_rec(nat,nat,X0,X2,huffma2021818691e_Leaf(nat,X1,sK15(aa(nat,fun(nat,nat),X0,X1)))),aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),sK16(aa(nat,fun(nat,nat),X0,X1))))
        | ~ ord_less_eq(nat,X3,X4)
        | ord_less_eq(nat,aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X3),aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X4)) )
    | ~ spl18_128
    | ~ spl18_139 ),
    inference(superposition,[],[f1874,f1648]) ).

tff(f7927,plain,
    ( spl18_381
    | ~ spl18_127
    | ~ spl18_147 ),
    inference(avatar_split_clause,[],[f1985,f1979,f1643,f7925]) ).

tff(f7925,plain,
    ( spl18_381
  <=> ! [X1: $tType,X0: $tType,X5: fun(nat,fun(huffma1450048681e_tree(huffma1450048681e_tree(X0)),fun(huffma1450048681e_tree(huffma1450048681e_tree(X0)),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))))),X3: nat,X4: huffma1450048681e_tree(X0),X7: huffma1450048681e_tree(X0),X6: fun(nat,fun(X0,X1)),X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))))] : ( huffma1280178957ee_rec(X0,X1,X6,X2,huffma1146269203erNode(X0,X3,X4,X7)) = aa(X1,X1,aa(X1,fun(X1,X1),aa(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)),huffma107959123e_case(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))),X2,X5,huffma2021818691e_Leaf(huffma1450048681e_tree(X0),X3,X4)),X7),huffma1280178957ee_rec(X0,X1,X6,X2,X4)),huffma1280178957ee_rec(X0,X1,X6,X2,X7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_381])]) ).

tff(f1985,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X3: nat,X6: fun(nat,fun(X0,X1)),X7: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X5: fun(nat,fun(huffma1450048681e_tree(huffma1450048681e_tree(X0)),fun(huffma1450048681e_tree(huffma1450048681e_tree(X0)),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))))] : ( huffma1280178957ee_rec(X0,X1,X6,X2,huffma1146269203erNode(X0,X3,X4,X7)) = aa(X1,X1,aa(X1,fun(X1,X1),aa(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)),huffma107959123e_case(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))),X2,X5,huffma2021818691e_Leaf(huffma1450048681e_tree(X0),X3,X4)),X7),huffma1280178957ee_rec(X0,X1,X6,X2,X4)),huffma1280178957ee_rec(X0,X1,X6,X2,X7)) )
    | ~ spl18_127
    | ~ spl18_147 ),
    inference(superposition,[],[f1980,f1644]) ).

tff(f7923,plain,
    ( spl18_380
    | ~ spl18_128
    | ~ spl18_147 ),
    inference(avatar_split_clause,[],[f1984,f1979,f1647,f7921]) ).

tff(f7921,plain,
    ( spl18_380
  <=> ! [X1: $tType,X0: $tType,X5: fun(nat,fun(huffma1450048681e_tree(huffma1450048681e_tree(X0)),fun(huffma1450048681e_tree(huffma1450048681e_tree(X0)),fun(fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))),fun(fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))))))),X3: nat,X4: huffma1450048681e_tree(X0),X7: huffma1450048681e_tree(X0),X6: fun(nat,fun(X0,X1)),X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))))] : ( huffma1280178957ee_rec(X0,X1,X6,X2,huffma1146269203erNode(X0,X3,X4,X7)) = aa(X1,X1,aa(X1,fun(X1,X1),aa(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)),huffma1280178957ee_rec(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))),X2,X5,huffma2021818691e_Leaf(huffma1450048681e_tree(X0),X3,X4)),X7),huffma1280178957ee_rec(X0,X1,X6,X2,X4)),huffma1280178957ee_rec(X0,X1,X6,X2,X7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_380])]) ).

tff(f1984,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X3: nat,X6: fun(nat,fun(X0,X1)),X7: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X5: fun(nat,fun(huffma1450048681e_tree(huffma1450048681e_tree(X0)),fun(huffma1450048681e_tree(huffma1450048681e_tree(X0)),fun(fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))),fun(fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))))))] : ( huffma1280178957ee_rec(X0,X1,X6,X2,huffma1146269203erNode(X0,X3,X4,X7)) = aa(X1,X1,aa(X1,fun(X1,X1),aa(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)),huffma1280178957ee_rec(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))),X2,X5,huffma2021818691e_Leaf(huffma1450048681e_tree(X0),X3,X4)),X7),huffma1280178957ee_rec(X0,X1,X6,X2,X4)),huffma1280178957ee_rec(X0,X1,X6,X2,X7)) )
    | ~ spl18_128
    | ~ spl18_147 ),
    inference(superposition,[],[f1980,f1648]) ).

tff(f7891,plain,
    ( spl18_379
    | ~ spl18_125
    | ~ spl18_131 ),
    inference(avatar_split_clause,[],[f1776,f1766,f1580,f7889]) ).

tff(f7889,plain,
    ( spl18_379
  <=> ! [X2: nat,X0: nat,X1: fun(nat,fun(nat,bool))] :
        ( ord_less(nat,X0,sK8(aa(nat,fun(nat,bool),X1,X0)))
        | ( sK8(aa(nat,fun(nat,bool),X1,X0)) = X0 )
        | sP0(sK8(aa(nat,fun(nat,bool),X1,X0)),X0,X1)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X1,X0),X2))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X1,X0),zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_379])]) ).

tff(f1766,plain,
    ( spl18_131
  <=> ! [X2: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        | ord_less(nat,X1,X2)
        | ( X1 = X2 )
        | sP0(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_131])]) ).

tff(f1776,plain,
    ( ! [X2: nat,X0: nat,X1: fun(nat,fun(nat,bool))] :
        ( ord_less(nat,X0,sK8(aa(nat,fun(nat,bool),X1,X0)))
        | ( sK8(aa(nat,fun(nat,bool),X1,X0)) = X0 )
        | sP0(sK8(aa(nat,fun(nat,bool),X1,X0)),X0,X1)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X1,X0),X2))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X1,X0),zero_zero(nat))) )
    | ~ spl18_125
    | ~ spl18_131 ),
    inference(resolution,[],[f1767,f1581]) ).

tff(f1767,plain,
    ( ! [X2: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        | ord_less(nat,X1,X2)
        | ( X1 = X2 )
        | sP0(X2,X1,X0) )
    | ~ spl18_131 ),
    inference(avatar_component_clause,[],[f1766]) ).

tff(f7869,plain,
    ( spl18_378
    | ~ spl18_114
    | ~ spl18_139 ),
    inference(avatar_split_clause,[],[f1890,f1873,f1487,f7867]) ).

tff(f7867,plain,
    ( spl18_378
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat] :
        ( ~ ord_less(nat,zero_zero(nat),aa(nat,nat,huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)),sK16(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)))))
        | ~ ord_less_eq(nat,X2,X3)
        | ord_less_eq(nat,aa(nat,nat,huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)),X2),aa(nat,nat,huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)),X3))
        | ( sK15(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1))) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_378])]) ).

tff(f1487,plain,
    ( spl18_114
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: nat] :
        ( ( zero_zero(nat) = aa(X0,nat,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3) )
        | ( X2 = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_114])]) ).

tff(f1890,plain,
    ( ! [X2: nat,X3: nat,X0: nat,X1: nat] :
        ( ~ ord_less(nat,zero_zero(nat),aa(nat,nat,huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)),sK16(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)))))
        | ~ ord_less_eq(nat,X2,X3)
        | ord_less_eq(nat,aa(nat,nat,huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)),X2),aa(nat,nat,huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)),X3))
        | ( sK15(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1))) = X1 ) )
    | ~ spl18_114
    | ~ spl18_139 ),
    inference(superposition,[],[f1874,f1488]) ).

tff(f1488,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: nat] :
        ( ( zero_zero(nat) = aa(X0,nat,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3) )
        | ( X2 = X3 ) )
    | ~ spl18_114 ),
    inference(avatar_component_clause,[],[f1487]) ).

tff(f7851,plain,
    ( spl18_377
    | ~ spl18_73
    | ~ spl18_146 ),
    inference(avatar_split_clause,[],[f1971,f1957,f942,f7849]) ).

tff(f7849,plain,
    ( spl18_377
  <=> ! [X0: $tType,X2: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0),X3: nat,X1: nat] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),sK6(X0,huffma1146269203erNode(X0,X3,X4,X5))) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X4,X5),sK6(X0,huffma1146269203erNode(X0,X3,X4,X5))) )
        | member(X0,sK6(X0,huffma1146269203erNode(X0,X3,X4,X5)),huffma675207370phabet(X0,X2))
        | ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X4,X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_377])]) ).

tff(f1957,plain,
    ( spl18_146
  <=> ! [X0: $tType,X5: huffma1450048681e_tree(X0),X3: nat,X4: nat,X6: X0,X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X5,huffma1146269203erNode(X0,X3,X2,X1)),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X2,X1),X6) )
        | ~ member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X3,X2,X1)))
        | member(X0,X6,huffma675207370phabet(X0,X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_146])]) ).

tff(f1971,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),sK6(X0,huffma1146269203erNode(X0,X3,X4,X5))) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X4,X5),sK6(X0,huffma1146269203erNode(X0,X3,X4,X5))) )
        | member(X0,sK6(X0,huffma1146269203erNode(X0,X3,X4,X5)),huffma675207370phabet(X0,X2))
        | ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X4,X5)) )
    | ~ spl18_73
    | ~ spl18_146 ),
    inference(resolution,[],[f1958,f943]) ).

tff(f1958,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X6: X0,X4: nat,X5: huffma1450048681e_tree(X0)] :
        ( ~ member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X3,X2,X1)))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X5,huffma1146269203erNode(X0,X3,X2,X1)),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X2,X1),X6) )
        | member(X0,X6,huffma675207370phabet(X0,X5)) )
    | ~ spl18_146 ),
    inference(avatar_component_clause,[],[f1957]) ).

tff(f7633,plain,
    ( spl18_376
    | ~ spl18_127
    | ~ spl18_145 ),
    inference(avatar_split_clause,[],[f1941,f1931,f1643,f7631]) ).

tff(f7631,plain,
    ( spl18_376
  <=> ! [X1: $tType,X0: $tType,X2: fun(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)))),X3: nat,X8: huffma1450048681e_tree(X0),X6: fun(nat,fun(X0,X1)),X7: huffma1450048681e_tree(X0),X4: nat,X5: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)))))] : ( huffma107959123e_case(X0,X1,X6,aa(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X2,X3),huffma1146269203erNode(X0,X4,X7,X8)) = aa(huffma1450048681e_tree(X0),X1,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),huffma107959123e_case(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X5,huffma2021818691e_Leaf(nat,X3,X4)),X7),X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_376])]) ).

tff(f1941,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)))),X3: nat,X8: huffma1450048681e_tree(X0),X6: fun(nat,fun(X0,X1)),X7: huffma1450048681e_tree(X0),X4: nat,X5: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)))))] : ( huffma107959123e_case(X0,X1,X6,aa(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X2,X3),huffma1146269203erNode(X0,X4,X7,X8)) = aa(huffma1450048681e_tree(X0),X1,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),huffma107959123e_case(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X5,huffma2021818691e_Leaf(nat,X3,X4)),X7),X8) )
    | ~ spl18_127
    | ~ spl18_145 ),
    inference(superposition,[],[f1932,f1644]) ).

tff(f7629,plain,
    ( spl18_375
    | ~ spl18_128
    | ~ spl18_145 ),
    inference(avatar_split_clause,[],[f1940,f1931,f1647,f7627]) ).

tff(f7627,plain,
    ( spl18_375
  <=> ! [X1: $tType,X0: $tType,X2: fun(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)))),X3: nat,X8: huffma1450048681e_tree(X0),X6: fun(nat,fun(X0,X1)),X7: huffma1450048681e_tree(X0),X4: nat,X5: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),fun(fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)))))))] : ( huffma107959123e_case(X0,X1,X6,aa(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X2,X3),huffma1146269203erNode(X0,X4,X7,X8)) = aa(huffma1450048681e_tree(X0),X1,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),huffma1280178957ee_rec(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X5,huffma2021818691e_Leaf(nat,X3,X4)),X7),X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_375])]) ).

tff(f1940,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)))),X3: nat,X8: huffma1450048681e_tree(X0),X6: fun(nat,fun(X0,X1)),X7: huffma1450048681e_tree(X0),X4: nat,X5: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),fun(fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)))))))] : ( huffma107959123e_case(X0,X1,X6,aa(nat,fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X2,X3),huffma1146269203erNode(X0,X4,X7,X8)) = aa(huffma1450048681e_tree(X0),X1,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),huffma1280178957ee_rec(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X5,huffma2021818691e_Leaf(nat,X3,X4)),X7),X8) )
    | ~ spl18_128
    | ~ spl18_145 ),
    inference(superposition,[],[f1932,f1648]) ).

tff(f7625,plain,
    ( spl18_374
    | ~ spl18_140
    | ~ spl18_144 ),
    inference(avatar_split_clause,[],[f1925,f1918,f1877,f7623]) ).

tff(f7623,plain,
    ( spl18_374
  <=> ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X10: nat,X1: nat,X8: huffma1450048681e_tree(X0),X6: X0,X9: huffma1450048681e_tree(X0),X7: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,X5,X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),X6) )
        | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X2,X3,X4)))
        | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X7,X8,X9)))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X10,X5,huffma1146269203erNode(X0,X7,X8,X9)),X6) = X6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_374])]) ).

tff(f1877,plain,
    ( spl18_140
  <=> ! [X0: $tType,X5: huffma1450048681e_tree(X0),X3: nat,X4: nat,X6: X0,X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X5,huffma1146269203erNode(X0,X3,X2,X1)),X6) = X6 )
        | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X3,X2,X1)))
        | member(X0,X6,huffma675207370phabet(X0,X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_140])]) ).

tff(f1918,plain,
    ( spl18_144
  <=> ! [X0: $tType,X5: nat,X3: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X2: nat,X6: X0,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,huffma1146269203erNode(X0,X5,X4,X3),X1),X6) = huffma1401021291ibling(X0,X1,X6) )
        | ~ member(X0,X6,huffma675207370phabet(X0,X1))
        | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X5,X4,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_144])]) ).

tff(f1925,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X10: nat,X1: nat,X8: huffma1450048681e_tree(X0),X6: X0,X9: huffma1450048681e_tree(X0),X7: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,X5,X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),X6) )
        | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X2,X3,X4)))
        | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X7,X8,X9)))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X10,X5,huffma1146269203erNode(X0,X7,X8,X9)),X6) = X6 ) )
    | ~ spl18_140
    | ~ spl18_144 ),
    inference(resolution,[],[f1919,f1878]) ).

tff(f1878,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X6: X0,X4: nat,X5: huffma1450048681e_tree(X0)] :
        ( member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X3,X2,X1)))
        | member(X0,X6,huffma675207370phabet(X0,X5))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X5,huffma1146269203erNode(X0,X3,X2,X1)),X6) = X6 ) )
    | ~ spl18_140 ),
    inference(avatar_component_clause,[],[f1877]) ).

tff(f1919,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0),X6: X0,X4: huffma1450048681e_tree(X0),X5: nat] :
        ( ~ member(X0,X6,huffma675207370phabet(X0,X1))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,huffma1146269203erNode(X0,X5,X4,X3),X1),X6) = huffma1401021291ibling(X0,X1,X6) )
        | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X5,X4,X3))) )
    | ~ spl18_144 ),
    inference(avatar_component_clause,[],[f1918]) ).

tff(f7621,plain,
    ( spl18_373
    | ~ spl18_141
    | ~ spl18_144 ),
    inference(avatar_split_clause,[],[f1924,f1918,f1881,f7619]) ).

tff(f7619,plain,
    ( spl18_373
  <=> ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X10: nat,X1: nat,X8: huffma1450048681e_tree(X0),X6: X0,X9: huffma1450048681e_tree(X0),X7: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,X5,X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),X6) )
        | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X2,X3,X4)))
        | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X7,X8,X9)))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X10,huffma1146269203erNode(X0,X7,X8,X9),X5),X6) = X6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_373])]) ).

tff(f1881,plain,
    ( spl18_141
  <=> ! [X0: $tType,X5: nat,X3: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X2: nat,X6: X0,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,huffma1146269203erNode(X0,X5,X4,X3),X1),X6) = X6 )
        | member(X0,X6,huffma675207370phabet(X0,X1))
        | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X5,X4,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_141])]) ).

tff(f1924,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X10: nat,X1: nat,X8: huffma1450048681e_tree(X0),X6: X0,X9: huffma1450048681e_tree(X0),X7: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,X5,X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),X6) )
        | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X2,X3,X4)))
        | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X7,X8,X9)))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X10,huffma1146269203erNode(X0,X7,X8,X9),X5),X6) = X6 ) )
    | ~ spl18_141
    | ~ spl18_144 ),
    inference(resolution,[],[f1919,f1882]) ).

tff(f1882,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0),X6: X0,X4: huffma1450048681e_tree(X0),X5: nat] :
        ( member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X5,X4,X3)))
        | member(X0,X6,huffma675207370phabet(X0,X1))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,huffma1146269203erNode(X0,X5,X4,X3),X1),X6) = X6 ) )
    | ~ spl18_141 ),
    inference(avatar_component_clause,[],[f1881]) ).

tff(f7544,plain,
    ( spl18_372
    | ~ spl18_131
    | ~ spl18_133 ),
    inference(avatar_split_clause,[],[f1802,f1795,f1766,f7542]) ).

tff(f7542,plain,
    ( spl18_372
  <=> ! [X0: fun(nat,fun(nat,bool)),X3: nat,X2: nat,X1: nat] :
        ( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        | ~ ord_less(nat,X2,sK8(aa(nat,fun(nat,bool),X0,X1)))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X3))
        | ord_less(nat,X1,zero_zero(nat))
        | ( zero_zero(nat) = X1 )
        | sP0(zero_zero(nat),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_372])]) ).

tff(f1802,plain,
    ( ! [X2: nat,X3: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        | ~ ord_less(nat,X2,sK8(aa(nat,fun(nat,bool),X0,X1)))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X3))
        | ord_less(nat,X1,zero_zero(nat))
        | ( zero_zero(nat) = X1 )
        | sP0(zero_zero(nat),X1,X0) )
    | ~ spl18_131
    | ~ spl18_133 ),
    inference(resolution,[],[f1796,f1767]) ).

tff(f7409,plain,
    ( spl18_371
    | ~ spl18_137
    | ~ spl18_145 ),
    inference(avatar_split_clause,[],[f1934,f1931,f1844,f7407]) ).

tff(f7407,plain,
    ( spl18_371
  <=> ! [X2: $tType,X0: $tType,X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X2))),X3: fun(nat,fun(X0,X2)),X1: huffma1450048681e_tree(X0)] :
        ( ( aa(huffma1450048681e_tree(X0),X2,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X2),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X2)),X4,sK9(X0,X1)),sK10(X0,X1)),sK11(X0,X1)) = huffma107959123e_case(X0,X2,X3,X4,X1) )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_371])]) ).

tff(f1934,plain,
    ( ! [X0: $tType,X2: $tType,X3: fun(nat,fun(X0,X2)),X1: huffma1450048681e_tree(X0),X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X2)))] :
        ( ( aa(huffma1450048681e_tree(X0),X2,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X2),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X2)),X4,sK9(X0,X1)),sK10(X0,X1)),sK11(X0,X1)) = huffma107959123e_case(X0,X2,X3,X4,X1) )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) )
    | ~ spl18_137
    | ~ spl18_145 ),
    inference(superposition,[],[f1932,f1845]) ).

tff(f7405,plain,
    ( spl18_370
    | ~ spl18_131
    | ~ spl18_136 ),
    inference(avatar_split_clause,[],[f1848,f1840,f1766,f7403]) ).

tff(f7403,plain,
    ( spl18_370
  <=> ! [X0: nat,X3: nat,X2: fun(nat,fun(nat,bool)),X1: nat] :
        ( ~ ord_less(nat,X0,sK7(X1,aa(nat,fun(nat,bool),X2,X3)))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X3),X1))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X3),zero_zero(nat)))
        | ord_less(nat,X3,X0)
        | ( X0 = X3 )
        | sP0(X0,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_370])]) ).

tff(f1848,plain,
    ( ! [X2: fun(nat,fun(nat,bool)),X3: nat,X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,sK7(X1,aa(nat,fun(nat,bool),X2,X3)))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X3),X1))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X3),zero_zero(nat)))
        | ord_less(nat,X3,X0)
        | ( X0 = X3 )
        | sP0(X0,X3,X2) )
    | ~ spl18_131
    | ~ spl18_136 ),
    inference(resolution,[],[f1841,f1767]) ).

tff(f7295,plain,
    ( spl18_369
    | ~ spl18_140
    | ~ spl18_146 ),
    inference(avatar_split_clause,[],[f1969,f1957,f1877,f7293]) ).

tff(f7293,plain,
    ( spl18_369
  <=> ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: nat,X8: nat,X6: X0,X7: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X4,X5),X6) )
        | member(X0,X6,huffma675207370phabet(X0,X2))
        | member(X0,X6,huffma675207370phabet(X0,X7))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X8,X7,huffma1146269203erNode(X0,X3,X4,X5)),X6) = X6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_369])]) ).

tff(f1969,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: nat,X8: nat,X6: X0,X7: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X4,X5),X6) )
        | member(X0,X6,huffma675207370phabet(X0,X2))
        | member(X0,X6,huffma675207370phabet(X0,X7))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X8,X7,huffma1146269203erNode(X0,X3,X4,X5)),X6) = X6 ) )
    | ~ spl18_140
    | ~ spl18_146 ),
    inference(resolution,[],[f1958,f1878]) ).

tff(f7291,plain,
    ( spl18_368
    | ~ spl18_141
    | ~ spl18_146 ),
    inference(avatar_split_clause,[],[f1968,f1957,f1881,f7289]) ).

tff(f7289,plain,
    ( spl18_368
  <=> ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: nat,X8: nat,X6: X0,X7: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X4,X5),X6) )
        | member(X0,X6,huffma675207370phabet(X0,X2))
        | member(X0,X6,huffma675207370phabet(X0,X7))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X8,huffma1146269203erNode(X0,X3,X4,X5),X7),X6) = X6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_368])]) ).

tff(f1968,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: nat,X8: nat,X6: X0,X7: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X4,X5),X6) )
        | member(X0,X6,huffma675207370phabet(X0,X2))
        | member(X0,X6,huffma675207370phabet(X0,X7))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X8,huffma1146269203erNode(X0,X3,X4,X5),X7),X6) = X6 ) )
    | ~ spl18_141
    | ~ spl18_146 ),
    inference(resolution,[],[f1958,f1882]) ).

tff(f7268,plain,
    ( spl18_367
    | ~ spl18_127
    | ~ spl18_136 ),
    inference(avatar_split_clause,[],[f1858,f1840,f1643,f7266]) ).

tff(f7266,plain,
    ( spl18_367
  <=> ! [X4: nat,X0: fun(nat,fun(nat,bool)),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X2: nat,X1: nat] :
        ( ~ pp(huffma107959123e_case(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ~ ord_less(nat,X2,sK7(X4,aa(nat,fun(nat,bool),X0,X1)))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X4))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_367])]) ).

tff(f1858,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X0: fun(nat,fun(nat,bool)),X1: nat,X4: nat] :
        ( ~ pp(huffma107959123e_case(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ~ ord_less(nat,X2,sK7(X4,aa(nat,fun(nat,bool),X0,X1)))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X4))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat))) )
    | ~ spl18_127
    | ~ spl18_136 ),
    inference(superposition,[],[f1841,f1644]) ).

tff(f7264,plain,
    ( spl18_366
    | ~ spl18_128
    | ~ spl18_136 ),
    inference(avatar_split_clause,[],[f1857,f1840,f1647,f7262]) ).

tff(f7262,plain,
    ( spl18_366
  <=> ! [X4: nat,X0: fun(nat,fun(nat,bool)),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X2: nat,X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ~ ord_less(nat,X2,sK7(X4,aa(nat,fun(nat,bool),X0,X1)))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X4))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_366])]) ).

tff(f1857,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X0: fun(nat,fun(nat,bool)),X1: nat,X4: nat] :
        ( ~ pp(huffma1280178957ee_rec(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ~ ord_less(nat,X2,sK7(X4,aa(nat,fun(nat,bool),X0,X1)))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X4))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat))) )
    | ~ spl18_128
    | ~ spl18_136 ),
    inference(superposition,[],[f1841,f1648]) ).

tff(f7034,plain,
    ( spl18_365
    | ~ spl18_127
    | ~ spl18_134 ),
    inference(avatar_split_clause,[],[f1831,f1799,f1643,f7032]) ).

tff(f7032,plain,
    ( spl18_365
  <=> ! [X1: $tType,X0: $tType,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X4: fun(X0,X1),X3: nat,X2: fun(nat,fun(X0,X1))] :
        ( ( aa(X0,X1,X4,sK17(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4)) != huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,sK17(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4))) )
        | ( aa(nat,fun(X0,X1),X2,X3) = X4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_365])]) ).

tff(f1831,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X4: fun(X0,X1),X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)))] :
        ( ( aa(X0,X1,X4,sK17(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4)) != huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,sK17(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4))) )
        | ( aa(nat,fun(X0,X1),X2,X3) = X4 ) )
    | ~ spl18_127
    | ~ spl18_134 ),
    inference(superposition,[],[f1800,f1644]) ).

tff(f7030,plain,
    ( spl18_364
    | ~ spl18_128
    | ~ spl18_134 ),
    inference(avatar_split_clause,[],[f1830,f1799,f1647,f7028]) ).

tff(f7028,plain,
    ( spl18_364
  <=> ! [X1: $tType,X0: $tType,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X4: fun(X0,X1),X3: nat,X2: fun(nat,fun(X0,X1))] :
        ( ( huffma1280178957ee_rec(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,sK17(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4))) != aa(X0,X1,X4,sK17(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4)) )
        | ( aa(nat,fun(X0,X1),X2,X3) = X4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_364])]) ).

tff(f1830,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X4: fun(X0,X1),X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))))] :
        ( ( huffma1280178957ee_rec(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,sK17(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4))) != aa(X0,X1,X4,sK17(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4)) )
        | ( aa(nat,fun(X0,X1),X2,X3) = X4 ) )
    | ~ spl18_128
    | ~ spl18_134 ),
    inference(superposition,[],[f1800,f1648]) ).

tff(f7020,plain,
    ( spl18_363
    | ~ spl18_127
    | ~ spl18_134 ),
    inference(avatar_split_clause,[],[f1818,f1799,f1643,f7018]) ).

tff(f7018,plain,
    ( spl18_363
  <=> ! [X1: $tType,X0: $tType,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X4: fun(X0,X1),X3: nat,X2: fun(nat,fun(X0,X1))] :
        ( ( aa(X0,X1,X4,sK17(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3))) != huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,sK17(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3)))) )
        | ( aa(nat,fun(X0,X1),X2,X3) = X4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_363])]) ).

tff(f1818,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X4: fun(X0,X1),X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)))] :
        ( ( aa(X0,X1,X4,sK17(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3))) != huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,sK17(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3)))) )
        | ( aa(nat,fun(X0,X1),X2,X3) = X4 ) )
    | ~ spl18_127
    | ~ spl18_134 ),
    inference(superposition,[],[f1800,f1644]) ).

tff(f7016,plain,
    ( spl18_362
    | ~ spl18_128
    | ~ spl18_134 ),
    inference(avatar_split_clause,[],[f1817,f1799,f1647,f7014]) ).

tff(f7014,plain,
    ( spl18_362
  <=> ! [X1: $tType,X0: $tType,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X4: fun(X0,X1),X3: nat,X2: fun(nat,fun(X0,X1))] :
        ( ( huffma1280178957ee_rec(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,sK17(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3)))) != aa(X0,X1,X4,sK17(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3))) )
        | ( aa(nat,fun(X0,X1),X2,X3) = X4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_362])]) ).

tff(f1817,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X4: fun(X0,X1),X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))))] :
        ( ( huffma1280178957ee_rec(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,sK17(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3)))) != aa(X0,X1,X4,sK17(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3))) )
        | ( aa(nat,fun(X0,X1),X2,X3) = X4 ) )
    | ~ spl18_128
    | ~ spl18_134 ),
    inference(superposition,[],[f1800,f1648]) ).

tff(f7012,plain,
    ( spl18_361
    | ~ spl18_127
    | ~ spl18_133 ),
    inference(avatar_split_clause,[],[f1812,f1795,f1643,f7010]) ).

tff(f7010,plain,
    ( spl18_361
  <=> ! [X4: nat,X0: fun(nat,fun(nat,bool)),X3: nat,X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X1: nat] :
        ( ~ pp(huffma107959123e_case(nat,bool,X0,X2,huffma2021818691e_Leaf(nat,X1,zero_zero(nat))))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X3))
        | ~ ord_less(nat,X3,sK8(aa(nat,fun(nat,bool),X0,X1)))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_361])]) ).

tff(f1812,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X3: nat,X0: fun(nat,fun(nat,bool)),X1: nat,X4: nat] :
        ( ~ pp(huffma107959123e_case(nat,bool,X0,X2,huffma2021818691e_Leaf(nat,X1,zero_zero(nat))))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X3))
        | ~ ord_less(nat,X3,sK8(aa(nat,fun(nat,bool),X0,X1)))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X4)) )
    | ~ spl18_127
    | ~ spl18_133 ),
    inference(superposition,[],[f1796,f1644]) ).

tff(f7008,plain,
    ( spl18_360
    | ~ spl18_128
    | ~ spl18_133 ),
    inference(avatar_split_clause,[],[f1811,f1795,f1647,f7006]) ).

tff(f7006,plain,
    ( spl18_360
  <=> ! [X4: nat,X0: fun(nat,fun(nat,bool)),X3: nat,X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(nat,bool,X0,X2,huffma2021818691e_Leaf(nat,X1,zero_zero(nat))))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X3))
        | ~ ord_less(nat,X3,sK8(aa(nat,fun(nat,bool),X0,X1)))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_360])]) ).

tff(f1811,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X3: nat,X0: fun(nat,fun(nat,bool)),X1: nat,X4: nat] :
        ( ~ pp(huffma1280178957ee_rec(nat,bool,X0,X2,huffma2021818691e_Leaf(nat,X1,zero_zero(nat))))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X3))
        | ~ ord_less(nat,X3,sK8(aa(nat,fun(nat,bool),X0,X1)))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X4)) )
    | ~ spl18_128
    | ~ spl18_133 ),
    inference(superposition,[],[f1796,f1648]) ).

tff(f6889,plain,
    ( spl18_359
    | ~ spl18_145
    | ~ spl18_147 ),
    inference(avatar_split_clause,[],[f1986,f1979,f1931,f6887]) ).

tff(f6887,plain,
    ( spl18_359
  <=> ! [X1: $tType,X0: $tType,X3: nat,X4: huffma1450048681e_tree(X0),X7: fun(nat,fun(X0,X1)),X6: fun(nat,fun(X0,fun(X1,fun(X1,X1)))),X5: huffma1450048681e_tree(X0),X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))))] : ( huffma1280178957ee_rec(X0,X1,X7,X2,huffma1146269203erNode(X0,X3,X4,X5)) = aa(X1,X1,aa(X1,fun(X1,X1),huffma107959123e_case(X0,fun(X1,fun(X1,X1)),X6,X2,huffma1146269203erNode(X0,X3,X4,X5)),huffma1280178957ee_rec(X0,X1,X7,X2,X4)),huffma1280178957ee_rec(X0,X1,X7,X2,X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_359])]) ).

tff(f1986,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X3: nat,X6: fun(nat,fun(X0,fun(X1,fun(X1,X1)))),X7: fun(nat,fun(X0,X1)),X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] : ( huffma1280178957ee_rec(X0,X1,X7,X2,huffma1146269203erNode(X0,X3,X4,X5)) = aa(X1,X1,aa(X1,fun(X1,X1),huffma107959123e_case(X0,fun(X1,fun(X1,X1)),X6,X2,huffma1146269203erNode(X0,X3,X4,X5)),huffma1280178957ee_rec(X0,X1,X7,X2,X4)),huffma1280178957ee_rec(X0,X1,X7,X2,X5)) )
    | ~ spl18_145
    | ~ spl18_147 ),
    inference(superposition,[],[f1980,f1932]) ).

tff(f6885,plain,
    ( spl18_358
    | ~ spl18_49
    | ~ spl18_146 ),
    inference(avatar_split_clause,[],[f1970,f1957,f808,f6883]) ).

tff(f6883,plain,
    ( spl18_358
  <=> ! [X0: $tType,X2: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0),X3: nat,X1: nat] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),sK14(X0,huffma1146269203erNode(X0,X3,X4,X5))) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X4,X5),sK14(X0,huffma1146269203erNode(X0,X3,X4,X5))) )
        | member(X0,sK14(X0,huffma1146269203erNode(X0,X3,X4,X5)),huffma675207370phabet(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_358])]) ).

tff(f1970,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),sK14(X0,huffma1146269203erNode(X0,X3,X4,X5))) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X4,X5),sK14(X0,huffma1146269203erNode(X0,X3,X4,X5))) )
        | member(X0,sK14(X0,huffma1146269203erNode(X0,X3,X4,X5)),huffma675207370phabet(X0,X2)) )
    | ~ spl18_49
    | ~ spl18_146 ),
    inference(resolution,[],[f1958,f809]) ).

tff(f6875,plain,
    ( spl18_357
    | ~ spl18_124
    | ~ spl18_145 ),
    inference(avatar_split_clause,[],[f1951,f1931,f1576,f6873]) ).

tff(f6873,plain,
    ( spl18_357
  <=> ! [X1: $tType,X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X3: nat,X4: huffma1450048681e_tree(X0),X7: fun(huffma1450048681e_tree(X0),X1),X6: fun(nat,fun(X0,X1)),X5: huffma1450048681e_tree(X0)] :
        ( ord_less_eq(X1,huffma107959123e_case(X0,X1,X6,X2,huffma1146269203erNode(X0,X3,X4,X5)),aa(huffma1450048681e_tree(X0),X1,X7,X5))
        | ~ ord_less_eq(fun(huffma1450048681e_tree(X0),X1),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X3),X4),X7)
        | ~ ord(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_357])]) ).

tff(f1951,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X3: nat,X6: fun(nat,fun(X0,X1)),X7: fun(huffma1450048681e_tree(X0),X1),X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ord_less_eq(X1,huffma107959123e_case(X0,X1,X6,X2,huffma1146269203erNode(X0,X3,X4,X5)),aa(huffma1450048681e_tree(X0),X1,X7,X5))
        | ~ ord_less_eq(fun(huffma1450048681e_tree(X0),X1),aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X3),X4),X7)
        | ~ ord(X1) )
    | ~ spl18_124
    | ~ spl18_145 ),
    inference(superposition,[],[f1577,f1932]) ).

tff(f6871,plain,
    ( spl18_356
    | ~ spl18_124
    | ~ spl18_145 ),
    inference(avatar_split_clause,[],[f1950,f1931,f1576,f6869]) ).

tff(f6869,plain,
    ( spl18_356
  <=> ! [X1: $tType,X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X6: fun(nat,fun(X0,X1)),X4: huffma1450048681e_tree(X0),X7: fun(huffma1450048681e_tree(X0),X1),X5: huffma1450048681e_tree(X0),X3: nat] :
        ( ord_less_eq(X1,aa(huffma1450048681e_tree(X0),X1,X7,X5),huffma107959123e_case(X0,X1,X6,X2,huffma1146269203erNode(X0,X3,X4,X5)))
        | ~ ord_less_eq(fun(huffma1450048681e_tree(X0),X1),X7,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X3),X4))
        | ~ ord(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_356])]) ).

tff(f1950,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X3: nat,X6: fun(nat,fun(X0,X1)),X7: fun(huffma1450048681e_tree(X0),X1),X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ord_less_eq(X1,aa(huffma1450048681e_tree(X0),X1,X7,X5),huffma107959123e_case(X0,X1,X6,X2,huffma1146269203erNode(X0,X3,X4,X5)))
        | ~ ord_less_eq(fun(huffma1450048681e_tree(X0),X1),X7,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)),X2,X3),X4))
        | ~ ord(X1) )
    | ~ spl18_124
    | ~ spl18_145 ),
    inference(superposition,[],[f1577,f1932]) ).

tff(f6767,plain,
    ( spl18_355
    | ~ spl18_127
    | ~ spl18_129 ),
    inference(avatar_split_clause,[],[f1755,f1722,f1643,f6765]) ).

tff(f6765,plain,
    ( spl18_355
  <=> ! [X4: nat,X0: fun(nat,fun(nat,nat)),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),nat))),X2: nat,X1: nat] :
        ( ord_less_eq(nat,aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X4),huffma107959123e_case(nat,nat,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ~ ord_less_eq(nat,X4,X2)
        | ord_less(nat,sK15(aa(nat,fun(nat,nat),X0,X1)),sK16(aa(nat,fun(nat,nat),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_355])]) ).

tff(f1755,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),nat))),X0: fun(nat,fun(nat,nat)),X1: nat,X4: nat] :
        ( ord_less_eq(nat,aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X4),huffma107959123e_case(nat,nat,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ~ ord_less_eq(nat,X4,X2)
        | ord_less(nat,sK15(aa(nat,fun(nat,nat),X0,X1)),sK16(aa(nat,fun(nat,nat),X0,X1))) )
    | ~ spl18_127
    | ~ spl18_129 ),
    inference(superposition,[],[f1723,f1644]) ).

tff(f6763,plain,
    ( spl18_354
    | ~ spl18_128
    | ~ spl18_129 ),
    inference(avatar_split_clause,[],[f1754,f1722,f1647,f6761]) ).

tff(f6761,plain,
    ( spl18_354
  <=> ! [X4: nat,X0: fun(nat,fun(nat,nat)),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(nat,fun(nat,nat))))),X2: nat,X1: nat] :
        ( ord_less_eq(nat,aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X4),huffma1280178957ee_rec(nat,nat,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ~ ord_less_eq(nat,X4,X2)
        | ord_less(nat,sK15(aa(nat,fun(nat,nat),X0,X1)),sK16(aa(nat,fun(nat,nat),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_354])]) ).

tff(f1754,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(nat,fun(nat,nat))))),X0: fun(nat,fun(nat,nat)),X1: nat,X4: nat] :
        ( ord_less_eq(nat,aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X4),huffma1280178957ee_rec(nat,nat,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ~ ord_less_eq(nat,X4,X2)
        | ord_less(nat,sK15(aa(nat,fun(nat,nat),X0,X1)),sK16(aa(nat,fun(nat,nat),X0,X1))) )
    | ~ spl18_128
    | ~ spl18_129 ),
    inference(superposition,[],[f1723,f1648]) ).

tff(f6759,plain,
    ( spl18_353
    | ~ spl18_127
    | ~ spl18_129 ),
    inference(avatar_split_clause,[],[f1751,f1722,f1643,f6757]) ).

tff(f6757,plain,
    ( spl18_353
  <=> ! [X2: nat,X4: nat,X0: fun(nat,fun(nat,nat)),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),nat))),X1: nat] :
        ( ord_less_eq(nat,huffma107959123e_case(nat,nat,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)),aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X4))
        | ~ ord_less_eq(nat,X2,X4)
        | ord_less(nat,sK15(aa(nat,fun(nat,nat),X0,X1)),sK16(aa(nat,fun(nat,nat),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_353])]) ).

tff(f1751,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),nat))),X0: fun(nat,fun(nat,nat)),X1: nat,X4: nat] :
        ( ord_less_eq(nat,huffma107959123e_case(nat,nat,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)),aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X4))
        | ~ ord_less_eq(nat,X2,X4)
        | ord_less(nat,sK15(aa(nat,fun(nat,nat),X0,X1)),sK16(aa(nat,fun(nat,nat),X0,X1))) )
    | ~ spl18_127
    | ~ spl18_129 ),
    inference(superposition,[],[f1723,f1644]) ).

tff(f6755,plain,
    ( spl18_352
    | ~ spl18_128
    | ~ spl18_129 ),
    inference(avatar_split_clause,[],[f1750,f1722,f1647,f6753]) ).

tff(f6753,plain,
    ( spl18_352
  <=> ! [X2: nat,X4: nat,X0: fun(nat,fun(nat,nat)),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(nat,fun(nat,nat))))),X1: nat] :
        ( ord_less_eq(nat,huffma1280178957ee_rec(nat,nat,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)),aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X4))
        | ~ ord_less_eq(nat,X2,X4)
        | ord_less(nat,sK15(aa(nat,fun(nat,nat),X0,X1)),sK16(aa(nat,fun(nat,nat),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_352])]) ).

tff(f1750,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(nat,fun(nat,nat))))),X0: fun(nat,fun(nat,nat)),X1: nat,X4: nat] :
        ( ord_less_eq(nat,huffma1280178957ee_rec(nat,nat,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)),aa(nat,nat,aa(nat,fun(nat,nat),X0,X1),X4))
        | ~ ord_less_eq(nat,X2,X4)
        | ord_less(nat,sK15(aa(nat,fun(nat,nat),X0,X1)),sK16(aa(nat,fun(nat,nat),X0,X1))) )
    | ~ spl18_128
    | ~ spl18_129 ),
    inference(superposition,[],[f1723,f1648]) ).

tff(f6684,plain,
    ( spl18_351
    | ~ spl18_126
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1717,f1647,f1639,f6682]) ).

tff(f6682,plain,
    ( spl18_351
  <=> ! [X0: fun(nat,fun(nat,bool)),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X2: nat,X1: nat] :
        ( pp(huffma1280178957ee_rec(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,sK7(X2,aa(nat,fun(nat,bool),X0,X1)))))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_351])]) ).

tff(f1717,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( pp(huffma1280178957ee_rec(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,sK7(X2,aa(nat,fun(nat,bool),X0,X1)))))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat))) )
    | ~ spl18_126
    | ~ spl18_128 ),
    inference(superposition,[],[f1640,f1648]) ).

tff(f6680,plain,
    ( spl18_350
    | ~ spl18_126
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1686,f1643,f1639,f6678]) ).

tff(f6678,plain,
    ( spl18_350
  <=> ! [X0: fun(nat,fun(nat,bool)),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X2: nat,X1: nat] :
        ( pp(huffma107959123e_case(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,sK7(X2,aa(nat,fun(nat,bool),X0,X1)))))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_350])]) ).

tff(f1686,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( pp(huffma107959123e_case(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,sK7(X2,aa(nat,fun(nat,bool),X0,X1)))))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat))) )
    | ~ spl18_126
    | ~ spl18_127 ),
    inference(superposition,[],[f1640,f1644]) ).

tff(f6630,plain,
    ( spl18_349
    | ~ spl18_125
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1718,f1647,f1580,f6628]) ).

tff(f6628,plain,
    ( spl18_349
  <=> ! [X0: fun(nat,fun(nat,bool)),X3: nat,X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(nat,bool,X0,X2,huffma2021818691e_Leaf(nat,X1,sK8(aa(nat,fun(nat,bool),X0,X1)))))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X3))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_349])]) ).

tff(f1718,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X3: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(nat,bool,X0,X2,huffma2021818691e_Leaf(nat,X1,sK8(aa(nat,fun(nat,bool),X0,X1)))))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X3))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat))) )
    | ~ spl18_125
    | ~ spl18_128 ),
    inference(superposition,[],[f1581,f1648]) ).

tff(f6626,plain,
    ( spl18_348
    | ~ spl18_125
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1687,f1643,f1580,f6624]) ).

tff(f6624,plain,
    ( spl18_348
  <=> ! [X0: fun(nat,fun(nat,bool)),X3: nat,X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X1: nat] :
        ( ~ pp(huffma107959123e_case(nat,bool,X0,X2,huffma2021818691e_Leaf(nat,X1,sK8(aa(nat,fun(nat,bool),X0,X1)))))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X3))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_348])]) ).

tff(f1687,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X3: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( ~ pp(huffma107959123e_case(nat,bool,X0,X2,huffma2021818691e_Leaf(nat,X1,sK8(aa(nat,fun(nat,bool),X0,X1)))))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X3))
        | ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat))) )
    | ~ spl18_125
    | ~ spl18_127 ),
    inference(superposition,[],[f1581,f1644]) ).

tff(f6600,plain,
    ( spl18_347
    | ~ spl18_155
    | ~ spl18_185 ),
    inference(avatar_split_clause,[],[f2423,f2420,f2074,f6598]) ).

tff(f6598,plain,
    ( spl18_347
  <=> ! [X0: nat] :
        ( ( zero_zero(int) = semiring_1_of_nat(int,X0) )
        | ~ ord_less_eq(nat,X0,zero_zero(nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_347])]) ).

tff(f2420,plain,
    ( spl18_185
  <=> ! [X0: nat] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int))
        | ( zero_zero(int) = semiring_1_of_nat(int,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_185])]) ).

tff(f2423,plain,
    ( ! [X0: nat] :
        ( ( zero_zero(int) = semiring_1_of_nat(int,X0) )
        | ~ ord_less_eq(nat,X0,zero_zero(nat)) )
    | ~ spl18_155
    | ~ spl18_185 ),
    inference(resolution,[],[f2421,f2075]) ).

tff(f2421,plain,
    ( ! [X0: nat] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int))
        | ( zero_zero(int) = semiring_1_of_nat(int,X0) ) )
    | ~ spl18_185 ),
    inference(avatar_component_clause,[],[f2420]) ).

tff(f6561,plain,
    ( spl18_346
    | ~ spl18_112
    | ~ spl18_146 ),
    inference(avatar_split_clause,[],[f1974,f1957,f1479,f6559]) ).

tff(f6559,plain,
    ( spl18_346
  <=> ! [X0: $tType,X5: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X6: X0,X3: nat,X1: nat] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X4,X5),X6) )
        | member(X0,X6,huffma675207370phabet(X0,X2))
        | ( zero_zero(nat) = aa(X0,nat,huffma1352802255e_freq(X0,huffma1146269203erNode(X0,X3,X4,X5)),X6) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_346])]) ).

tff(f1974,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: nat,X6: X0,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X4,X5),X6) )
        | member(X0,X6,huffma675207370phabet(X0,X2))
        | ( zero_zero(nat) = aa(X0,nat,huffma1352802255e_freq(X0,huffma1146269203erNode(X0,X3,X4,X5)),X6) ) )
    | ~ spl18_112
    | ~ spl18_146 ),
    inference(resolution,[],[f1958,f1480]) ).

tff(f6557,plain,
    ( spl18_345
    | ~ spl18_140
    | ~ spl18_143 ),
    inference(avatar_split_clause,[],[f1909,f1905,f1877,f6555]) ).

tff(f6555,plain,
    ( spl18_345
  <=> ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: nat,X8: nat,X6: X0,X7: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X3,X4),X6) )
        | member(X0,X6,huffma675207370phabet(X0,X7))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X8,X7,huffma1146269203erNode(X0,X2,X3,X4)),X6) = X6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_345])]) ).

tff(f1905,plain,
    ( spl18_143
  <=> ! [X0: $tType,X5: nat,X4: huffma1450048681e_tree(X0),X2: nat,X6: X0,X3: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,huffma1146269203erNode(X0,X5,X4,X3),X1),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X5,X4,X3),X6) )
        | ~ member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X5,X4,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_143])]) ).

tff(f1909,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: nat,X8: nat,X6: X0,X7: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X3,X4),X6) )
        | member(X0,X6,huffma675207370phabet(X0,X7))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X8,X7,huffma1146269203erNode(X0,X2,X3,X4)),X6) = X6 ) )
    | ~ spl18_140
    | ~ spl18_143 ),
    inference(resolution,[],[f1906,f1878]) ).

tff(f1906,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0),X6: X0,X4: huffma1450048681e_tree(X0),X5: nat] :
        ( ~ member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X5,X4,X3)))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,huffma1146269203erNode(X0,X5,X4,X3),X1),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X5,X4,X3),X6) ) )
    | ~ spl18_143 ),
    inference(avatar_component_clause,[],[f1905]) ).

tff(f6553,plain,
    ( spl18_344
    | ~ spl18_141
    | ~ spl18_143 ),
    inference(avatar_split_clause,[],[f1908,f1905,f1881,f6551]) ).

tff(f6551,plain,
    ( spl18_344
  <=> ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: nat,X8: nat,X6: X0,X7: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X3,X4),X6) )
        | member(X0,X6,huffma675207370phabet(X0,X7))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X8,huffma1146269203erNode(X0,X2,X3,X4),X7),X6) = X6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_344])]) ).

tff(f1908,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: nat,X8: nat,X6: X0,X7: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X3,X4),X6) )
        | member(X0,X6,huffma675207370phabet(X0,X7))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X8,huffma1146269203erNode(X0,X2,X3,X4),X7),X6) = X6 ) )
    | ~ spl18_141
    | ~ spl18_143 ),
    inference(resolution,[],[f1906,f1882]) ).

tff(f6549,plain,
    ( spl18_343
    | ~ spl18_132
    | ~ spl18_141 ),
    inference(avatar_split_clause,[],[f1901,f1881,f1770,f6547]) ).

tff(f6547,plain,
    ( spl18_343
  <=> ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X10: huffma1450048681e_tree(X0),X1: X0,X8: nat,X6: nat,X9: huffma1450048681e_tree(X0),X7: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( member(X0,X1,huffma675207370phabet(X0,huffma1146269203erNode(X0,X3,X4,X5)))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X6,huffma1146269203erNode(X0,X3,X4,X5),X2),X1) = X1 )
        | ( huffma1401021291ibling(X0,X2,X1) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X7,X2,huffma1146269203erNode(X0,X8,X9,X10)),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_343])]) ).

tff(f1901,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X10: huffma1450048681e_tree(X0),X1: X0,X8: nat,X6: nat,X9: huffma1450048681e_tree(X0),X7: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( member(X0,X1,huffma675207370phabet(X0,huffma1146269203erNode(X0,X3,X4,X5)))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X6,huffma1146269203erNode(X0,X3,X4,X5),X2),X1) = X1 )
        | ( huffma1401021291ibling(X0,X2,X1) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X7,X2,huffma1146269203erNode(X0,X8,X9,X10)),X1) ) )
    | ~ spl18_132
    | ~ spl18_141 ),
    inference(resolution,[],[f1882,f1771]) ).

tff(f6545,plain,
    ( spl18_342
    | ~ spl18_132
    | ~ spl18_140 ),
    inference(avatar_split_clause,[],[f1897,f1877,f1770,f6543]) ).

tff(f6543,plain,
    ( spl18_342
  <=> ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X10: huffma1450048681e_tree(X0),X1: X0,X8: nat,X6: nat,X9: huffma1450048681e_tree(X0),X7: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( member(X0,X1,huffma675207370phabet(X0,huffma1146269203erNode(X0,X3,X4,X5)))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X6,X2,huffma1146269203erNode(X0,X3,X4,X5)),X1) = X1 )
        | ( huffma1401021291ibling(X0,X2,X1) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X7,X2,huffma1146269203erNode(X0,X8,X9,X10)),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_342])]) ).

tff(f1897,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X10: huffma1450048681e_tree(X0),X1: X0,X8: nat,X6: nat,X9: huffma1450048681e_tree(X0),X7: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( member(X0,X1,huffma675207370phabet(X0,huffma1146269203erNode(X0,X3,X4,X5)))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X6,X2,huffma1146269203erNode(X0,X3,X4,X5)),X1) = X1 )
        | ( huffma1401021291ibling(X0,X2,X1) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X7,X2,huffma1146269203erNode(X0,X8,X9,X10)),X1) ) )
    | ~ spl18_132
    | ~ spl18_140 ),
    inference(resolution,[],[f1878,f1771]) ).

tff(f6540,plain,
    ( spl18_341
    | ~ spl18_73
    | ~ spl18_143 ),
    inference(avatar_split_clause,[],[f1911,f1905,f942,f6538]) ).

tff(f6538,plain,
    ( spl18_341
  <=> ! [X0: $tType,X5: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X2: nat,X1: nat] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),sK6(X0,huffma1146269203erNode(X0,X2,X3,X4))) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X3,X4),sK6(X0,huffma1146269203erNode(X0,X2,X3,X4))) )
        | ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X2,X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_341])]) ).

tff(f1911,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),sK6(X0,huffma1146269203erNode(X0,X2,X3,X4))) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X3,X4),sK6(X0,huffma1146269203erNode(X0,X2,X3,X4))) )
        | ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X2,X3,X4)) )
    | ~ spl18_73
    | ~ spl18_143 ),
    inference(resolution,[],[f1906,f943]) ).

tff(f6536,plain,
    ( spl18_340
    | ~ spl18_66
    | ~ spl18_171 ),
    inference(avatar_split_clause,[],[f2284,f2228,f902,f6534]) ).

tff(f6534,plain,
    ( spl18_340
  <=> ! [X0: fun(int,bool)] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | member(int,sK4(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_340])]) ).

tff(f2284,plain,
    ( ! [X0: fun(int,bool)] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | member(int,sK4(X0),X0) )
    | ~ spl18_66
    | ~ spl18_171 ),
    inference(resolution,[],[f2229,f903]) ).

tff(f6498,plain,
    ( spl18_339
    | ~ spl18_114
    | ~ spl18_134 ),
    inference(avatar_split_clause,[],[f1837,f1799,f1487,f6496]) ).

tff(f6496,plain,
    ( spl18_339
  <=> ! [X0: $tType,X3: fun(X0,nat),X2: X0,X1: nat] :
        ( ( zero_zero(nat) != aa(X0,nat,X3,sK17(nat,X0,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3)) )
        | ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)) = X3 )
        | ( sK17(nat,X0,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3) = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_339])]) ).

tff(f1837,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,nat),X1: nat] :
        ( ( zero_zero(nat) != aa(X0,nat,X3,sK17(nat,X0,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3)) )
        | ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)) = X3 )
        | ( sK17(nat,X0,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3) = X2 ) )
    | ~ spl18_114
    | ~ spl18_134 ),
    inference(superposition,[],[f1800,f1488]) ).

tff(f6494,plain,
    ( spl18_338
    | ~ spl18_114
    | ~ spl18_134 ),
    inference(avatar_split_clause,[],[f1824,f1799,f1487,f6492]) ).

tff(f6492,plain,
    ( spl18_338
  <=> ! [X0: $tType,X3: fun(X0,nat),X2: X0,X1: nat] :
        ( ( zero_zero(nat) != aa(X0,nat,X3,sK17(nat,X0,X3,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)))) )
        | ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)) = X3 )
        | ( sK17(nat,X0,X3,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2))) = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_338])]) ).

tff(f1824,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,nat),X1: nat] :
        ( ( zero_zero(nat) != aa(X0,nat,X3,sK17(nat,X0,X3,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)))) )
        | ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)) = X3 )
        | ( sK17(nat,X0,X3,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2))) = X2 ) )
    | ~ spl18_114
    | ~ spl18_134 ),
    inference(superposition,[],[f1800,f1488]) ).

tff(f6346,plain,
    ( spl18_337
    | ~ spl18_31
    | ~ spl18_145 ),
    inference(avatar_split_clause,[],[f1949,f1931,f725,f6344]) ).

tff(f6344,plain,
    ( spl18_337
  <=> ! [X0: $tType,X5: fun(nat,fun(X0,bool)),X4: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X2: nat,X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)))] :
        ( ( fTrue = huffma107959123e_case(X0,bool,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)) )
        | ( fFalse = aa(huffma1450048681e_tree(X0),bool,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)),X1,X2),X3),X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_337])]) ).

tff(f1949,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X4: huffma1450048681e_tree(X0),X5: fun(nat,fun(X0,bool))] :
        ( ( fTrue = huffma107959123e_case(X0,bool,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)) )
        | ( fFalse = aa(huffma1450048681e_tree(X0),bool,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)),X1,X2),X3),X4) ) )
    | ~ spl18_31
    | ~ spl18_145 ),
    inference(superposition,[],[f1932,f726]) ).

tff(f6342,plain,
    ( spl18_336
    | ~ spl18_31
    | ~ spl18_145 ),
    inference(avatar_split_clause,[],[f1939,f1931,f725,f6340]) ).

tff(f6340,plain,
    ( spl18_336
  <=> ! [X0: $tType,X3: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0),X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X1: fun(nat,fun(X0,bool))] :
        ( ( fTrue = aa(huffma1450048681e_tree(X0),bool,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)),X2,X3),X4),X5) )
        | ( fFalse = huffma107959123e_case(X0,bool,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_336])]) ).

tff(f1939,plain,
    ( ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X3: nat,X1: fun(nat,fun(X0,bool)),X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( fTrue = aa(huffma1450048681e_tree(X0),bool,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)),X2,X3),X4),X5) )
        | ( fFalse = huffma107959123e_case(X0,bool,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)) ) )
    | ~ spl18_31
    | ~ spl18_145 ),
    inference(superposition,[],[f1932,f726]) ).

tff(f6338,plain,
    ( spl18_335
    | ~ spl18_120
    | ~ spl18_131 ),
    inference(avatar_split_clause,[],[f1775,f1766,f1539,f6336]) ).

tff(f6336,plain,
    ( spl18_335
  <=> ! [X2: nat,X0: nat,X1: fun(nat,fun(nat,bool))] :
        ( ord_less(nat,X0,zero_zero(nat))
        | ( zero_zero(nat) = X0 )
        | sP0(zero_zero(nat),X0,X1)
        | ord_less(nat,zero_zero(nat),sK8(aa(nat,fun(nat,bool),X1,X0)))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X1,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_335])]) ).

tff(f1775,plain,
    ( ! [X2: nat,X0: nat,X1: fun(nat,fun(nat,bool))] :
        ( ord_less(nat,X0,zero_zero(nat))
        | ( zero_zero(nat) = X0 )
        | sP0(zero_zero(nat),X0,X1)
        | ord_less(nat,zero_zero(nat),sK8(aa(nat,fun(nat,bool),X1,X0)))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X1,X0),X2)) )
    | ~ spl18_120
    | ~ spl18_131 ),
    inference(resolution,[],[f1767,f1540]) ).

tff(f6334,plain,
    ( spl18_334
    | ~ spl18_79
    | ~ spl18_161 ),
    inference(avatar_split_clause,[],[f2235,f2164,f1008,f6332]) ).

tff(f6332,plain,
    ( spl18_334
  <=> ! [X0: nat] :
        ( ( zero_zero(int) = semiring_1_of_nat(int,X0) )
        | ord_less(nat,zero_zero(nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_334])]) ).

tff(f1008,plain,
    ( spl18_79
  <=> ! [X0: nat] :
        ( ord_less(nat,zero_zero(nat),X0)
        | ~ ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_79])]) ).

tff(f2235,plain,
    ( ! [X0: nat] :
        ( ( zero_zero(int) = semiring_1_of_nat(int,X0) )
        | ord_less(nat,zero_zero(nat),X0) )
    | ~ spl18_79
    | ~ spl18_161 ),
    inference(resolution,[],[f2165,f1009]) ).

tff(f1009,plain,
    ( ! [X0: nat] :
        ( ~ ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0))
        | ord_less(nat,zero_zero(nat),X0) )
    | ~ spl18_79 ),
    inference(avatar_component_clause,[],[f1008]) ).

tff(f6272,plain,
    ( spl18_333
    | ~ spl18_88
    | ~ spl18_146 ),
    inference(avatar_split_clause,[],[f1975,f1957,f1044,f6270]) ).

tff(f6270,plain,
    ( spl18_333
  <=> ! [X0: $tType,X5: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X6: X0,X3: nat,X1: nat] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X4,X5),X6) )
        | member(X0,X6,huffma675207370phabet(X0,X2))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X4,X5),X6) = X6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_333])]) ).

tff(f1975,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: nat,X6: X0,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X4,X5),X6) )
        | member(X0,X6,huffma675207370phabet(X0,X2))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X4,X5),X6) = X6 ) )
    | ~ spl18_88
    | ~ spl18_146 ),
    inference(resolution,[],[f1958,f1045]) ).

tff(f6268,plain,
    ( spl18_332
    | ~ spl18_112
    | ~ spl18_144 ),
    inference(avatar_split_clause,[],[f1926,f1918,f1479,f6266]) ).

tff(f6266,plain,
    ( spl18_332
  <=> ! [X0: $tType,X5: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X2: nat,X6: X0,X3: huffma1450048681e_tree(X0),X1: nat] :
        ( ( huffma1401021291ibling(X0,X5,X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),X6) )
        | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X2,X3,X4)))
        | ( zero_zero(nat) = aa(X0,nat,huffma1352802255e_freq(X0,X5),X6) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_332])]) ).

tff(f1926,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: nat,X6: X0,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,X5,X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),X6) )
        | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X2,X3,X4)))
        | ( zero_zero(nat) = aa(X0,nat,huffma1352802255e_freq(X0,X5),X6) ) )
    | ~ spl18_112
    | ~ spl18_144 ),
    inference(resolution,[],[f1919,f1480]) ).

tff(f6264,plain,
    ( spl18_331
    | ~ spl18_114
    | ~ spl18_129 ),
    inference(avatar_split_clause,[],[f1753,f1722,f1487,f6262]) ).

tff(f6262,plain,
    ( spl18_331
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat] :
        ( ord_less_eq(nat,aa(nat,nat,huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)),X3),zero_zero(nat))
        | ~ ord_less_eq(nat,X3,X2)
        | ord_less(nat,sK15(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1))),sK16(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1))))
        | ( X1 = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_331])]) ).

tff(f1753,plain,
    ( ! [X2: nat,X3: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,aa(nat,nat,huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)),X3),zero_zero(nat))
        | ~ ord_less_eq(nat,X3,X2)
        | ord_less(nat,sK15(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1))),sK16(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1))))
        | ( X1 = X2 ) )
    | ~ spl18_114
    | ~ spl18_129 ),
    inference(superposition,[],[f1723,f1488]) ).

tff(f6260,plain,
    ( spl18_330
    | ~ spl18_113
    | ~ spl18_126 ),
    inference(avatar_split_clause,[],[f1650,f1639,f1483,f6258]) ).

tff(f6258,plain,
    ( spl18_330
  <=> ! [X2: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat)))
        | ~ sP0(sK7(X2,aa(nat,fun(nat,bool),X0,X1)),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_330])]) ).

tff(f1650,plain,
    ( ! [X2: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat)))
        | ~ sP0(sK7(X2,aa(nat,fun(nat,bool),X0,X1)),X1,X0) )
    | ~ spl18_113
    | ~ spl18_126 ),
    inference(resolution,[],[f1640,f1484]) ).

tff(f6219,plain,
    ( spl18_329
    | ~ spl18_76
    | ~ spl18_162 ),
    inference(avatar_split_clause,[],[f2179,f2168,f954,f6217]) ).

tff(f6217,plain,
    ( spl18_329
  <=> ! [X0: int,X1: int] :
        ( ( X0 = X1 )
        | ord_less(int,X1,X0)
        | ord_less(int,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_329])]) ).

tff(f2179,plain,
    ( ! [X0: int,X1: int] :
        ( ( X0 = X1 )
        | ord_less(int,X1,X0)
        | ord_less(int,X0,X1) )
    | ~ spl18_76
    | ~ spl18_162 ),
    inference(duplicate_literal_removal,[],[f2171]) ).

tff(f2171,plain,
    ( ! [X0: int,X1: int] :
        ( ( X0 = X1 )
        | ord_less(int,X1,X0)
        | ( X0 = X1 )
        | ord_less(int,X0,X1) )
    | ~ spl18_76
    | ~ spl18_162 ),
    inference(resolution,[],[f2169,f955]) ).

tff(f6089,plain,
    ( spl18_328
    | ~ spl18_137
    | ~ spl18_146 ),
    inference(avatar_split_clause,[],[f1977,f1957,f1844,f6087]) ).

tff(f6087,plain,
    ( spl18_328
  <=> ! [X0: $tType,X4: huffma1450048681e_tree(X0),X3: nat,X2: X0,X1: huffma1450048681e_tree(X0)] :
        ( ~ member(X0,X2,huffma675207370phabet(X0,X1))
        | ( huffma1401021291ibling(X0,X1,X2) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X4,X1),X2) )
        | member(X0,X2,huffma675207370phabet(X0,X4))
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_328])]) ).

tff(f1977,plain,
    ( ! [X0: $tType,X2: X0,X3: nat,X1: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0)] :
        ( ~ member(X0,X2,huffma675207370phabet(X0,X1))
        | ( huffma1401021291ibling(X0,X1,X2) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X4,X1),X2) )
        | member(X0,X2,huffma675207370phabet(X0,X4))
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) )
    | ~ spl18_137
    | ~ spl18_146 ),
    inference(superposition,[],[f1958,f1845]) ).

tff(f6085,plain,
    ( spl18_327
    | ~ spl18_73
    | ~ spl18_144 ),
    inference(avatar_split_clause,[],[f1923,f1918,f942,f6083]) ).

tff(f6083,plain,
    ( spl18_327
  <=> ! [X0: $tType,X2: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X1: nat] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),sK6(X0,X5)) = huffma1401021291ibling(X0,X5,sK6(X0,X5)) )
        | member(X0,sK6(X0,X5),huffma675207370phabet(X0,huffma1146269203erNode(X0,X2,X3,X4)))
        | ~ huffma1518433673istent(X0,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_327])]) ).

tff(f1923,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),sK6(X0,X5)) = huffma1401021291ibling(X0,X5,sK6(X0,X5)) )
        | member(X0,sK6(X0,X5),huffma675207370phabet(X0,huffma1146269203erNode(X0,X2,X3,X4)))
        | ~ huffma1518433673istent(X0,X5) )
    | ~ spl18_73
    | ~ spl18_144 ),
    inference(resolution,[],[f1919,f943]) ).

tff(f6081,plain,
    ( spl18_326
    | ~ spl18_119
    | ~ spl18_131 ),
    inference(avatar_split_clause,[],[f1774,f1766,f1524,f6079]) ).

tff(f6079,plain,
    ( spl18_326
  <=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( ord_less(nat,X0,X1)
        | ( X0 = X1 )
        | sP0(X1,X0,X2)
        | ord_less_eq(nat,sK7(X1,aa(nat,fun(nat,bool),X2,X0)),X1)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X0),zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_326])]) ).

tff(f1774,plain,
    ( ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( ord_less(nat,X0,X1)
        | ( X0 = X1 )
        | sP0(X1,X0,X2)
        | ord_less_eq(nat,sK7(X1,aa(nat,fun(nat,bool),X2,X0)),X1)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X0),zero_zero(nat))) )
    | ~ spl18_119
    | ~ spl18_131 ),
    inference(resolution,[],[f1767,f1525]) ).

tff(f6077,plain,
    ( spl18_325
    | ~ spl18_123
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1713,f1647,f1572,f6075]) ).

tff(f6075,plain,
    ( spl18_325
  <=> ! [X0: fun(nat,fun(int,bool)),X3: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X2: int,X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(int,bool,X0,X3,huffma2021818691e_Leaf(int,X1,X2)))
        | pp(aa(int,bool,aa(nat,fun(int,bool),X0,X1),semiring_1_of_nat(int,sK5(aa(nat,fun(int,bool),X0,X1)))))
        | ~ ord_less_eq(int,zero_zero(int),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_325])]) ).

tff(f1713,plain,
    ( ! [X2: int,X3: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(int,bool,X0,X3,huffma2021818691e_Leaf(int,X1,X2)))
        | pp(aa(int,bool,aa(nat,fun(int,bool),X0,X1),semiring_1_of_nat(int,sK5(aa(nat,fun(int,bool),X0,X1)))))
        | ~ ord_less_eq(int,zero_zero(int),X2) )
    | ~ spl18_123
    | ~ spl18_128 ),
    inference(superposition,[],[f1573,f1648]) ).

tff(f6073,plain,
    ( spl18_324
    | ~ spl18_122
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1711,f1647,f1568,f6071]) ).

tff(f6071,plain,
    ( spl18_324
  <=> ! [X0: fun(nat,fun(int,bool)),X3: int,X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,sK2(aa(nat,fun(int,bool),X0,X1))))))
        | ~ ord_less_eq(int,zero_zero(int),X3)
        | pp(aa(int,bool,aa(nat,fun(int,bool),X0,X1),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_324])]) ).

tff(f1711,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X3: int,X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,sK2(aa(nat,fun(int,bool),X0,X1))))))
        | ~ ord_less_eq(int,zero_zero(int),X3)
        | pp(aa(int,bool,aa(nat,fun(int,bool),X0,X1),X3)) )
    | ~ spl18_122
    | ~ spl18_128 ),
    inference(superposition,[],[f1569,f1648]) ).

tff(f6069,plain,
    ( spl18_323
    | ~ spl18_39
    | ~ spl18_159 ),
    inference(avatar_split_clause,[],[f2162,f2090,f761,f6067]) ).

tff(f6067,plain,
    ( spl18_323
  <=> ! [X0: fun(int,bool)] :
        ( ~ member(int,zero_zero(int),X0)
        | ord_less_eq(int,zero_zero(int),sK4(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_323])]) ).

tff(f2162,plain,
    ( ! [X0: fun(int,bool)] :
        ( ~ member(int,zero_zero(int),X0)
        | ord_less_eq(int,zero_zero(int),sK4(X0)) )
    | ~ spl18_39
    | ~ spl18_159 ),
    inference(superposition,[],[f2091,f763]) ).

tff(f6065,plain,
    ( spl18_322
    | ~ spl18_123
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1682,f1643,f1572,f6063]) ).

tff(f6063,plain,
    ( spl18_322
  <=> ! [X0: fun(nat,fun(int,bool)),X3: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X2: int,X1: nat] :
        ( ~ pp(huffma107959123e_case(int,bool,X0,X3,huffma2021818691e_Leaf(int,X1,X2)))
        | pp(aa(int,bool,aa(nat,fun(int,bool),X0,X1),semiring_1_of_nat(int,sK5(aa(nat,fun(int,bool),X0,X1)))))
        | ~ ord_less_eq(int,zero_zero(int),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_322])]) ).

tff(f1682,plain,
    ( ! [X2: int,X3: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ~ pp(huffma107959123e_case(int,bool,X0,X3,huffma2021818691e_Leaf(int,X1,X2)))
        | pp(aa(int,bool,aa(nat,fun(int,bool),X0,X1),semiring_1_of_nat(int,sK5(aa(nat,fun(int,bool),X0,X1)))))
        | ~ ord_less_eq(int,zero_zero(int),X2) )
    | ~ spl18_123
    | ~ spl18_127 ),
    inference(superposition,[],[f1573,f1644]) ).

tff(f6061,plain,
    ( spl18_321
    | ~ spl18_122
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1680,f1643,f1568,f6059]) ).

tff(f6059,plain,
    ( spl18_321
  <=> ! [X0: fun(nat,fun(int,bool)),X3: int,X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X1: nat] :
        ( ~ pp(huffma107959123e_case(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,sK2(aa(nat,fun(int,bool),X0,X1))))))
        | ~ ord_less_eq(int,zero_zero(int),X3)
        | pp(aa(int,bool,aa(nat,fun(int,bool),X0,X1),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_321])]) ).

tff(f1680,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X3: int,X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ~ pp(huffma107959123e_case(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,sK2(aa(nat,fun(int,bool),X0,X1))))))
        | ~ ord_less_eq(int,zero_zero(int),X3)
        | pp(aa(int,bool,aa(nat,fun(int,bool),X0,X1),X3)) )
    | ~ spl18_122
    | ~ spl18_127 ),
    inference(superposition,[],[f1569,f1644]) ).

tff(f5924,plain,
    ( spl18_320
    | ~ spl18_112
    | ~ spl18_143 ),
    inference(avatar_split_clause,[],[f1914,f1905,f1479,f5922]) ).

tff(f5922,plain,
    ( spl18_320
  <=> ! [X0: $tType,X5: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X6: X0,X2: nat,X1: nat] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X3,X4),X6) )
        | ( zero_zero(nat) = aa(X0,nat,huffma1352802255e_freq(X0,huffma1146269203erNode(X0,X2,X3,X4)),X6) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_320])]) ).

tff(f1914,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: nat,X6: X0,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X3,X4),X6) )
        | ( zero_zero(nat) = aa(X0,nat,huffma1352802255e_freq(X0,huffma1146269203erNode(X0,X2,X3,X4)),X6) ) )
    | ~ spl18_112
    | ~ spl18_143 ),
    inference(resolution,[],[f1906,f1480]) ).

tff(f5920,plain,
    ( spl18_319
    | ~ spl18_39
    | ~ spl18_157 ),
    inference(avatar_split_clause,[],[f2151,f2082,f761,f5918]) ).

tff(f5918,plain,
    ( spl18_319
  <=> ! [X0: fun(int,bool)] :
        ( member(int,zero_zero(int),X0)
        | ord_less_eq(int,zero_zero(int),sK3(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_319])]) ).

tff(f2151,plain,
    ( ! [X0: fun(int,bool)] :
        ( member(int,zero_zero(int),X0)
        | ord_less_eq(int,zero_zero(int),sK3(X0)) )
    | ~ spl18_39
    | ~ spl18_157 ),
    inference(superposition,[],[f2083,f763]) ).

tff(f5916,plain,
    ( spl18_318
    | ~ spl18_127
    | ~ spl18_131 ),
    inference(avatar_split_clause,[],[f1781,f1766,f1643,f5914]) ).

tff(f5914,plain,
    ( spl18_318
  <=> ! [X4: nat,X0: fun(nat,fun(nat,fun(nat,bool))),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(nat,bool)))),X2: nat,X1: nat] :
        ( pp(aa(nat,bool,huffma107959123e_case(nat,fun(nat,bool),X0,X3,huffma2021818691e_Leaf(nat,X1,X2)),X4))
        | ord_less(nat,X2,X4)
        | ( X2 = X4 )
        | sP0(X4,X2,aa(nat,fun(nat,fun(nat,bool)),X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_318])]) ).

tff(f1781,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(nat,bool)))),X0: fun(nat,fun(nat,fun(nat,bool))),X1: nat,X4: nat] :
        ( pp(aa(nat,bool,huffma107959123e_case(nat,fun(nat,bool),X0,X3,huffma2021818691e_Leaf(nat,X1,X2)),X4))
        | ord_less(nat,X2,X4)
        | ( X2 = X4 )
        | sP0(X4,X2,aa(nat,fun(nat,fun(nat,bool)),X0,X1)) )
    | ~ spl18_127
    | ~ spl18_131 ),
    inference(superposition,[],[f1767,f1644]) ).

tff(f5912,plain,
    ( spl18_317
    | ~ spl18_128
    | ~ spl18_131 ),
    inference(avatar_split_clause,[],[f1780,f1766,f1647,f5910]) ).

tff(f5910,plain,
    ( spl18_317
  <=> ! [X4: nat,X0: fun(nat,fun(nat,fun(nat,bool))),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)))))),X2: nat,X1: nat] :
        ( pp(aa(nat,bool,huffma1280178957ee_rec(nat,fun(nat,bool),X0,X3,huffma2021818691e_Leaf(nat,X1,X2)),X4))
        | ord_less(nat,X2,X4)
        | ( X2 = X4 )
        | sP0(X4,X2,aa(nat,fun(nat,fun(nat,bool)),X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_317])]) ).

tff(f1780,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)))))),X0: fun(nat,fun(nat,fun(nat,bool))),X1: nat,X4: nat] :
        ( pp(aa(nat,bool,huffma1280178957ee_rec(nat,fun(nat,bool),X0,X3,huffma2021818691e_Leaf(nat,X1,X2)),X4))
        | ord_less(nat,X2,X4)
        | ( X2 = X4 )
        | sP0(X4,X2,aa(nat,fun(nat,fun(nat,bool)),X0,X1)) )
    | ~ spl18_128
    | ~ spl18_131 ),
    inference(superposition,[],[f1767,f1648]) ).

tff(f5908,plain,
    ( spl18_316
    | ~ spl18_120
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1716,f1647,f1539,f5906]) ).

tff(f5906,plain,
    ( spl18_316
  <=> ! [X0: fun(nat,fun(nat,bool)),X3: nat,X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(nat,bool,X0,X2,huffma2021818691e_Leaf(nat,X1,zero_zero(nat))))
        | ord_less(nat,zero_zero(nat),sK8(aa(nat,fun(nat,bool),X0,X1)))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_316])]) ).

tff(f1716,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X3: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(nat,bool,X0,X2,huffma2021818691e_Leaf(nat,X1,zero_zero(nat))))
        | ord_less(nat,zero_zero(nat),sK8(aa(nat,fun(nat,bool),X0,X1)))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X3)) )
    | ~ spl18_120
    | ~ spl18_128 ),
    inference(superposition,[],[f1540,f1648]) ).

tff(f5904,plain,
    ( spl18_315
    | ~ spl18_119
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1715,f1647,f1524,f5902]) ).

tff(f5902,plain,
    ( spl18_315
  <=> ! [X0: fun(nat,fun(nat,bool)),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X2: nat,X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ord_less_eq(nat,sK7(X2,aa(nat,fun(nat,bool),X0,X1)),X2)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_315])]) ).

tff(f1715,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ord_less_eq(nat,sK7(X2,aa(nat,fun(nat,bool),X0,X1)),X2)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat))) )
    | ~ spl18_119
    | ~ spl18_128 ),
    inference(superposition,[],[f1525,f1648]) ).

tff(f5900,plain,
    ( spl18_314
    | ~ spl18_120
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1685,f1643,f1539,f5898]) ).

tff(f5898,plain,
    ( spl18_314
  <=> ! [X0: fun(nat,fun(nat,bool)),X3: nat,X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X1: nat] :
        ( ~ pp(huffma107959123e_case(nat,bool,X0,X2,huffma2021818691e_Leaf(nat,X1,zero_zero(nat))))
        | ord_less(nat,zero_zero(nat),sK8(aa(nat,fun(nat,bool),X0,X1)))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_314])]) ).

tff(f1685,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X3: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( ~ pp(huffma107959123e_case(nat,bool,X0,X2,huffma2021818691e_Leaf(nat,X1,zero_zero(nat))))
        | ord_less(nat,zero_zero(nat),sK8(aa(nat,fun(nat,bool),X0,X1)))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X3)) )
    | ~ spl18_120
    | ~ spl18_127 ),
    inference(superposition,[],[f1540,f1644]) ).

tff(f5896,plain,
    ( spl18_313
    | ~ spl18_119
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1684,f1643,f1524,f5894]) ).

tff(f5894,plain,
    ( spl18_313
  <=> ! [X0: fun(nat,fun(nat,bool)),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X2: nat,X1: nat] :
        ( ~ pp(huffma107959123e_case(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ord_less_eq(nat,sK7(X2,aa(nat,fun(nat,bool),X0,X1)),X2)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_313])]) ).

tff(f1684,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( ~ pp(huffma107959123e_case(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ord_less_eq(nat,sK7(X2,aa(nat,fun(nat,bool),X0,X1)),X2)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat))) )
    | ~ spl18_119
    | ~ spl18_127 ),
    inference(superposition,[],[f1525,f1644]) ).

tff(f5843,plain,
    ( spl18_312
    | ~ spl18_65
    | ~ spl18_145 ),
    inference(avatar_split_clause,[],[f1955,f1931,f896,f5841]) ).

tff(f5841,plain,
    ( spl18_312
  <=> ! [X0: $tType,X5: fun(nat,fun(X0,bool)),X4: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X2: nat,X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)))] :
        ( pp(huffma107959123e_case(X0,bool,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)))
        | ~ member(huffma1450048681e_tree(X0),X4,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)),X1,X2),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_312])]) ).

tff(f1955,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X4: huffma1450048681e_tree(X0),X5: fun(nat,fun(X0,bool))] :
        ( pp(huffma107959123e_case(X0,bool,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)))
        | ~ member(huffma1450048681e_tree(X0),X4,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)),X1,X2),X3)) )
    | ~ spl18_65
    | ~ spl18_145 ),
    inference(superposition,[],[f897,f1932]) ).

tff(f5839,plain,
    ( spl18_311
    | ~ spl18_37
    | ~ spl18_66 ),
    inference(avatar_split_clause,[],[f918,f902,f752,f5837]) ).

tff(f5837,plain,
    ( spl18_311
  <=> ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
        ( member(X0,X1,X2)
        | ( fFalse = aa(X0,bool,X2,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_311])]) ).

tff(f918,plain,
    ( ! [X0: $tType,X2: fun(X0,bool),X1: X0] :
        ( member(X0,X1,X2)
        | ( fFalse = aa(X0,bool,X2,X1) ) )
    | ~ spl18_37
    | ~ spl18_66 ),
    inference(resolution,[],[f903,f753]) ).

tff(f5835,plain,
    ( spl18_310
    | ~ spl18_66
    | ~ spl18_145 ),
    inference(avatar_split_clause,[],[f1954,f1931,f902,f5833]) ).

tff(f5833,plain,
    ( spl18_310
  <=> ! [X0: $tType,X5: fun(nat,fun(X0,bool)),X4: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X2: nat,X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)))] :
        ( ~ pp(huffma107959123e_case(X0,bool,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)))
        | member(huffma1450048681e_tree(X0),X4,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)),X1,X2),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_310])]) ).

tff(f1954,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X4: huffma1450048681e_tree(X0),X5: fun(nat,fun(X0,bool))] :
        ( ~ pp(huffma107959123e_case(X0,bool,X5,X1,huffma1146269203erNode(X0,X2,X3,X4)))
        | member(huffma1450048681e_tree(X0),X4,aa(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool),aa(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)),X1,X2),X3)) )
    | ~ spl18_66
    | ~ spl18_145 ),
    inference(superposition,[],[f903,f1932]) ).

tff(f5831,plain,
    ( spl18_309
    | ~ spl18_95
    | ~ spl18_136 ),
    inference(avatar_split_clause,[],[f1850,f1840,f1215,f5829]) ).

tff(f5829,plain,
    ( spl18_309
  <=> ! [X4: nat,X0: nat,X3: nat,X2: fun(nat,bool),X1: nat] :
        ( ~ ord_less(nat,X0,sK7(X1,X2))
        | ~ pp(aa(nat,bool,X2,X1))
        | pp(aa(nat,bool,X2,zero_zero(nat)))
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X2,X0),X4,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_309])]) ).

tff(f1850,plain,
    ( ! [X2: fun(nat,bool),X3: nat,X0: nat,X1: nat,X4: nat] :
        ( ~ ord_less(nat,X0,sK7(X1,X2))
        | ~ pp(aa(nat,bool,X2,X1))
        | pp(aa(nat,bool,X2,zero_zero(nat)))
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X2,X0),X4,X3)) ) )
    | ~ spl18_95
    | ~ spl18_136 ),
    inference(resolution,[],[f1841,f1216]) ).

tff(f5035,plain,
    ( spl18_308
    | ~ spl18_88
    | ~ spl18_144 ),
    inference(avatar_split_clause,[],[f1927,f1918,f1044,f5033]) ).

tff(f5033,plain,
    ( spl18_308
  <=> ! [X0: $tType,X5: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X2: nat,X6: X0,X3: huffma1450048681e_tree(X0),X1: nat] :
        ( ( huffma1401021291ibling(X0,X5,X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),X6) )
        | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X2,X3,X4)))
        | ( huffma1401021291ibling(X0,X5,X6) = X6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_308])]) ).

tff(f1927,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: nat,X6: X0,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,X5,X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),X6) )
        | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X2,X3,X4)))
        | ( huffma1401021291ibling(X0,X5,X6) = X6 ) )
    | ~ spl18_88
    | ~ spl18_144 ),
    inference(resolution,[],[f1919,f1045]) ).

tff(f5031,plain,
    ( spl18_307
    | ~ spl18_49
    | ~ spl18_144 ),
    inference(avatar_split_clause,[],[f1922,f1918,f808,f5029]) ).

tff(f5029,plain,
    ( spl18_307
  <=> ! [X0: $tType,X2: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X1: nat] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),sK14(X0,X5)) = huffma1401021291ibling(X0,X5,sK14(X0,X5)) )
        | member(X0,sK14(X0,X5),huffma675207370phabet(X0,huffma1146269203erNode(X0,X2,X3,X4))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_307])]) ).

tff(f1922,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),sK14(X0,X5)) = huffma1401021291ibling(X0,X5,sK14(X0,X5)) )
        | member(X0,sK14(X0,X5),huffma675207370phabet(X0,huffma1146269203erNode(X0,X2,X3,X4))) )
    | ~ spl18_49
    | ~ spl18_144 ),
    inference(resolution,[],[f1919,f809]) ).

tff(f5027,plain,
    ( spl18_306
    | ~ spl18_49
    | ~ spl18_143 ),
    inference(avatar_split_clause,[],[f1910,f1905,f808,f5025]) ).

tff(f5025,plain,
    ( spl18_306
  <=> ! [X0: $tType,X5: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X2: nat,X1: nat] : ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),sK14(X0,huffma1146269203erNode(X0,X2,X3,X4))) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X3,X4),sK14(X0,huffma1146269203erNode(X0,X2,X3,X4))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_306])]) ).

tff(f1910,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] : ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),sK14(X0,huffma1146269203erNode(X0,X2,X3,X4))) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X3,X4),sK14(X0,huffma1146269203erNode(X0,X2,X3,X4))) )
    | ~ spl18_49
    | ~ spl18_143 ),
    inference(resolution,[],[f1906,f809]) ).

tff(f5023,plain,
    ( spl18_305
    | ~ spl18_31
    | ~ spl18_272 ),
    inference(avatar_split_clause,[],[f4500,f4411,f725,f5021]) ).

tff(f5021,plain,
    ( spl18_305
  <=> ! [X0: bool,X1: bool] :
        ( ~ ord_less(bool,X0,X1)
        | ( fFalse = X1 )
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_305])]) ).

tff(f4411,plain,
    ( spl18_272
  <=> ! [X0: bool] :
        ( ~ ord_less(bool,fTrue,X0)
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_272])]) ).

tff(f4500,plain,
    ( ! [X0: bool,X1: bool] :
        ( ~ ord_less(bool,X0,X1)
        | ( fFalse = X1 )
        | ( fFalse = X0 ) )
    | ~ spl18_31
    | ~ spl18_272 ),
    inference(superposition,[],[f4412,f726]) ).

tff(f4412,plain,
    ( ! [X0: bool] :
        ( ~ ord_less(bool,fTrue,X0)
        | ( fFalse = X0 ) )
    | ~ spl18_272 ),
    inference(avatar_component_clause,[],[f4411]) ).

tff(f5019,plain,
    ( spl18_304
    | ~ spl18_137
    | ~ spl18_141 ),
    inference(avatar_split_clause,[],[f1903,f1881,f1844,f5017]) ).

tff(f5017,plain,
    ( spl18_304
  <=> ! [X0: $tType,X4: nat,X3: huffma1450048681e_tree(X0),X2: X0,X1: huffma1450048681e_tree(X0)] :
        ( member(X0,X2,huffma675207370phabet(X0,X1))
        | member(X0,X2,huffma675207370phabet(X0,X3))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X1,X3),X2) = X2 )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_304])]) ).

tff(f1903,plain,
    ( ! [X0: $tType,X2: X0,X3: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0),X4: nat] :
        ( member(X0,X2,huffma675207370phabet(X0,X1))
        | member(X0,X2,huffma675207370phabet(X0,X3))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X1,X3),X2) = X2 )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) )
    | ~ spl18_137
    | ~ spl18_141 ),
    inference(superposition,[],[f1882,f1845]) ).

tff(f5015,plain,
    ( spl18_303
    | ~ spl18_137
    | ~ spl18_140 ),
    inference(avatar_split_clause,[],[f1899,f1877,f1844,f5013]) ).

tff(f5013,plain,
    ( spl18_303
  <=> ! [X0: $tType,X4: nat,X3: huffma1450048681e_tree(X0),X2: X0,X1: huffma1450048681e_tree(X0)] :
        ( member(X0,X2,huffma675207370phabet(X0,X1))
        | member(X0,X2,huffma675207370phabet(X0,X3))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X3,X1),X2) = X2 )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_303])]) ).

tff(f1899,plain,
    ( ! [X0: $tType,X2: X0,X3: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0),X4: nat] :
        ( member(X0,X2,huffma675207370phabet(X0,X1))
        | member(X0,X2,huffma675207370phabet(X0,X3))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X3,X1),X2) = X2 )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) )
    | ~ spl18_137
    | ~ spl18_140 ),
    inference(superposition,[],[f1878,f1845]) ).

tff(f5011,plain,
    ( spl18_302
    | ~ spl18_95
    | ~ spl18_133 ),
    inference(avatar_split_clause,[],[f1804,f1795,f1215,f5009]) ).

tff(f5009,plain,
    ( spl18_302
  <=> ! [X4: nat,X0: fun(nat,bool),X3: nat,X2: nat,X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ ord_less(nat,X1,sK8(X0))
        | pp(aa(nat,bool,X0,X2))
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X0,zero_zero(nat)),X4,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_302])]) ).

tff(f1804,plain,
    ( ! [X2: nat,X3: nat,X0: fun(nat,bool),X1: nat,X4: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ ord_less(nat,X1,sK8(X0))
        | pp(aa(nat,bool,X0,X2))
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X0,zero_zero(nat)),X4,X3)) ) )
    | ~ spl18_95
    | ~ spl18_133 ),
    inference(resolution,[],[f1796,f1216]) ).

tff(f5007,plain,
    ( spl18_301
    | ~ spl18_90
    | ~ spl18_129 ),
    inference(avatar_split_clause,[],[f1752,f1722,f1052,f5005]) ).

tff(f5005,plain,
    ( spl18_301
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,aa(nat,nat,huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)),X2),X0)
        | ~ ord_less_eq(nat,X2,X1)
        | ord_less(nat,sK15(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1))),sK16(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_301])]) ).

tff(f1752,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,aa(nat,nat,huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)),X2),X0)
        | ~ ord_less_eq(nat,X2,X1)
        | ord_less(nat,sK15(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1))),sK16(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)))) )
    | ~ spl18_90
    | ~ spl18_129 ),
    inference(superposition,[],[f1723,f1053]) ).

tff(f5003,plain,
    ( spl18_300
    | ~ spl18_90
    | ~ spl18_129 ),
    inference(avatar_split_clause,[],[f1748,f1722,f1052,f5001]) ).

tff(f5001,plain,
    ( spl18_300
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,aa(nat,nat,huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)),X2))
        | ~ ord_less_eq(nat,X1,X2)
        | ord_less(nat,sK15(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1))),sK16(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_300])]) ).

tff(f1748,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,aa(nat,nat,huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)),X2))
        | ~ ord_less_eq(nat,X1,X2)
        | ord_less(nat,sK15(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1))),sK16(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)))) )
    | ~ spl18_90
    | ~ spl18_129 ),
    inference(superposition,[],[f1723,f1053]) ).

tff(f4999,plain,
    ( spl18_299
    | ~ spl18_74
    | ~ spl18_129 ),
    inference(avatar_split_clause,[],[f1745,f1722,f946,f4997]) ).

tff(f4997,plain,
    ( spl18_299
  <=> ! [X2: fun(nat,nat),X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less(nat,sK15(X2),sK16(X2))
        | ( aa(nat,nat,X2,X1) = aa(nat,nat,X2,X0) )
        | ord_less(nat,aa(nat,nat,X2,X0),aa(nat,nat,X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_299])]) ).

tff(f1745,plain,
    ( ! [X2: fun(nat,nat),X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less(nat,sK15(X2),sK16(X2))
        | ( aa(nat,nat,X2,X1) = aa(nat,nat,X2,X0) )
        | ord_less(nat,aa(nat,nat,X2,X0),aa(nat,nat,X2,X1)) )
    | ~ spl18_74
    | ~ spl18_129 ),
    inference(resolution,[],[f1723,f947]) ).

tff(f4995,plain,
    ( spl18_298
    | ~ spl18_75
    | ~ spl18_129 ),
    inference(avatar_split_clause,[],[f1744,f1722,f950,f4993]) ).

tff(f1744,plain,
    ( ! [X2: fun(nat,nat),X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less(nat,sK15(X2),sK16(X2))
        | ~ ord_less_eq(nat,aa(nat,nat,X2,X1),aa(nat,nat,X2,X0))
        | ( aa(nat,nat,X2,X1) = aa(nat,nat,X2,X0) ) )
    | ~ spl18_75
    | ~ spl18_129 ),
    inference(resolution,[],[f1723,f951]) ).

tff(f4991,plain,
    ( spl18_297
    | ~ spl18_127
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1720,f1647,f1643,f4989]) ).

tff(f4989,plain,
    ( spl18_297
  <=> ! [X1: $tType,X0: $tType,X2: fun(nat,fun(nat,fun(X0,X1))),X6: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X4: nat,X7: X0,X5: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(fun(X0,X1),fun(fun(X0,X1),fun(X0,X1)))))),X3: nat] : ( huffma107959123e_case(X0,X1,aa(nat,fun(nat,fun(X0,X1)),X2,X3),X6,huffma2021818691e_Leaf(X0,X4,X7)) = aa(X0,X1,huffma1280178957ee_rec(nat,fun(X0,X1),X2,X5,huffma2021818691e_Leaf(nat,X3,X4)),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_297])]) ).

tff(f1720,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(nat,fun(X0,X1))),X3: nat,X6: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X7: X0,X4: nat,X5: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(fun(X0,X1),fun(fun(X0,X1),fun(X0,X1))))))] : ( huffma107959123e_case(X0,X1,aa(nat,fun(nat,fun(X0,X1)),X2,X3),X6,huffma2021818691e_Leaf(X0,X4,X7)) = aa(X0,X1,huffma1280178957ee_rec(nat,fun(X0,X1),X2,X5,huffma2021818691e_Leaf(nat,X3,X4)),X7) )
    | ~ spl18_127
    | ~ spl18_128 ),
    inference(superposition,[],[f1644,f1648]) ).

tff(f4987,plain,
    ( spl18_296
    | ~ spl18_127
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1690,f1647,f1643,f4985]) ).

tff(f4985,plain,
    ( spl18_296
  <=> ! [X1: $tType,X0: $tType,X5: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(X0,X1)))),X4: nat,X2: fun(nat,fun(nat,fun(X0,X1))),X7: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X6: X0,X3: nat] : ( huffma1280178957ee_rec(X0,X1,aa(nat,fun(nat,fun(X0,X1)),X2,X3),X7,huffma2021818691e_Leaf(X0,X4,X6)) = aa(X0,X1,huffma107959123e_case(nat,fun(X0,X1),X2,X5,huffma2021818691e_Leaf(nat,X3,X4)),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_296])]) ).

tff(f1690,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(nat,fun(X0,X1))),X3: nat,X6: X0,X7: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X4: nat,X5: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(X0,X1))))] : ( huffma1280178957ee_rec(X0,X1,aa(nat,fun(nat,fun(X0,X1)),X2,X3),X7,huffma2021818691e_Leaf(X0,X4,X6)) = aa(X0,X1,huffma107959123e_case(nat,fun(X0,X1),X2,X5,huffma2021818691e_Leaf(nat,X3,X4)),X6) )
    | ~ spl18_127
    | ~ spl18_128 ),
    inference(superposition,[],[f1648,f1644]) ).

tff(f4983,plain,
    ( spl18_295
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1689,f1647,f4981]) ).

tff(f4981,plain,
    ( spl18_295
  <=> ! [X1: $tType,X0: $tType,X5: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(fun(X0,X1),fun(fun(X0,X1),fun(X0,X1)))))),X4: nat,X2: fun(nat,fun(nat,fun(X0,X1))),X7: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X6: X0,X3: nat] : ( huffma1280178957ee_rec(X0,X1,aa(nat,fun(nat,fun(X0,X1)),X2,X3),X7,huffma2021818691e_Leaf(X0,X4,X6)) = aa(X0,X1,huffma1280178957ee_rec(nat,fun(X0,X1),X2,X5,huffma2021818691e_Leaf(nat,X3,X4)),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_295])]) ).

tff(f1689,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(nat,fun(X0,X1))),X3: nat,X6: X0,X7: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X4: nat,X5: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(fun(X0,X1),fun(fun(X0,X1),fun(X0,X1))))))] : ( huffma1280178957ee_rec(X0,X1,aa(nat,fun(nat,fun(X0,X1)),X2,X3),X7,huffma2021818691e_Leaf(X0,X4,X6)) = aa(X0,X1,huffma1280178957ee_rec(nat,fun(X0,X1),X2,X5,huffma2021818691e_Leaf(nat,X3,X4)),X6) )
    | ~ spl18_128 ),
    inference(superposition,[],[f1648,f1648]) ).

tff(f4974,plain,
    ( spl18_294
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1666,f1643,f4972]) ).

tff(f4972,plain,
    ( spl18_294
  <=> ! [X1: $tType,X0: $tType,X2: fun(nat,fun(nat,fun(X0,X1))),X6: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X4: nat,X7: X0,X5: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(X0,X1)))),X3: nat] : ( huffma107959123e_case(X0,X1,aa(nat,fun(nat,fun(X0,X1)),X2,X3),X6,huffma2021818691e_Leaf(X0,X4,X7)) = aa(X0,X1,huffma107959123e_case(nat,fun(X0,X1),X2,X5,huffma2021818691e_Leaf(nat,X3,X4)),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_294])]) ).

tff(f1666,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(nat,fun(X0,X1))),X3: nat,X6: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X7: X0,X4: nat,X5: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(X0,X1))))] : ( huffma107959123e_case(X0,X1,aa(nat,fun(nat,fun(X0,X1)),X2,X3),X6,huffma2021818691e_Leaf(X0,X4,X7)) = aa(X0,X1,huffma107959123e_case(nat,fun(X0,X1),X2,X5,huffma2021818691e_Leaf(nat,X3,X4)),X7) )
    | ~ spl18_127 ),
    inference(superposition,[],[f1644,f1644]) ).

tff(f4970,plain,
    ( spl18_293
    | ~ spl18_92
    | ~ spl18_124 ),
    inference(avatar_split_clause,[],[f1615,f1576,f1203,f4968]) ).

tff(f4968,plain,
    ( spl18_293
  <=> ! [X1: $tType,X0: $tType,X4: X0,X3: fun(X0,X1),X2: fun(X0,X1)] :
        ( ~ ord_less_eq(fun(X0,X1),X2,X3)
        | ~ ord(X1)
        | ~ ord_less_eq(X1,aa(X0,X1,X3,X4),aa(X0,X1,X2,X4))
        | ( aa(X0,X1,X3,X4) = aa(X0,X1,X2,X4) )
        | ~ order(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_293])]) ).

tff(f1615,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(X0,X1),X3: fun(X0,X1),X4: X0] :
        ( ~ ord_less_eq(fun(X0,X1),X2,X3)
        | ~ ord(X1)
        | ~ ord_less_eq(X1,aa(X0,X1,X3,X4),aa(X0,X1,X2,X4))
        | ( aa(X0,X1,X3,X4) = aa(X0,X1,X2,X4) )
        | ~ order(X1) )
    | ~ spl18_92
    | ~ spl18_124 ),
    inference(resolution,[],[f1577,f1204]) ).

tff(f4955,plain,
    ( spl18_292
    | ~ spl18_94
    | ~ spl18_131 ),
    inference(avatar_split_clause,[],[f1779,f1766,f1211,f4953]) ).

tff(f4953,plain,
    ( spl18_292
  <=> ! [X4: nat,X0: nat,X3: nat,X2: fun(nat,fun(nat,bool)),X1: nat] :
        ( ord_less(nat,X0,X1)
        | ( X0 = X1 )
        | sP0(X1,X0,X2)
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,aa(nat,bool,aa(nat,fun(nat,bool),X2,X0),X1),X3,X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_292])]) ).

tff(f1779,plain,
    ( ! [X2: fun(nat,fun(nat,bool)),X3: nat,X0: nat,X1: nat,X4: nat] :
        ( ord_less(nat,X0,X1)
        | ( X0 = X1 )
        | sP0(X1,X0,X2)
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,aa(nat,bool,aa(nat,fun(nat,bool),X2,X0),X1),X3,X4)) ) )
    | ~ spl18_94
    | ~ spl18_131 ),
    inference(resolution,[],[f1767,f1212]) ).

tff(f4876,plain,
    ( spl18_291
    | ~ spl18_88
    | ~ spl18_143 ),
    inference(avatar_split_clause,[],[f1915,f1905,f1044,f4874]) ).

tff(f4874,plain,
    ( spl18_291
  <=> ! [X0: $tType,X5: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X6: X0,X2: nat,X1: nat] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X3,X4),X6) )
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X3,X4),X6) = X6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_291])]) ).

tff(f1915,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: nat,X6: X0,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,huffma1146269203erNode(X0,X2,X3,X4),X5),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X3,X4),X6) )
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X3,X4),X6) = X6 ) )
    | ~ spl18_88
    | ~ spl18_143 ),
    inference(resolution,[],[f1906,f1045]) ).

tff(f4872,plain,
    ( spl18_290
    | ~ spl18_81
    | spl18_195 ),
    inference(avatar_split_clause,[],[f2699,f2568,f1016,f4870]) ).

tff(f4870,plain,
    ( spl18_290
  <=> ! [X0: bool,X1: bool] :
        ( ~ ord_less(bool,fTrue,X0)
        | ( X0 = X1 )
        | ( fFalse = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_290])]) ).

tff(f2568,plain,
    ( spl18_195
  <=> ord_less(bool,fTrue,fFalse) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_195])]) ).

tff(f2699,plain,
    ( ! [X0: bool,X1: bool] :
        ( ~ ord_less(bool,fTrue,X0)
        | ( X0 = X1 )
        | ( fFalse = X1 ) )
    | ~ spl18_81
    | spl18_195 ),
    inference(superposition,[],[f2570,f1017]) ).

tff(f2570,plain,
    ( ~ ord_less(bool,fTrue,fFalse)
    | spl18_195 ),
    inference(avatar_component_clause,[],[f2568]) ).

tff(f4868,plain,
    ( spl18_289
    | ~ spl18_109
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1712,f1647,f1448,f4866]) ).

tff(f4866,plain,
    ( spl18_289
  <=> ! [X0: fun(nat,fun(int,bool)),X3: nat,X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,sK3(aa(nat,fun(int,bool),X0,X1)))))
        | pp(aa(int,bool,aa(nat,fun(int,bool),X0,X1),semiring_1_of_nat(int,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_289])]) ).

tff(f1712,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X3: nat,X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,sK3(aa(nat,fun(int,bool),X0,X1)))))
        | pp(aa(int,bool,aa(nat,fun(int,bool),X0,X1),semiring_1_of_nat(int,X3))) )
    | ~ spl18_109
    | ~ spl18_128 ),
    inference(superposition,[],[f1449,f1648]) ).

tff(f4864,plain,
    ( spl18_288
    | ~ spl18_110
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1708,f1647,f1452,f4862]) ).

tff(f4862,plain,
    ( spl18_288
  <=> ! [X0: fun(nat,fun(int,bool)),X3: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X2: nat,X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(int,bool,X0,X3,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,X2))))
        | pp(aa(int,bool,aa(nat,fun(int,bool),X0,X1),sK4(aa(nat,fun(int,bool),X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_288])]) ).

tff(f1708,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(int,bool,X0,X3,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,X2))))
        | pp(aa(int,bool,aa(nat,fun(int,bool),X0,X1),sK4(aa(nat,fun(int,bool),X0,X1)))) )
    | ~ spl18_110
    | ~ spl18_128 ),
    inference(superposition,[],[f1453,f1648]) ).

tff(f4860,plain,
    ( spl18_287
    | ~ spl18_109
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1681,f1643,f1448,f4858]) ).

tff(f4858,plain,
    ( spl18_287
  <=> ! [X0: fun(nat,fun(int,bool)),X3: nat,X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X1: nat] :
        ( ~ pp(huffma107959123e_case(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,sK3(aa(nat,fun(int,bool),X0,X1)))))
        | pp(aa(int,bool,aa(nat,fun(int,bool),X0,X1),semiring_1_of_nat(int,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_287])]) ).

tff(f1681,plain,
    ( ! [X2: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X3: nat,X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ~ pp(huffma107959123e_case(int,bool,X0,X2,huffma2021818691e_Leaf(int,X1,sK3(aa(nat,fun(int,bool),X0,X1)))))
        | pp(aa(int,bool,aa(nat,fun(int,bool),X0,X1),semiring_1_of_nat(int,X3))) )
    | ~ spl18_109
    | ~ spl18_127 ),
    inference(superposition,[],[f1449,f1644]) ).

tff(f4856,plain,
    ( spl18_286
    | ~ spl18_110
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1677,f1643,f1452,f4854]) ).

tff(f4854,plain,
    ( spl18_286
  <=> ! [X0: fun(nat,fun(int,bool)),X3: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X2: nat,X1: nat] :
        ( ~ pp(huffma107959123e_case(int,bool,X0,X3,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,X2))))
        | pp(aa(int,bool,aa(nat,fun(int,bool),X0,X1),sK4(aa(nat,fun(int,bool),X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_286])]) ).

tff(f1677,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ~ pp(huffma107959123e_case(int,bool,X0,X3,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,X2))))
        | pp(aa(int,bool,aa(nat,fun(int,bool),X0,X1),sK4(aa(nat,fun(int,bool),X0,X1)))) )
    | ~ spl18_110
    | ~ spl18_127 ),
    inference(superposition,[],[f1453,f1644]) ).

tff(f4838,plain,
    ( ~ spl18_20
    | spl18_285
    | ~ spl18_76
    | ~ spl18_124 ),
    inference(avatar_split_clause,[],[f1613,f1576,f954,f4836,f675]) ).

tff(f675,plain,
    ( spl18_20
  <=> ord(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_20])]) ).

tff(f4836,plain,
    ( spl18_285
  <=> ! [X0: $tType,X3: X0,X2: fun(X0,int),X1: fun(X0,int)] :
        ( ~ ord_less_eq(fun(X0,int),X1,X2)
        | ord_less(int,aa(X0,int,X1,X3),aa(X0,int,X2,X3))
        | ( aa(X0,int,X2,X3) = aa(X0,int,X1,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_285])]) ).

tff(f1613,plain,
    ( ! [X0: $tType,X2: fun(X0,int),X3: X0,X1: fun(X0,int)] :
        ( ~ ord_less_eq(fun(X0,int),X1,X2)
        | ~ ord(int)
        | ( aa(X0,int,X2,X3) = aa(X0,int,X1,X3) )
        | ord_less(int,aa(X0,int,X1,X3),aa(X0,int,X2,X3)) )
    | ~ spl18_76
    | ~ spl18_124 ),
    inference(resolution,[],[f1577,f955]) ).

tff(f4807,plain,
    ( ~ spl18_21
    | spl18_284
    | ~ spl18_75
    | ~ spl18_124 ),
    inference(avatar_split_clause,[],[f1611,f1576,f950,f4805,f680]) ).

tff(f680,plain,
    ( spl18_21
  <=> ord(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_21])]) ).

tff(f1611,plain,
    ( ! [X0: $tType,X2: fun(X0,nat),X3: X0,X1: fun(X0,nat)] :
        ( ~ ord_less_eq(fun(X0,nat),X1,X2)
        | ~ ord(nat)
        | ~ ord_less_eq(nat,aa(X0,nat,X2,X3),aa(X0,nat,X1,X3))
        | ( aa(X0,nat,X2,X3) = aa(X0,nat,X1,X3) ) )
    | ~ spl18_75
    | ~ spl18_124 ),
    inference(resolution,[],[f1577,f951]) ).

tff(f4520,plain,
    ( spl18_283
    | ~ spl18_127
    | ~ spl18_145 ),
    inference(avatar_split_clause,[],[f1943,f1931,f1643,f4518]) ).

tff(f4518,plain,
    ( spl18_283
  <=> ! [X0: $tType,X1: $tType,X5: fun(nat,fun(huffma1450048681e_tree(huffma1450048681e_tree(X0)),fun(huffma1450048681e_tree(huffma1450048681e_tree(X0)),fun(huffma1450048681e_tree(X0),X1)))),X4: huffma1450048681e_tree(X0),X6: fun(nat,fun(X0,X1)),X3: nat,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X7: huffma1450048681e_tree(X0)] : ( huffma107959123e_case(X0,X1,X6,X2,huffma1146269203erNode(X0,X3,X4,X7)) = aa(huffma1450048681e_tree(X0),X1,huffma107959123e_case(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),X2,X5,huffma2021818691e_Leaf(huffma1450048681e_tree(X0),X3,X4)),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_283])]) ).

tff(f1943,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X3: nat,X6: fun(nat,fun(X0,X1)),X7: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X5: fun(nat,fun(huffma1450048681e_tree(huffma1450048681e_tree(X0)),fun(huffma1450048681e_tree(huffma1450048681e_tree(X0)),fun(huffma1450048681e_tree(X0),X1))))] : ( huffma107959123e_case(X0,X1,X6,X2,huffma1146269203erNode(X0,X3,X4,X7)) = aa(huffma1450048681e_tree(X0),X1,huffma107959123e_case(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),X2,X5,huffma2021818691e_Leaf(huffma1450048681e_tree(X0),X3,X4)),X7) )
    | ~ spl18_127
    | ~ spl18_145 ),
    inference(superposition,[],[f1932,f1644]) ).

tff(f4516,plain,
    ( spl18_282
    | ~ spl18_128
    | ~ spl18_145 ),
    inference(avatar_split_clause,[],[f1942,f1931,f1647,f4514]) ).

tff(f4514,plain,
    ( spl18_282
  <=> ! [X0: $tType,X1: $tType,X5: fun(nat,fun(huffma1450048681e_tree(huffma1450048681e_tree(X0)),fun(huffma1450048681e_tree(huffma1450048681e_tree(X0)),fun(fun(huffma1450048681e_tree(X0),X1),fun(fun(huffma1450048681e_tree(X0),X1),fun(huffma1450048681e_tree(X0),X1)))))),X4: huffma1450048681e_tree(X0),X6: fun(nat,fun(X0,X1)),X3: nat,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X7: huffma1450048681e_tree(X0)] : ( huffma107959123e_case(X0,X1,X6,X2,huffma1146269203erNode(X0,X3,X4,X7)) = aa(huffma1450048681e_tree(X0),X1,huffma1280178957ee_rec(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),X2,X5,huffma2021818691e_Leaf(huffma1450048681e_tree(X0),X3,X4)),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_282])]) ).

tff(f1942,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X3: nat,X6: fun(nat,fun(X0,X1)),X7: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X5: fun(nat,fun(huffma1450048681e_tree(huffma1450048681e_tree(X0)),fun(huffma1450048681e_tree(huffma1450048681e_tree(X0)),fun(fun(huffma1450048681e_tree(X0),X1),fun(fun(huffma1450048681e_tree(X0),X1),fun(huffma1450048681e_tree(X0),X1))))))] : ( huffma107959123e_case(X0,X1,X6,X2,huffma1146269203erNode(X0,X3,X4,X7)) = aa(huffma1450048681e_tree(X0),X1,huffma1280178957ee_rec(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1),X2,X5,huffma2021818691e_Leaf(huffma1450048681e_tree(X0),X3,X4)),X7) )
    | ~ spl18_128
    | ~ spl18_145 ),
    inference(superposition,[],[f1932,f1648]) ).

tff(f4512,plain,
    ( spl18_281
    | ~ spl18_137
    | ~ spl18_143 ),
    inference(avatar_split_clause,[],[f1916,f1905,f1844,f4510]) ).

tff(f1916,plain,
    ( ! [X0: $tType,X2: X0,X3: nat,X1: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0)] :
        ( ~ member(X0,X2,huffma675207370phabet(X0,X1))
        | ( huffma1401021291ibling(X0,X1,X2) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X1,X4),X2) )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) )
    | ~ spl18_137
    | ~ spl18_143 ),
    inference(superposition,[],[f1906,f1845]) ).

tff(f4508,plain,
    ( spl18_280
    | ~ spl18_124
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1705,f1647,f1576,f4506]) ).

tff(f4506,plain,
    ( spl18_280
  <=> ! [X1: $tType,X0: $tType,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X3: nat,X4: X0,X2: fun(nat,fun(X0,X1)),X6: fun(X0,X1)] :
        ( ord_less_eq(X1,huffma1280178957ee_rec(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,X4)),aa(X0,X1,X6,X4))
        | ~ ord_less_eq(fun(X0,X1),aa(nat,fun(X0,X1),X2,X3),X6)
        | ~ ord(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_280])]) ).

tff(f1705,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X6: fun(X0,X1),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))))] :
        ( ord_less_eq(X1,huffma1280178957ee_rec(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,X4)),aa(X0,X1,X6,X4))
        | ~ ord_less_eq(fun(X0,X1),aa(nat,fun(X0,X1),X2,X3),X6)
        | ~ ord(X1) )
    | ~ spl18_124
    | ~ spl18_128 ),
    inference(superposition,[],[f1577,f1648]) ).

tff(f4499,plain,
    ( spl18_279
    | ~ spl18_124
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1704,f1647,f1576,f4497]) ).

tff(f4497,plain,
    ( spl18_279
  <=> ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X6: fun(X0,X1),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X3: nat] :
        ( ord_less_eq(X1,aa(X0,X1,X6,X4),huffma1280178957ee_rec(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,X4)))
        | ~ ord_less_eq(fun(X0,X1),X6,aa(nat,fun(X0,X1),X2,X3))
        | ~ ord(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_279])]) ).

tff(f1704,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X6: fun(X0,X1),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))))] :
        ( ord_less_eq(X1,aa(X0,X1,X6,X4),huffma1280178957ee_rec(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,X4)))
        | ~ ord_less_eq(fun(X0,X1),X6,aa(nat,fun(X0,X1),X2,X3))
        | ~ ord(X1) )
    | ~ spl18_124
    | ~ spl18_128 ),
    inference(superposition,[],[f1577,f1648]) ).

tff(f4495,plain,
    ( spl18_278
    | ~ spl18_124
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1674,f1643,f1576,f4493]) ).

tff(f4493,plain,
    ( spl18_278
  <=> ! [X1: $tType,X0: $tType,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X3: nat,X4: X0,X2: fun(nat,fun(X0,X1)),X6: fun(X0,X1)] :
        ( ord_less_eq(X1,huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,X4)),aa(X0,X1,X6,X4))
        | ~ ord_less_eq(fun(X0,X1),aa(nat,fun(X0,X1),X2,X3),X6)
        | ~ ord(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_278])]) ).

tff(f1674,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X6: fun(X0,X1),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)))] :
        ( ord_less_eq(X1,huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,X4)),aa(X0,X1,X6,X4))
        | ~ ord_less_eq(fun(X0,X1),aa(nat,fun(X0,X1),X2,X3),X6)
        | ~ ord(X1) )
    | ~ spl18_124
    | ~ spl18_127 ),
    inference(superposition,[],[f1577,f1644]) ).

tff(f4491,plain,
    ( spl18_277
    | ~ spl18_124
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1673,f1643,f1576,f4489]) ).

tff(f4489,plain,
    ( spl18_277
  <=> ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X6: fun(X0,X1),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X3: nat] :
        ( ord_less_eq(X1,aa(X0,X1,X6,X4),huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,X4)))
        | ~ ord_less_eq(fun(X0,X1),X6,aa(nat,fun(X0,X1),X2,X3))
        | ~ ord(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_277])]) ).

tff(f1673,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X6: fun(X0,X1),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)))] :
        ( ord_less_eq(X1,aa(X0,X1,X6,X4),huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,X4)))
        | ~ ord_less_eq(fun(X0,X1),X6,aa(nat,fun(X0,X1),X2,X3))
        | ~ ord(X1) )
    | ~ spl18_124
    | ~ spl18_127 ),
    inference(superposition,[],[f1577,f1644]) ).

tff(f4487,plain,
    ( spl18_276
    | ~ spl18_94
    | ~ spl18_126 ),
    inference(avatar_split_clause,[],[f1654,f1639,f1211,f4485]) ).

tff(f4485,plain,
    ( spl18_276
  <=> ! [X0: fun(nat,bool),X3: nat,X2: nat,X1: nat] :
        ( ~ pp(aa(nat,bool,X0,X1))
        | pp(aa(nat,bool,X0,zero_zero(nat)))
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X0,sK7(X1,X0)),X2,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_276])]) ).

tff(f1654,plain,
    ( ! [X2: nat,X3: nat,X0: fun(nat,bool),X1: nat] :
        ( ~ pp(aa(nat,bool,X0,X1))
        | pp(aa(nat,bool,X0,zero_zero(nat)))
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X0,sK7(X1,X0)),X2,X3)) ) )
    | ~ spl18_94
    | ~ spl18_126 ),
    inference(resolution,[],[f1640,f1212]) ).

tff(f4425,plain,
    ( spl18_275
    | ~ spl18_95
    | ~ spl18_125 ),
    inference(avatar_split_clause,[],[f1631,f1580,f1215,f4423]) ).

tff(f4423,plain,
    ( spl18_275
  <=> ! [X0: fun(nat,bool),X3: nat,X2: nat,X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ pp(aa(nat,bool,X0,zero_zero(nat)))
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X0,sK8(X0)),X3,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_275])]) ).

tff(f1631,plain,
    ( ! [X2: nat,X3: nat,X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ pp(aa(nat,bool,X0,zero_zero(nat)))
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X0,sK8(X0)),X3,X2)) ) )
    | ~ spl18_95
    | ~ spl18_125 ),
    inference(resolution,[],[f1581,f1216]) ).

tff(f4421,plain,
    ( spl18_274
    | ~ spl18_95
    | ~ spl18_123 ),
    inference(avatar_split_clause,[],[f1603,f1572,f1215,f4419]) ).

tff(f1603,plain,
    ( ! [X2: nat,X3: nat,X0: fun(int,bool),X1: int] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ ord_less_eq(int,zero_zero(int),X1)
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,X1),X3,X2)) ) )
    | ~ spl18_95
    | ~ spl18_123 ),
    inference(resolution,[],[f1573,f1216]) ).

tff(f4417,plain,
    ( spl18_273
    | ~ spl18_95
    | ~ spl18_122 ),
    inference(avatar_split_clause,[],[f1585,f1568,f1215,f4415]) ).

tff(f4415,plain,
    ( spl18_273
  <=> ! [X0: int,X3: nat,X2: nat,X1: fun(int,bool)] :
        ( ~ ord_less_eq(int,zero_zero(int),X0)
        | pp(aa(int,bool,X1,X0))
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(int,bool,X1,semiring_1_of_nat(int,sK2(X1))),X3,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_273])]) ).

tff(f1585,plain,
    ( ! [X2: nat,X3: nat,X0: int,X1: fun(int,bool)] :
        ( ~ ord_less_eq(int,zero_zero(int),X0)
        | pp(aa(int,bool,X1,X0))
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(int,bool,X1,semiring_1_of_nat(int,sK2(X1))),X3,X2)) ) )
    | ~ spl18_95
    | ~ spl18_122 ),
    inference(resolution,[],[f1569,f1216]) ).

tff(f4413,plain,
    ( spl18_272
    | spl18_150
    | ~ spl18_181 ),
    inference(avatar_split_clause,[],[f3804,f2396,f2033,f4411]) ).

tff(f2033,plain,
    ( spl18_150
  <=> ord_less(bool,fTrue,zero_zero(bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_150])]) ).

tff(f3804,plain,
    ( ! [X0: bool] :
        ( ~ ord_less(bool,fTrue,X0)
        | ( fFalse = X0 ) )
    | spl18_150
    | ~ spl18_181 ),
    inference(superposition,[],[f2035,f2397]) ).

tff(f2035,plain,
    ( ~ ord_less(bool,fTrue,zero_zero(bool))
    | spl18_150 ),
    inference(avatar_component_clause,[],[f2033]) ).

tff(f4305,plain,
    ( spl18_271
    | ~ spl18_140 ),
    inference(avatar_split_clause,[],[f1898,f1877,f4303]) ).

tff(f4303,plain,
    ( spl18_271
  <=> ! [X0: $tType,X5: nat,X4: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X2: nat,X1: X0] :
        ( member(X0,X1,huffma675207370phabet(X0,huffma1146269203erNode(X0,X2,X3,X4)))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X5,huffma1146269203erNode(X0,X2,X3,X4),huffma1146269203erNode(X0,X2,X3,X4)),X1) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_271])]) ).

tff(f1898,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: X0,X4: huffma1450048681e_tree(X0),X5: nat] :
        ( member(X0,X1,huffma675207370phabet(X0,huffma1146269203erNode(X0,X2,X3,X4)))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X5,huffma1146269203erNode(X0,X2,X3,X4),huffma1146269203erNode(X0,X2,X3,X4)),X1) = X1 ) )
    | ~ spl18_140 ),
    inference(factoring,[],[f1878]) ).

tff(f4301,plain,
    ( spl18_270
    | ~ spl18_113
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1719,f1647,f1483,f4299]) ).

tff(f4299,plain,
    ( spl18_270
  <=> ! [X4: nat,X0: fun(nat,fun(nat,fun(nat,bool))),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)))))),X2: nat,X1: nat] :
        ( ~ pp(aa(nat,bool,huffma1280178957ee_rec(nat,fun(nat,bool),X0,X3,huffma2021818691e_Leaf(nat,X1,X2)),X4))
        | ~ sP0(X4,X2,aa(nat,fun(nat,fun(nat,bool)),X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_270])]) ).

tff(f1719,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)))))),X0: fun(nat,fun(nat,fun(nat,bool))),X1: nat,X4: nat] :
        ( ~ pp(aa(nat,bool,huffma1280178957ee_rec(nat,fun(nat,bool),X0,X3,huffma2021818691e_Leaf(nat,X1,X2)),X4))
        | ~ sP0(X4,X2,aa(nat,fun(nat,fun(nat,bool)),X0,X1)) )
    | ~ spl18_113
    | ~ spl18_128 ),
    inference(superposition,[],[f1484,f1648]) ).

tff(f4297,plain,
    ( spl18_269
    | ~ spl18_113
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1688,f1643,f1483,f4295]) ).

tff(f4295,plain,
    ( spl18_269
  <=> ! [X4: nat,X0: fun(nat,fun(nat,fun(nat,bool))),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(nat,bool)))),X2: nat,X1: nat] :
        ( ~ pp(aa(nat,bool,huffma107959123e_case(nat,fun(nat,bool),X0,X3,huffma2021818691e_Leaf(nat,X1,X2)),X4))
        | ~ sP0(X4,X2,aa(nat,fun(nat,fun(nat,bool)),X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_269])]) ).

tff(f1688,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(nat,bool)))),X0: fun(nat,fun(nat,fun(nat,bool))),X1: nat,X4: nat] :
        ( ~ pp(aa(nat,bool,huffma107959123e_case(nat,fun(nat,bool),X0,X3,huffma2021818691e_Leaf(nat,X1,X2)),X4))
        | ~ sP0(X4,X2,aa(nat,fun(nat,fun(nat,bool)),X0,X1)) )
    | ~ spl18_113
    | ~ spl18_127 ),
    inference(superposition,[],[f1484,f1644]) ).

tff(f4293,plain,
    ( spl18_268
    | ~ spl18_95
    | ~ spl18_120 ),
    inference(avatar_split_clause,[],[f1555,f1539,f1215,f4291]) ).

tff(f1555,plain,
    ( ! [X2: nat,X3: nat,X0: fun(nat,bool),X1: nat] :
        ( ord_less(nat,zero_zero(nat),sK8(X0))
        | pp(aa(nat,bool,X0,X1))
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X0,zero_zero(nat)),X3,X2)) ) )
    | ~ spl18_95
    | ~ spl18_120 ),
    inference(resolution,[],[f1540,f1216]) ).

tff(f4289,plain,
    ( spl18_267
    | ~ spl18_95
    | ~ spl18_119 ),
    inference(avatar_split_clause,[],[f1547,f1524,f1215,f4287]) ).

tff(f1547,plain,
    ( ! [X2: nat,X3: nat,X0: nat,X1: fun(nat,bool)] :
        ( ord_less_eq(nat,sK7(X0,X1),X0)
        | pp(aa(nat,bool,X1,zero_zero(nat)))
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(nat,bool,X1,X0),X3,X2)) ) )
    | ~ spl18_95
    | ~ spl18_119 ),
    inference(resolution,[],[f1525,f1216]) ).

tff(f4228,plain,
    ( spl18_266
    | ~ spl18_126
    | ~ spl18_136 ),
    inference(avatar_split_clause,[],[f1859,f1840,f1639,f4226]) ).

tff(f4226,plain,
    ( spl18_266
  <=> ! [X2: nat,X0: nat,X1: fun(nat,bool)] :
        ( ~ ord_less(nat,sK7(X0,X1),sK7(X2,X1))
        | ~ pp(aa(nat,bool,X1,X2))
        | pp(aa(nat,bool,X1,zero_zero(nat)))
        | ~ pp(aa(nat,bool,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_266])]) ).

tff(f1859,plain,
    ( ! [X2: nat,X0: nat,X1: fun(nat,bool)] :
        ( ~ ord_less(nat,sK7(X0,X1),sK7(X2,X1))
        | ~ pp(aa(nat,bool,X1,X2))
        | pp(aa(nat,bool,X1,zero_zero(nat)))
        | ~ pp(aa(nat,bool,X1,X0)) )
    | ~ spl18_126
    | ~ spl18_136 ),
    inference(duplicate_literal_removal,[],[f1847]) ).

tff(f1847,plain,
    ( ! [X2: nat,X0: nat,X1: fun(nat,bool)] :
        ( ~ ord_less(nat,sK7(X0,X1),sK7(X2,X1))
        | ~ pp(aa(nat,bool,X1,X2))
        | pp(aa(nat,bool,X1,zero_zero(nat)))
        | ~ pp(aa(nat,bool,X1,X0))
        | pp(aa(nat,bool,X1,zero_zero(nat))) )
    | ~ spl18_126
    | ~ spl18_136 ),
    inference(resolution,[],[f1841,f1640]) ).

tff(f4224,plain,
    ( spl18_265
    | ~ spl18_31
    | ~ spl18_134 ),
    inference(avatar_split_clause,[],[f1836,f1799,f725,f4222]) ).

tff(f4222,plain,
    ( spl18_265
  <=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
        ( ( fTrue != aa(X0,bool,X2,sK17(bool,X0,X1,X2)) )
        | ( X1 = X2 )
        | ( fFalse = aa(X0,bool,X1,sK17(bool,X0,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_265])]) ).

tff(f1836,plain,
    ( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
        ( ( fTrue != aa(X0,bool,X2,sK17(bool,X0,X1,X2)) )
        | ( X1 = X2 )
        | ( fFalse = aa(X0,bool,X1,sK17(bool,X0,X1,X2)) ) )
    | ~ spl18_31
    | ~ spl18_134 ),
    inference(superposition,[],[f1800,f726]) ).

tff(f4220,plain,
    ( spl18_264
    | ~ spl18_31
    | ~ spl18_134 ),
    inference(avatar_split_clause,[],[f1823,f1799,f725,f4218]) ).

tff(f4218,plain,
    ( spl18_264
  <=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
        ( ( fTrue != aa(X0,bool,X2,sK17(bool,X0,X2,X1)) )
        | ( X1 = X2 )
        | ( fFalse = aa(X0,bool,X1,sK17(bool,X0,X2,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_264])]) ).

tff(f1823,plain,
    ( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
        ( ( fTrue != aa(X0,bool,X2,sK17(bool,X0,X2,X1)) )
        | ( X1 = X2 )
        | ( fFalse = aa(X0,bool,X1,sK17(bool,X0,X2,X1)) ) )
    | ~ spl18_31
    | ~ spl18_134 ),
    inference(superposition,[],[f1800,f726]) ).

tff(f4216,plain,
    ( spl18_263
    | ~ spl18_112
    | ~ spl18_132 ),
    inference(avatar_split_clause,[],[f1792,f1770,f1479,f4214]) ).

tff(f4214,plain,
    ( spl18_263
  <=> ! [X0: $tType,X5: huffma1450048681e_tree(X0),X3: nat,X4: huffma1450048681e_tree(X0),X6: X0,X2: huffma1450048681e_tree(X0),X1: nat] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),X6) = huffma1401021291ibling(X0,X2,X6) )
        | ( zero_zero(nat) = aa(X0,nat,huffma1352802255e_freq(X0,X2),X6) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_263])]) ).

tff(f1792,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: nat,X6: X0,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),X6) = huffma1401021291ibling(X0,X2,X6) )
        | ( zero_zero(nat) = aa(X0,nat,huffma1352802255e_freq(X0,X2),X6) ) )
    | ~ spl18_112
    | ~ spl18_132 ),
    inference(resolution,[],[f1771,f1480]) ).

tff(f4206,plain,
    ( spl18_262
    | ~ spl18_29
    | ~ spl18_144 ),
    inference(avatar_split_clause,[],[f1921,f1918,f715,f4204]) ).

tff(f4204,plain,
    ( spl18_262
  <=> ! [X0: nat,X3: huffma1450048681e_tree(a1),X2: huffma1450048681e_tree(a1),X1: nat] :
        ( ( huffma1401021291ibling(a1,t_1,a) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,huffma1146269203erNode(a1,X1,X2,X3),t_1),a) )
        | member(a1,a,huffma675207370phabet(a1,huffma1146269203erNode(a1,X1,X2,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_262])]) ).

tff(f1921,plain,
    ( ! [X2: huffma1450048681e_tree(a1),X3: huffma1450048681e_tree(a1),X0: nat,X1: nat] :
        ( ( huffma1401021291ibling(a1,t_1,a) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,huffma1146269203erNode(a1,X1,X2,X3),t_1),a) )
        | member(a1,a,huffma675207370phabet(a1,huffma1146269203erNode(a1,X1,X2,X3))) )
    | ~ spl18_29
    | ~ spl18_144 ),
    inference(resolution,[],[f1919,f717]) ).

tff(f4148,plain,
    ( spl18_261
    | ~ spl18_87
    | ~ spl18_129 ),
    inference(avatar_split_clause,[],[f1743,f1722,f1040,f4146]) ).

tff(f1743,plain,
    ( ! [X2: fun(nat,nat),X3: nat,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less(nat,sK15(X2),sK16(X2))
        | ~ ord_less_eq(nat,aa(nat,nat,X2,X1),X3)
        | ord_less_eq(nat,aa(nat,nat,X2,X0),X3) )
    | ~ spl18_87
    | ~ spl18_129 ),
    inference(resolution,[],[f1723,f1041]) ).

tff(f4144,plain,
    ( spl18_260
    | ~ spl18_104
    | ~ spl18_124 ),
    inference(avatar_split_clause,[],[f1614,f1576,f1278,f4142]) ).

tff(f4142,plain,
    ( spl18_260
  <=> ! [X1: $tType,X0: $tType,X5: X1,X4: X0,X3: fun(X0,X1),X2: fun(X0,X1)] :
        ( ~ ord_less_eq(fun(X0,X1),X2,X3)
        | ~ ord(X1)
        | ~ ord_less_eq(X1,aa(X0,X1,X3,X4),X5)
        | ord_less_eq(X1,aa(X0,X1,X2,X4),X5)
        | ~ preorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_260])]) ).

tff(f1614,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(X0,X1),X3: fun(X0,X1),X4: X0,X5: X1] :
        ( ~ ord_less_eq(fun(X0,X1),X2,X3)
        | ~ ord(X1)
        | ~ ord_less_eq(X1,aa(X0,X1,X3,X4),X5)
        | ord_less_eq(X1,aa(X0,X1,X2,X4),X5)
        | ~ preorder(X1) )
    | ~ spl18_104
    | ~ spl18_124 ),
    inference(resolution,[],[f1577,f1279]) ).

tff(f4122,plain,
    ( spl18_259
    | ~ spl18_117
    | ~ spl18_137 ),
    inference(avatar_split_clause,[],[f1865,f1844,f1499,f4120]) ).

tff(f4120,plain,
    ( spl18_259
  <=> ! [X0: $tType,X4: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X2: nat,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma1146269203erNode(X0,X2,X3,X4) != X1 )
        | ( sK11(X0,X1) = X4 )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_259])]) ).

tff(f1499,plain,
    ( spl18_117
  <=> ! [X0: $tType,X2: huffma1450048681e_tree(X0),X6: nat,X4: huffma1450048681e_tree(X0),X3: nat,X5: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
        ( ( X1 = X4 )
        | ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_117])]) ).

tff(f1865,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0)] :
        ( ( huffma1146269203erNode(X0,X2,X3,X4) != X1 )
        | ( sK11(X0,X1) = X4 )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) )
    | ~ spl18_117
    | ~ spl18_137 ),
    inference(superposition,[],[f1500,f1845]) ).

tff(f1500,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X6: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) )
        | ( X1 = X4 ) )
    | ~ spl18_117 ),
    inference(avatar_component_clause,[],[f1499]) ).

tff(f4118,plain,
    ( spl18_258
    | ~ spl18_116
    | ~ spl18_137 ),
    inference(avatar_split_clause,[],[f1863,f1844,f1495,f4116]) ).

tff(f4116,plain,
    ( spl18_258
  <=> ! [X0: $tType,X4: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X2: nat,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma1146269203erNode(X0,X2,X3,X4) != X1 )
        | ( sK10(X0,X1) = X3 )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_258])]) ).

tff(f1495,plain,
    ( spl18_116
  <=> ! [X0: $tType,X6: nat,X4: huffma1450048681e_tree(X0),X3: nat,X5: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
        ( ( X2 = X5 )
        | ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_116])]) ).

tff(f1863,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0)] :
        ( ( huffma1146269203erNode(X0,X2,X3,X4) != X1 )
        | ( sK10(X0,X1) = X3 )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) )
    | ~ spl18_116
    | ~ spl18_137 ),
    inference(superposition,[],[f1496,f1845]) ).

tff(f1496,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X6: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) )
        | ( X2 = X5 ) )
    | ~ spl18_116 ),
    inference(avatar_component_clause,[],[f1495]) ).

tff(f4114,plain,
    ( spl18_242
    | ~ spl18_31
    | ~ spl18_195 ),
    inference(avatar_split_clause,[],[f3396,f2568,f725,f3518]) ).

tff(f3518,plain,
    ( spl18_242
  <=> ! [X0: bool] :
        ( ord_less(bool,X0,fFalse)
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_242])]) ).

tff(f3396,plain,
    ( ! [X0: bool] :
        ( ord_less(bool,X0,fFalse)
        | ( fFalse = X0 ) )
    | ~ spl18_31
    | ~ spl18_195 ),
    inference(superposition,[],[f2569,f726]) ).

tff(f2569,plain,
    ( ord_less(bool,fTrue,fFalse)
    | ~ spl18_195 ),
    inference(avatar_component_clause,[],[f2568]) ).

tff(f4113,plain,
    ( spl18_257
    | ~ spl18_31
    | ~ spl18_130 ),
    inference(avatar_split_clause,[],[f1762,f1740,f725,f4111]) ).

tff(f4111,plain,
    ( spl18_257
  <=> ! [X3: nat,X4: bool,X0: nat,X5: bool,X2: bool,X1: nat] :
        ( ( fTrue = X5 )
        | ( X4 = X5 )
        | ( X2 = X5 )
        | ( fFalse = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X0,huffma2021818691e_Leaf(bool,X1,X2),huffma2021818691e_Leaf(bool,X3,X4)),X5) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_257])]) ).

tff(f1740,plain,
    ( spl18_130
  <=> ! [X0: $tType,X5: X0,X3: nat,X4: nat,X6: X0,X2: nat,X1: X0] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,huffma2021818691e_Leaf(X0,X3,X5),huffma2021818691e_Leaf(X0,X2,X1)),X6) = X6 )
        | ( X1 = X6 )
        | ( X5 = X6 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_130])]) ).

tff(f1762,plain,
    ( ! [X2: bool,X3: nat,X0: nat,X1: nat,X4: bool,X5: bool] :
        ( ( fTrue = X5 )
        | ( X4 = X5 )
        | ( X2 = X5 )
        | ( fFalse = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X0,huffma2021818691e_Leaf(bool,X1,X2),huffma2021818691e_Leaf(bool,X3,X4)),X5) ) )
    | ~ spl18_31
    | ~ spl18_130 ),
    inference(superposition,[],[f1741,f726]) ).

tff(f1741,plain,
    ( ! [X0: $tType,X2: nat,X3: nat,X1: X0,X6: X0,X4: nat,X5: X0] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,huffma2021818691e_Leaf(X0,X3,X5),huffma2021818691e_Leaf(X0,X2,X1)),X6) = X6 )
        | ( X1 = X6 )
        | ( X5 = X6 ) )
    | ~ spl18_130 ),
    inference(avatar_component_clause,[],[f1740]) ).

tff(f4105,plain,
    ( ~ spl18_21
    | spl18_256
    | ~ spl18_114
    | ~ spl18_124 ),
    inference(avatar_split_clause,[],[f1629,f1576,f1487,f4103,f680]) ).

tff(f1629,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: nat,X4: fun(X0,nat)] :
        ( ord_less_eq(nat,aa(X0,nat,X4,X3),zero_zero(nat))
        | ~ ord_less_eq(fun(X0,nat),X4,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)))
        | ~ ord(nat)
        | ( X2 = X3 ) )
    | ~ spl18_114
    | ~ spl18_124 ),
    inference(superposition,[],[f1577,f1488]) ).

tff(f4101,plain,
    ( spl18_255
    | ~ spl18_95
    | ~ spl18_113 ),
    inference(avatar_split_clause,[],[f1507,f1483,f1215,f4099]) ).

tff(f4099,plain,
    ( spl18_255
  <=> ! [X4: nat,X0: nat,X3: nat,X2: fun(nat,fun(nat,bool)),X1: nat] :
        ( ~ sP0(X0,X1,X2)
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0),X4,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_255])]) ).

tff(f1507,plain,
    ( ! [X2: fun(nat,fun(nat,bool)),X3: nat,X0: nat,X1: nat,X4: nat] :
        ( ~ sP0(X0,X1,X2)
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0),X4,X3)) ) )
    | ~ spl18_95
    | ~ spl18_113 ),
    inference(resolution,[],[f1484,f1216]) ).

tff(f3603,plain,
    ( spl18_254
    | ~ spl18_111
    | ~ spl18_137 ),
    inference(avatar_split_clause,[],[f1861,f1844,f1456,f3601]) ).

tff(f3601,plain,
    ( spl18_254
  <=> ! [X0: $tType,X4: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X2: nat,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma1146269203erNode(X0,X2,X3,X4) != X1 )
        | ( sK9(X0,X1) = X2 )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_254])]) ).

tff(f1456,plain,
    ( spl18_111
  <=> ! [X0: $tType,X5: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X6: nat,X3: nat,X1: huffma1450048681e_tree(X0)] :
        ( ( X3 = X6 )
        | ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_111])]) ).

tff(f1861,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0)] :
        ( ( huffma1146269203erNode(X0,X2,X3,X4) != X1 )
        | ( sK9(X0,X1) = X2 )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) )
    | ~ spl18_111
    | ~ spl18_137 ),
    inference(superposition,[],[f1457,f1845]) ).

tff(f1457,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X6: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) )
        | ( X3 = X6 ) )
    | ~ spl18_111 ),
    inference(avatar_component_clause,[],[f1456]) ).

tff(f3599,plain,
    ( spl18_253
    | ~ spl18_73
    | ~ spl18_132 ),
    inference(avatar_split_clause,[],[f1791,f1770,f942,f3597]) ).

tff(f3597,plain,
    ( spl18_253
  <=> ! [X0: $tType,X3: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X1: nat] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),sK6(X0,X2)) = huffma1401021291ibling(X0,X2,sK6(X0,X2)) )
        | ~ huffma1518433673istent(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_253])]) ).

tff(f1791,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),sK6(X0,X2)) = huffma1401021291ibling(X0,X2,sK6(X0,X2)) )
        | ~ huffma1518433673istent(X0,X2) )
    | ~ spl18_73
    | ~ spl18_132 ),
    inference(resolution,[],[f1771,f943]) ).

tff(f3595,plain,
    ( spl18_252
    | ~ spl18_106
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1710,f1647,f1286,f3593]) ).

tff(f3593,plain,
    ( spl18_252
  <=> ! [X0: fun(nat,fun(int,bool)),X3: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X2: nat,X1: nat] :
        ( pp(huffma1280178957ee_rec(int,bool,X0,X3,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,X2))))
        | ord_less_eq(int,zero_zero(int),sK3(aa(nat,fun(int,bool),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_252])]) ).

tff(f1286,plain,
    ( spl18_106
  <=> ! [X0: fun(int,bool),X3: nat] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,X3)))
        | ord_less_eq(int,zero_zero(int),sK3(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_106])]) ).

tff(f1710,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( pp(huffma1280178957ee_rec(int,bool,X0,X3,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,X2))))
        | ord_less_eq(int,zero_zero(int),sK3(aa(nat,fun(int,bool),X0,X1))) )
    | ~ spl18_106
    | ~ spl18_128 ),
    inference(superposition,[],[f1287,f1648]) ).

tff(f1287,plain,
    ( ! [X3: nat,X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,X3)))
        | ord_less_eq(int,zero_zero(int),sK3(X0)) )
    | ~ spl18_106 ),
    inference(avatar_component_clause,[],[f1286]) ).

tff(f3591,plain,
    ( spl18_251
    | ~ spl18_107
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1709,f1647,f1290,f3589]) ).

tff(f1709,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),fun(bool,fun(bool,bool))))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(int,bool,X0,X3,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,X2))))
        | ord_less_eq(int,zero_zero(int),sK4(aa(nat,fun(int,bool),X0,X1))) )
    | ~ spl18_107
    | ~ spl18_128 ),
    inference(superposition,[],[f1291,f1648]) ).

tff(f3580,plain,
    ( spl18_250
    | ~ spl18_31
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1702,f1647,f725,f3578]) ).

tff(f3578,plain,
    ( spl18_250
  <=> ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X4: X0,X3: nat,X1: fun(nat,fun(X0,bool))] :
        ( ( fTrue = aa(X0,bool,aa(nat,fun(X0,bool),X1,X3),X4) )
        | ( fFalse = huffma1280178957ee_rec(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_250])]) ).

tff(f1702,plain,
    ( ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X3: nat,X1: fun(nat,fun(X0,bool)),X4: X0] :
        ( ( fTrue = aa(X0,bool,aa(nat,fun(X0,bool),X1,X3),X4) )
        | ( fFalse = huffma1280178957ee_rec(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) ) )
    | ~ spl18_31
    | ~ spl18_128 ),
    inference(superposition,[],[f1648,f726]) ).

tff(f3576,plain,
    ( spl18_249
    | ~ spl18_31
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1697,f1647,f725,f3574]) ).

tff(f1697,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: fun(nat,fun(X0,bool)),X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))))] :
        ( ( fTrue = huffma1280178957ee_rec(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)) )
        | ( fFalse = aa(X0,bool,aa(nat,fun(X0,bool),X1,X2),X3) ) )
    | ~ spl18_31
    | ~ spl18_128 ),
    inference(superposition,[],[f1648,f726]) ).

tff(f3572,plain,
    ( spl18_248
    | ~ spl18_106
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1679,f1643,f1286,f3570]) ).

tff(f3570,plain,
    ( spl18_248
  <=> ! [X0: fun(nat,fun(int,bool)),X3: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X2: nat,X1: nat] :
        ( pp(huffma107959123e_case(int,bool,X0,X3,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,X2))))
        | ord_less_eq(int,zero_zero(int),sK3(aa(nat,fun(int,bool),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_248])]) ).

tff(f1679,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( pp(huffma107959123e_case(int,bool,X0,X3,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,X2))))
        | ord_less_eq(int,zero_zero(int),sK3(aa(nat,fun(int,bool),X0,X1))) )
    | ~ spl18_106
    | ~ spl18_127 ),
    inference(superposition,[],[f1287,f1644]) ).

tff(f3568,plain,
    ( spl18_247
    | ~ spl18_107
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1678,f1643,f1290,f3566]) ).

tff(f1678,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(int),fun(huffma1450048681e_tree(int),bool))),X0: fun(nat,fun(int,bool)),X1: nat] :
        ( ~ pp(huffma107959123e_case(int,bool,X0,X3,huffma2021818691e_Leaf(int,X1,semiring_1_of_nat(int,X2))))
        | ord_less_eq(int,zero_zero(int),sK4(aa(nat,fun(int,bool),X0,X1))) )
    | ~ spl18_107
    | ~ spl18_127 ),
    inference(superposition,[],[f1291,f1644]) ).

tff(f3564,plain,
    ( spl18_246
    | ~ spl18_31
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1672,f1643,f725,f3562]) ).

tff(f1672,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: fun(nat,fun(X0,bool)),X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)))] :
        ( ( fTrue = huffma107959123e_case(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)) )
        | ( fFalse = aa(X0,bool,aa(nat,fun(X0,bool),X1,X2),X3) ) )
    | ~ spl18_31
    | ~ spl18_127 ),
    inference(superposition,[],[f1644,f726]) ).

tff(f3560,plain,
    ( spl18_245
    | ~ spl18_31
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1665,f1643,f725,f3558]) ).

tff(f1665,plain,
    ( ! [X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X3: nat,X1: fun(nat,fun(X0,bool)),X4: X0] :
        ( ( fTrue = aa(X0,bool,aa(nat,fun(X0,bool),X1,X3),X4) )
        | ( fFalse = huffma107959123e_case(X0,bool,X1,X2,huffma2021818691e_Leaf(X0,X3,X4)) ) )
    | ~ spl18_31
    | ~ spl18_127 ),
    inference(superposition,[],[f1644,f726]) ).

tff(f3540,plain,
    ( ~ spl18_21
    | spl18_244
    | ~ spl18_87
    | ~ spl18_124 ),
    inference(avatar_split_clause,[],[f1610,f1576,f1040,f3538,f680]) ).

tff(f1610,plain,
    ( ! [X0: $tType,X2: fun(X0,nat),X3: X0,X1: fun(X0,nat),X4: nat] :
        ( ~ ord_less_eq(fun(X0,nat),X1,X2)
        | ~ ord(nat)
        | ~ ord_less_eq(nat,aa(X0,nat,X2,X3),X4)
        | ord_less_eq(nat,aa(X0,nat,X1,X3),X4) )
    | ~ spl18_87
    | ~ spl18_124 ),
    inference(resolution,[],[f1577,f1041]) ).

tff(f3536,plain,
    ( spl18_243
    | ~ spl18_95
    | ~ spl18_110 ),
    inference(avatar_split_clause,[],[f1469,f1452,f1215,f3534]) ).

tff(f1469,plain,
    ( ! [X2: nat,X3: nat,X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,sK4(X0)))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,semiring_1_of_nat(int,X2)),X3,X1)) ) )
    | ~ spl18_95
    | ~ spl18_110 ),
    inference(resolution,[],[f1453,f1216]) ).

tff(f3520,plain,
    ( spl18_242
    | ~ spl18_160
    | ~ spl18_165 ),
    inference(avatar_split_clause,[],[f3310,f2189,f2117,f3518]) ).

tff(f2117,plain,
    ( spl18_160
  <=> ! [X0: bool] :
        ( ord_less(bool,X0,zero_zero(bool))
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_160])]) ).

tff(f3310,plain,
    ( ! [X0: bool] :
        ( ord_less(bool,X0,fFalse)
        | ( fFalse = X0 ) )
    | ~ spl18_160
    | ~ spl18_165 ),
    inference(forward_demodulation,[],[f2118,f2191]) ).

tff(f2191,plain,
    ( ( fFalse = zero_zero(bool) )
    | ~ spl18_165 ),
    inference(avatar_component_clause,[],[f2189]) ).

tff(f2118,plain,
    ( ! [X0: bool] :
        ( ord_less(bool,X0,zero_zero(bool))
        | ( fFalse = X0 ) )
    | ~ spl18_160 ),
    inference(avatar_component_clause,[],[f2117]) ).

tff(f3516,plain,
    ( spl18_241
    | ~ spl18_95
    | ~ spl18_109 ),
    inference(avatar_split_clause,[],[f1460,f1448,f1215,f3514]) ).

tff(f1460,plain,
    ( ! [X2: nat,X3: nat,X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,X1)))
        | ( semiring_1_of_nat(int,X2) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,sK3(X0)),X3,X2)) ) )
    | ~ spl18_95
    | ~ spl18_109 ),
    inference(resolution,[],[f1449,f1216]) ).

tff(f3412,plain,
    ( spl18_240
    | ~ spl18_65
    | ~ spl18_136 ),
    inference(avatar_split_clause,[],[f1849,f1840,f896,f3410]) ).

tff(f1849,plain,
    ( ! [X2: fun(nat,bool),X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,sK7(X1,X2))
        | ~ pp(aa(nat,bool,X2,X1))
        | pp(aa(nat,bool,X2,zero_zero(nat)))
        | ~ member(nat,X0,X2) )
    | ~ spl18_65
    | ~ spl18_136 ),
    inference(resolution,[],[f1841,f897]) ).

tff(f3408,plain,
    ( spl18_239
    | ~ spl18_31
    | ~ spl18_134 ),
    inference(avatar_split_clause,[],[f1829,f1799,f725,f3406]) ).

tff(f1829,plain,
    ( ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
        ( ( aa(bool,X0,X2,fTrue) != aa(bool,X0,X1,fTrue) )
        | ( X1 = X2 )
        | ( fFalse = sK17(X0,bool,X1,X2) ) )
    | ~ spl18_31
    | ~ spl18_134 ),
    inference(superposition,[],[f1800,f726]) ).

tff(f3395,plain,
    ( spl18_238
    | ~ spl18_88
    | ~ spl18_132 ),
    inference(avatar_split_clause,[],[f1793,f1770,f1044,f3393]) ).

tff(f1793,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: nat,X6: X0,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),X6) = huffma1401021291ibling(X0,X2,X6) )
        | ( huffma1401021291ibling(X0,X2,X6) = X6 ) )
    | ~ spl18_88
    | ~ spl18_132 ),
    inference(resolution,[],[f1771,f1045]) ).

tff(f3391,plain,
    ( spl18_237
    | ~ spl18_119
    | ~ spl18_126 ),
    inference(avatar_split_clause,[],[f1660,f1639,f1524,f3389]) ).

tff(f3389,plain,
    ( spl18_237
  <=> ! [X0: fun(nat,bool),X1: nat] :
        ( ~ pp(aa(nat,bool,X0,X1))
        | pp(aa(nat,bool,X0,zero_zero(nat)))
        | ord_less_eq(nat,sK7(sK7(X1,X0),X0),sK7(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_237])]) ).

tff(f1660,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( ~ pp(aa(nat,bool,X0,X1))
        | pp(aa(nat,bool,X0,zero_zero(nat)))
        | ord_less_eq(nat,sK7(sK7(X1,X0),X0),sK7(X1,X0)) )
    | ~ spl18_119
    | ~ spl18_126 ),
    inference(duplicate_literal_removal,[],[f1651]) ).

tff(f1651,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( ~ pp(aa(nat,bool,X0,X1))
        | pp(aa(nat,bool,X0,zero_zero(nat)))
        | ord_less_eq(nat,sK7(sK7(X1,X0),X0),sK7(X1,X0))
        | pp(aa(nat,bool,X0,zero_zero(nat))) )
    | ~ spl18_119
    | ~ spl18_126 ),
    inference(resolution,[],[f1640,f1525]) ).

tff(f3379,plain,
    ( ~ spl18_19
    | spl18_236
    | ~ spl18_31
    | ~ spl18_124 ),
    inference(avatar_split_clause,[],[f1627,f1576,f725,f3377,f670]) ).

tff(f1627,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: fun(X0,bool)] :
        ( ord_less_eq(bool,aa(X0,bool,X3,X2),fTrue)
        | ~ ord_less_eq(fun(X0,bool),X3,X1)
        | ~ ord(bool)
        | ( fFalse = aa(X0,bool,X1,X2) ) )
    | ~ spl18_31
    | ~ spl18_124 ),
    inference(superposition,[],[f1577,f726]) ).

tff(f3367,plain,
    ( ~ spl18_19
    | spl18_235
    | ~ spl18_31
    | ~ spl18_124 ),
    inference(avatar_split_clause,[],[f1620,f1576,f725,f3365,f670]) ).

tff(f1620,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: fun(X0,bool)] :
        ( ord_less_eq(bool,fTrue,aa(X0,bool,X3,X2))
        | ~ ord_less_eq(fun(X0,bool),X1,X3)
        | ~ ord(bool)
        | ( fFalse = aa(X0,bool,X1,X2) ) )
    | ~ spl18_31
    | ~ spl18_124 ),
    inference(superposition,[],[f1577,f726]) ).

tff(f3363,plain,
    ( spl18_234
    | ~ spl18_95
    | ~ spl18_107 ),
    inference(avatar_split_clause,[],[f1439,f1290,f1215,f3361]) ).

tff(f3361,plain,
    ( spl18_234
  <=> ! [X0: fun(int,bool),X3: nat,X2: nat,X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK4(X0))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,semiring_1_of_nat(int,X2)),X3,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_234])]) ).

tff(f1439,plain,
    ( ! [X2: nat,X3: nat,X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK4(X0))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,semiring_1_of_nat(int,X2)),X3,X1)) ) )
    | ~ spl18_95
    | ~ spl18_107 ),
    inference(resolution,[],[f1291,f1216]) ).

tff(f3359,plain,
    ( spl18_233
    | ~ spl18_94
    | ~ spl18_106 ),
    inference(avatar_split_clause,[],[f1426,f1286,f1211,f3357]) ).

tff(f3357,plain,
    ( spl18_233
  <=> ! [X0: fun(int,bool),X3: nat,X2: nat,X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,semiring_1_of_nat(int,X2)),X1,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_233])]) ).

tff(f1426,plain,
    ( ! [X2: nat,X3: nat,X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,aa(int,bool,X0,semiring_1_of_nat(int,X2)),X1,X3)) ) )
    | ~ spl18_94
    | ~ spl18_106 ),
    inference(resolution,[],[f1287,f1212]) ).

tff(f3355,plain,
    ( spl18_232
    | ~ spl18_92
    | ~ spl18_103 ),
    inference(avatar_split_clause,[],[f1393,f1274,f1203,f3353]) ).

tff(f1393,plain,
    ( ! [X2: $tType,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ~ linordered_semidom(X2)
        | ~ ord_less_eq(X2,semiring_1_of_nat(X2,X1),semiring_1_of_nat(X2,X0))
        | ( semiring_1_of_nat(X2,X0) = semiring_1_of_nat(X2,X1) )
        | ~ order(X2) )
    | ~ spl18_92
    | ~ spl18_103 ),
    inference(resolution,[],[f1275,f1204]) ).

tff(f3309,plain,
    ( spl18_231
    | ~ spl18_31
    | spl18_195 ),
    inference(avatar_split_clause,[],[f2694,f2568,f725,f3307]) ).

tff(f3307,plain,
    ( spl18_231
  <=> ! [X0: bool] :
        ( ~ ord_less(bool,X0,fFalse)
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_231])]) ).

tff(f2694,plain,
    ( ! [X0: bool] :
        ( ~ ord_less(bool,X0,fFalse)
        | ( fFalse = X0 ) )
    | ~ spl18_31
    | spl18_195 ),
    inference(superposition,[],[f2570,f726]) ).

tff(f3175,plain,
    ( spl18_230
    | ~ spl18_65
    | ~ spl18_133 ),
    inference(avatar_split_clause,[],[f1803,f1795,f896,f3173]) ).

tff(f1803,plain,
    ( ! [X2: nat,X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ ord_less(nat,X1,sK8(X0))
        | pp(aa(nat,bool,X0,X2))
        | ~ member(nat,zero_zero(nat),X0) )
    | ~ spl18_65
    | ~ spl18_133 ),
    inference(resolution,[],[f1796,f897]) ).

tff(f3171,plain,
    ( spl18_229
    | ~ spl18_31
    | ~ spl18_121 ),
    inference(avatar_split_clause,[],[f1566,f1543,f725,f3169]) ).

tff(f3169,plain,
    ( spl18_229
  <=> ! [X4: bool,X0: nat,X3: nat,X2: bool,X1: nat] :
        ( ( fTrue = X2 )
        | ( X2 = X4 )
        | ( fFalse = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X0,huffma2021818691e_Leaf(bool,X1,X2),huffma2021818691e_Leaf(bool,X3,X4)),X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_229])]) ).

tff(f1566,plain,
    ( ! [X2: bool,X3: nat,X0: nat,X1: nat,X4: bool] :
        ( ( fTrue = X2 )
        | ( X2 = X4 )
        | ( fFalse = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X0,huffma2021818691e_Leaf(bool,X1,X2),huffma2021818691e_Leaf(bool,X3,X4)),X4) ) )
    | ~ spl18_31
    | ~ spl18_121 ),
    inference(superposition,[],[f1544,f726]) ).

tff(f3167,plain,
    ( spl18_228
    | ~ spl18_94
    | ~ spl18_95 ),
    inference(avatar_split_clause,[],[f1250,f1215,f1211,f3165]) ).

tff(f1250,plain,
    ( ! [X2: nat,X3: nat,X0: nat,X1: bool,X4: nat] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X1,X2,X0)) )
        | ( semiring_1_of_nat(int,X3) = semiring_1_of_nat(int,if(nat,X1,X3,X4)) ) )
    | ~ spl18_94
    | ~ spl18_95 ),
    inference(resolution,[],[f1216,f1212]) ).

tff(f3100,plain,
    ( spl18_227
    | ~ spl18_145 ),
    inference(avatar_split_clause,[],[f1944,f1931,f3098]) ).

tff(f1944,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X3: nat,X6: fun(nat,fun(X0,X1)),X7: fun(nat,fun(X0,X1)),X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] : ( huffma107959123e_case(X0,X1,X6,X2,huffma1146269203erNode(X0,X3,X4,X5)) = huffma107959123e_case(X0,X1,X7,X2,huffma1146269203erNode(X0,X3,X4,X5)) )
    | ~ spl18_145 ),
    inference(superposition,[],[f1932,f1932]) ).

tff(f3096,plain,
    ( spl18_226
    | ~ spl18_49
    | ~ spl18_132 ),
    inference(avatar_split_clause,[],[f1790,f1770,f808,f3094]) ).

tff(f1790,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] : ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,huffma1146269203erNode(X0,X3,X4,X5)),sK14(X0,X2)) = huffma1401021291ibling(X0,X2,sK14(X0,X2)) )
    | ~ spl18_49
    | ~ spl18_132 ),
    inference(resolution,[],[f1771,f809]) ).

tff(f3092,plain,
    ( spl18_225
    | ~ spl18_127
    | ~ spl18_131 ),
    inference(avatar_split_clause,[],[f1788,f1766,f1643,f3090]) ).

tff(f1788,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( pp(huffma107959123e_case(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ord_less(nat,X1,X2)
        | ( X1 = X2 )
        | sP0(X2,X1,X0) )
    | ~ spl18_127
    | ~ spl18_131 ),
    inference(superposition,[],[f1767,f1644]) ).

tff(f3088,plain,
    ( spl18_224
    | ~ spl18_128
    | ~ spl18_131 ),
    inference(avatar_split_clause,[],[f1787,f1766,f1647,f3086]) ).

tff(f3086,plain,
    ( spl18_224
  <=> ! [X0: fun(nat,fun(nat,bool)),X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X2: nat,X1: nat] :
        ( pp(huffma1280178957ee_rec(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ord_less(nat,X1,X2)
        | ( X1 = X2 )
        | sP0(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_224])]) ).

tff(f1787,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( pp(huffma1280178957ee_rec(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ord_less(nat,X1,X2)
        | ( X1 = X2 )
        | sP0(X2,X1,X0) )
    | ~ spl18_128
    | ~ spl18_131 ),
    inference(superposition,[],[f1767,f1648]) ).

tff(f3084,plain,
    ( spl18_223
    | ~ spl18_66
    | ~ spl18_131 ),
    inference(avatar_split_clause,[],[f1777,f1766,f902,f3082]) ).

tff(f3082,plain,
    ( spl18_223
  <=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( ord_less(nat,X0,X1)
        | ( X0 = X1 )
        | sP0(X1,X0,X2)
        | member(nat,X1,aa(nat,fun(nat,bool),X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_223])]) ).

tff(f1777,plain,
    ( ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( ord_less(nat,X0,X1)
        | ( X0 = X1 )
        | sP0(X1,X0,X2)
        | member(nat,X1,aa(nat,fun(nat,bool),X2,X0)) )
    | ~ spl18_66
    | ~ spl18_131 ),
    inference(resolution,[],[f1767,f903]) ).

tff(f3074,plain,
    ( ~ spl18_21
    | spl18_222
    | ~ spl18_90
    | ~ spl18_124 ),
    inference(avatar_split_clause,[],[f1628,f1576,f1052,f3072,f680]) ).

tff(f1628,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,nat),X1: nat] :
        ( ord_less_eq(nat,aa(X0,nat,X3,X2),X1)
        | ~ ord_less_eq(fun(X0,nat),X3,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)))
        | ~ ord(nat) )
    | ~ spl18_90
    | ~ spl18_124 ),
    inference(superposition,[],[f1577,f1053]) ).

tff(f3064,plain,
    ( ~ spl18_21
    | spl18_221
    | ~ spl18_90
    | ~ spl18_124 ),
    inference(avatar_split_clause,[],[f1621,f1576,f1052,f3062,f680]) ).

tff(f1621,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,nat),X1: nat] :
        ( ord_less_eq(nat,X1,aa(X0,nat,X3,X2))
        | ~ ord_less_eq(fun(X0,nat),huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3)
        | ~ ord(nat) )
    | ~ spl18_90
    | ~ spl18_124 ),
    inference(superposition,[],[f1577,f1053]) ).

tff(f3040,plain,
    ( ~ spl18_9
    | spl18_220
    | ~ spl18_75
    | ~ spl18_103 ),
    inference(avatar_split_clause,[],[f1390,f1274,f950,f3038,f620]) ).

tff(f1390,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ~ linordered_semidom(nat)
        | ~ ord_less_eq(nat,semiring_1_of_nat(nat,X1),semiring_1_of_nat(nat,X0))
        | ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) ) )
    | ~ spl18_75
    | ~ spl18_103 ),
    inference(resolution,[],[f1275,f951]) ).

tff(f3031,plain,
    ( ~ spl18_9
    | spl18_219
    | ~ spl18_72
    | ~ spl18_101 ),
    inference(avatar_split_clause,[],[f1346,f1266,f938,f3029,f620]) ).

tff(f938,plain,
    ( spl18_72
  <=> ! [X0: nat,X1: nat] :
        ( ord_less(nat,X0,X1)
        | ord_less(nat,X1,X0)
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_72])]) ).

tff(f1346,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less(nat,X0,X1)
        | ~ linordered_semidom(nat)
        | ord_less(nat,semiring_1_of_nat(nat,X1),semiring_1_of_nat(nat,X0))
        | ( semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,X1) ) )
    | ~ spl18_72
    | ~ spl18_101 ),
    inference(resolution,[],[f1267,f939]) ).

tff(f939,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less(nat,X1,X0)
        | ord_less(nat,X0,X1)
        | ( X0 = X1 ) )
    | ~ spl18_72 ),
    inference(avatar_component_clause,[],[f938]) ).

tff(f3014,plain,
    ( ~ spl18_16
    | spl18_218
    | ~ spl18_86
    | ~ spl18_92 ),
    inference(avatar_split_clause,[],[f1233,f1203,f1036,f3012,f655]) ).

tff(f1233,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X0),semiring_1_of_nat(int,X1))
        | ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
        | ~ order(int)
        | ~ ord_less_eq(nat,X1,X0) )
    | ~ spl18_86
    | ~ spl18_92 ),
    inference(resolution,[],[f1204,f1037]) ).

tff(f2953,plain,
    ( spl18_217
    | ~ spl18_31
    | ~ spl18_166 ),
    inference(avatar_split_clause,[],[f2827,f2193,f725,f2951]) ).

tff(f2951,plain,
    ( spl18_217
  <=> ! [X0: bool] :
        ( ord_less(bool,X0,X0)
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_217])]) ).

tff(f2193,plain,
    ( spl18_166
  <=> ord_less(bool,fTrue,fTrue) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_166])]) ).

tff(f2827,plain,
    ( ! [X0: bool] :
        ( ord_less(bool,X0,X0)
        | ( fFalse = X0 ) )
    | ~ spl18_31
    | ~ spl18_166 ),
    inference(superposition,[],[f2194,f726]) ).

tff(f2194,plain,
    ( ord_less(bool,fTrue,fTrue)
    | ~ spl18_166 ),
    inference(avatar_component_clause,[],[f2193]) ).

tff(f2949,plain,
    ( spl18_216
    | ~ spl18_65
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1707,f1647,f896,f2947]) ).

tff(f2947,plain,
    ( spl18_216
  <=> ! [X0: $tType,X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool))))),X3: X0,X2: nat,X1: fun(nat,fun(X0,bool))] :
        ( pp(huffma1280178957ee_rec(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)))
        | ~ member(X0,X3,aa(nat,fun(X0,bool),X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_216])]) ).

tff(f1707,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: fun(nat,fun(X0,bool)),X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))))] :
        ( pp(huffma1280178957ee_rec(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)))
        | ~ member(X0,X3,aa(nat,fun(X0,bool),X1,X2)) )
    | ~ spl18_65
    | ~ spl18_128 ),
    inference(superposition,[],[f897,f1648]) ).

tff(f2945,plain,
    ( spl18_215
    | ~ spl18_66
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1706,f1647,f902,f2943]) ).

tff(f1706,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: fun(nat,fun(X0,bool)),X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(bool,fun(bool,bool)))))] :
        ( ~ pp(huffma1280178957ee_rec(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)))
        | member(X0,X3,aa(nat,fun(X0,bool),X1,X2)) )
    | ~ spl18_66
    | ~ spl18_128 ),
    inference(superposition,[],[f903,f1648]) ).

tff(f2941,plain,
    ( spl18_214
    | ~ spl18_65
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1676,f1643,f896,f2939]) ).

tff(f2939,plain,
    ( spl18_214
  <=> ! [X0: $tType,X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool))),X3: X0,X2: nat,X1: fun(nat,fun(X0,bool))] :
        ( pp(huffma107959123e_case(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)))
        | ~ member(X0,X3,aa(nat,fun(X0,bool),X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_214])]) ).

tff(f1676,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: fun(nat,fun(X0,bool)),X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)))] :
        ( pp(huffma107959123e_case(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)))
        | ~ member(X0,X3,aa(nat,fun(X0,bool),X1,X2)) )
    | ~ spl18_65
    | ~ spl18_127 ),
    inference(superposition,[],[f897,f1644]) ).

tff(f2937,plain,
    ( spl18_213
    | ~ spl18_66
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1675,f1643,f902,f2935]) ).

tff(f1675,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: fun(nat,fun(X0,bool)),X4: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),bool)))] :
        ( ~ pp(huffma107959123e_case(X0,bool,X1,X4,huffma2021818691e_Leaf(X0,X2,X3)))
        | member(X0,X3,aa(nat,fun(X0,bool),X1,X2)) )
    | ~ spl18_66
    | ~ spl18_127 ),
    inference(superposition,[],[f903,f1644]) ).

tff(f2933,plain,
    ( spl18_212
    | ~ spl18_103
    | ~ spl18_104 ),
    inference(avatar_split_clause,[],[f1422,f1278,f1274,f2931]) ).

tff(f1422,plain,
    ( ! [X0: $tType,X2: X0,X3: nat,X1: nat] :
        ( ~ ord_less_eq(X0,semiring_1_of_nat(X0,X1),X2)
        | ord_less_eq(X0,semiring_1_of_nat(X0,X3),X2)
        | ~ preorder(X0)
        | ~ ord_less_eq(nat,X3,X1)
        | ~ linordered_semidom(X0) )
    | ~ spl18_103
    | ~ spl18_104 ),
    inference(resolution,[],[f1279,f1275]) ).

tff(f2798,plain,
    ( spl18_211
    | ~ spl18_127
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1692,f1647,f1643,f2796]) ).

tff(f1692,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X6: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)))] : ( huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,X4)) = huffma1280178957ee_rec(X0,X1,X2,X6,huffma2021818691e_Leaf(X0,X3,X4)) )
    | ~ spl18_127
    | ~ spl18_128 ),
    inference(superposition,[],[f1648,f1644]) ).

tff(f2794,plain,
    ( spl18_210
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1691,f1647,f2792]) ).

tff(f1691,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X6: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1)))))] : ( huffma1280178957ee_rec(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,X4)) = huffma1280178957ee_rec(X0,X1,X2,X6,huffma2021818691e_Leaf(X0,X3,X4)) )
    | ~ spl18_128 ),
    inference(superposition,[],[f1648,f1648]) ).

tff(f2790,plain,
    ( spl18_209
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1667,f1643,f2788]) ).

tff(f1667,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(nat,fun(X0,X1)),X3: nat,X6: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))),X4: X0,X5: fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1)))] : ( huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,X4)) = huffma107959123e_case(X0,X1,X2,X6,huffma2021818691e_Leaf(X0,X3,X4)) )
    | ~ spl18_127 ),
    inference(superposition,[],[f1644,f1644]) ).

tff(f2786,plain,
    ( spl18_208
    | ~ spl18_66
    | ~ spl18_126 ),
    inference(avatar_split_clause,[],[f1652,f1639,f902,f2784]) ).

tff(f1652,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( ~ pp(aa(nat,bool,X0,X1))
        | pp(aa(nat,bool,X0,zero_zero(nat)))
        | member(nat,sK7(X1,X0),X0) )
    | ~ spl18_66
    | ~ spl18_126 ),
    inference(resolution,[],[f1640,f903]) ).

tff(f2782,plain,
    ( spl18_207
    | ~ spl18_31
    | ~ spl18_118 ),
    inference(avatar_split_clause,[],[f1522,f1503,f725,f2780]) ).

tff(f2780,plain,
    ( spl18_207
  <=> ! [X4: bool,X0: nat,X3: nat,X2: bool,X1: nat] :
        ( ( fTrue = X4 )
        | ( fFalse = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X0,huffma2021818691e_Leaf(bool,X1,X2),huffma2021818691e_Leaf(bool,X3,X4)),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_207])]) ).

tff(f1522,plain,
    ( ! [X2: bool,X3: nat,X0: nat,X1: nat,X4: bool] :
        ( ( fTrue = X4 )
        | ( fFalse = huffma1401021291ibling(bool,huffma1146269203erNode(bool,X0,huffma2021818691e_Leaf(bool,X1,X2),huffma2021818691e_Leaf(bool,X3,X4)),X2) ) )
    | ~ spl18_31
    | ~ spl18_118 ),
    inference(superposition,[],[f1504,f726]) ).

tff(f2778,plain,
    ( spl18_206
    | ~ spl18_66
    | ~ spl18_95 ),
    inference(avatar_split_clause,[],[f1248,f1215,f902,f2776]) ).

tff(f2776,plain,
    ( spl18_206
  <=> ! [X1: $tType,X4: nat,X0: nat,X3: X1,X2: fun(X1,bool)] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(X1,bool,X2,X3),X4,X0)) )
        | member(X1,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_206])]) ).

tff(f1248,plain,
    ( ! [X1: $tType,X2: fun(X1,bool),X3: X1,X0: nat,X4: nat] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(X1,bool,X2,X3),X4,X0)) )
        | member(X1,X3,X2) )
    | ~ spl18_66
    | ~ spl18_95 ),
    inference(resolution,[],[f1216,f903]) ).

tff(f2774,plain,
    ( spl18_205
    | ~ spl18_65
    | ~ spl18_94 ),
    inference(avatar_split_clause,[],[f1243,f1211,f896,f2772]) ).

tff(f1243,plain,
    ( ! [X1: $tType,X2: fun(X1,bool),X3: X1,X0: nat,X4: nat] :
        ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,aa(X1,bool,X2,X3),X0,X4)) )
        | ~ member(X1,X3,X2) )
    | ~ spl18_65
    | ~ spl18_94 ),
    inference(resolution,[],[f1212,f897]) ).

tff(f2770,plain,
    ( spl18_204
    | ~ spl18_31
    | spl18_166 ),
    inference(avatar_split_clause,[],[f2331,f2193,f725,f2768]) ).

tff(f2768,plain,
    ( spl18_204
  <=> ! [X0: bool] :
        ( ~ ord_less(bool,X0,X0)
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_204])]) ).

tff(f2331,plain,
    ( ! [X0: bool] :
        ( ~ ord_less(bool,X0,X0)
        | ( fFalse = X0 ) )
    | ~ spl18_31
    | spl18_166 ),
    inference(superposition,[],[f2195,f726]) ).

tff(f2195,plain,
    ( ~ ord_less(bool,fTrue,fTrue)
    | spl18_166 ),
    inference(avatar_component_clause,[],[f2193]) ).

tff(f2766,plain,
    ( spl18_203
    | ~ spl18_76
    | ~ spl18_86 ),
    inference(avatar_split_clause,[],[f1183,f1036,f954,f2764]) ).

tff(f1183,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
        | ord_less(int,semiring_1_of_nat(int,X0),semiring_1_of_nat(int,X1)) )
    | ~ spl18_76
    | ~ spl18_86 ),
    inference(resolution,[],[f1037,f955]) ).

tff(f2730,plain,
    ( spl18_202
    | ~ spl18_77
    | ~ spl18_137 ),
    inference(avatar_split_clause,[],[f1860,f1844,f958,f2728]) ).

tff(f958,plain,
    ( spl18_77
  <=> ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X4: X0,X5: nat,X1: huffma1450048681e_tree(X0)] : ( huffma1146269203erNode(X0,X3,X2,X1) != huffma2021818691e_Leaf(X0,X5,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_77])]) ).

tff(f1860,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma2021818691e_Leaf(X0,X2,X3) != X1 )
        | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) )
    | ~ spl18_77
    | ~ spl18_137 ),
    inference(superposition,[],[f959,f1845]) ).

tff(f959,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X4: X0,X5: nat] : ( huffma1146269203erNode(X0,X3,X2,X1) != huffma2021818691e_Leaf(X0,X5,X4) )
    | ~ spl18_77 ),
    inference(avatar_component_clause,[],[f958]) ).

tff(f2726,plain,
    ( spl18_201
    | ~ spl18_65
    | ~ spl18_125 ),
    inference(avatar_split_clause,[],[f1630,f1580,f896,f2724]) ).

tff(f1630,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ pp(aa(nat,bool,X0,zero_zero(nat)))
        | ~ member(nat,sK8(X0),X0) )
    | ~ spl18_65
    | ~ spl18_125 ),
    inference(resolution,[],[f1581,f897]) ).

tff(f2722,plain,
    ( spl18_200
    | ~ spl18_65
    | ~ spl18_123 ),
    inference(avatar_split_clause,[],[f1602,f1572,f896,f2720]) ).

tff(f1602,plain,
    ( ! [X0: fun(int,bool),X1: int] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ~ ord_less_eq(int,zero_zero(int),X1)
        | ~ member(int,X1,X0) )
    | ~ spl18_65
    | ~ spl18_123 ),
    inference(resolution,[],[f1573,f897]) ).

tff(f2718,plain,
    ( spl18_199
    | ~ spl18_65
    | ~ spl18_122 ),
    inference(avatar_split_clause,[],[f1584,f1568,f896,f2716]) ).

tff(f2716,plain,
    ( spl18_199
  <=> ! [X0: int,X1: fun(int,bool)] :
        ( ~ ord_less_eq(int,zero_zero(int),X0)
        | pp(aa(int,bool,X1,X0))
        | ~ member(int,semiring_1_of_nat(int,sK2(X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_199])]) ).

tff(f1584,plain,
    ( ! [X0: int,X1: fun(int,bool)] :
        ( ~ ord_less_eq(int,zero_zero(int),X0)
        | pp(aa(int,bool,X1,X0))
        | ~ member(int,semiring_1_of_nat(int,sK2(X1)),X1) )
    | ~ spl18_65
    | ~ spl18_122 ),
    inference(resolution,[],[f1569,f897]) ).

tff(f2693,plain,
    ( ~ spl18_15
    | spl18_198
    | ~ spl18_86
    | ~ spl18_104 ),
    inference(avatar_split_clause,[],[f1416,f1278,f1036,f2691,f650]) ).

tff(f1416,plain,
    ( ! [X2: nat,X0: nat,X1: int] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X0),X1)
        | ord_less_eq(int,semiring_1_of_nat(int,X2),X1)
        | ~ preorder(int)
        | ~ ord_less_eq(nat,X2,X0) )
    | ~ spl18_86
    | ~ spl18_104 ),
    inference(resolution,[],[f1279,f1037]) ).

tff(f2676,plain,
    ( ~ spl18_9
    | spl18_197
    | ~ spl18_87
    | ~ spl18_103 ),
    inference(avatar_split_clause,[],[f1389,f1274,f1040,f2674,f620]) ).

tff(f1389,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ~ linordered_semidom(nat)
        | ~ ord_less_eq(nat,semiring_1_of_nat(nat,X1),X2)
        | ord_less_eq(nat,semiring_1_of_nat(nat,X0),X2) )
    | ~ spl18_87
    | ~ spl18_103 ),
    inference(resolution,[],[f1275,f1041]) ).

tff(f2575,plain,
    ( spl18_196
    | ~ spl18_106
    | ~ spl18_122 ),
    inference(avatar_split_clause,[],[f1583,f1568,f1286,f2573]) ).

tff(f1583,plain,
    ( ! [X0: int,X1: fun(int,bool)] :
        ( ~ ord_less_eq(int,zero_zero(int),X0)
        | pp(aa(int,bool,X1,X0))
        | ord_less_eq(int,zero_zero(int),sK3(X1)) )
    | ~ spl18_106
    | ~ spl18_122 ),
    inference(resolution,[],[f1569,f1287]) ).

tff(f2571,plain,
    ( ~ spl18_195
    | spl18_150
    | ~ spl18_165 ),
    inference(avatar_split_clause,[],[f2472,f2189,f2033,f2568]) ).

tff(f2472,plain,
    ( ~ ord_less(bool,fTrue,fFalse)
    | spl18_150
    | ~ spl18_165 ),
    inference(superposition,[],[f2035,f2191]) ).

tff(f2566,plain,
    ( spl18_194
    | ~ spl18_65
    | ~ spl18_120 ),
    inference(avatar_split_clause,[],[f1554,f1539,f896,f2564]) ).

tff(f1554,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( ord_less(nat,zero_zero(nat),sK8(X0))
        | pp(aa(nat,bool,X0,X1))
        | ~ member(nat,zero_zero(nat),X0) )
    | ~ spl18_65
    | ~ spl18_120 ),
    inference(resolution,[],[f1540,f897]) ).

tff(f2562,plain,
    ( spl18_193
    | ~ spl18_65
    | ~ spl18_119 ),
    inference(avatar_split_clause,[],[f1546,f1524,f896,f2560]) ).

tff(f1546,plain,
    ( ! [X0: nat,X1: fun(nat,bool)] :
        ( ord_less_eq(nat,sK7(X0,X1),X0)
        | pp(aa(nat,bool,X1,zero_zero(nat)))
        | ~ member(nat,X0,X1) )
    | ~ spl18_65
    | ~ spl18_119 ),
    inference(resolution,[],[f1525,f897]) ).

tff(f2558,plain,
    ( spl18_192
    | ~ spl18_53
    | ~ spl18_92 ),
    inference(avatar_split_clause,[],[f1238,f1203,f827,f2556]) ).

tff(f2556,plain,
    ( spl18_192
  <=> ! [X0: $tType,X1: nat] :
        ( ~ ord_less_eq(X0,semiring_1_of_nat(X0,X1),zero_zero(X0))
        | ( zero_zero(X0) = semiring_1_of_nat(X0,X1) )
        | ~ order(X0)
        | ~ linordered_semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_192])]) ).

tff(f1238,plain,
    ( ! [X0: $tType,X1: nat] :
        ( ~ ord_less_eq(X0,semiring_1_of_nat(X0,X1),zero_zero(X0))
        | ( zero_zero(X0) = semiring_1_of_nat(X0,X1) )
        | ~ order(X0)
        | ~ linordered_semidom(X0) )
    | ~ spl18_53
    | ~ spl18_92 ),
    inference(resolution,[],[f1204,f828]) ).

tff(f2554,plain,
    ( spl18_191
    | ~ spl18_58
    | ~ spl18_75 ),
    inference(avatar_split_clause,[],[f990,f950,f848,f2552]) ).

tff(f2552,plain,
    ( spl18_191
  <=> ! [X0: $tType,X2: X0,X1: huffma1450048681e_tree(X0)] :
        ( ~ ord_less_eq(nat,huffma945805758height(X0,X1),huffma410068972_depth(X0,X1,X2))
        | ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_191])]) ).

tff(f990,plain,
    ( ! [X0: $tType,X2: X0,X1: huffma1450048681e_tree(X0)] :
        ( ~ ord_less_eq(nat,huffma945805758height(X0,X1),huffma410068972_depth(X0,X1,X2))
        | ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,X2) ) )
    | ~ spl18_58
    | ~ spl18_75 ),
    inference(resolution,[],[f951,f849]) ).

tff(f2550,plain,
    ( spl18_190
    | ~ spl18_58
    | ~ spl18_74 ),
    inference(avatar_split_clause,[],[f980,f946,f848,f2548]) ).

tff(f2548,plain,
    ( spl18_190
  <=> ! [X0: $tType,X2: X0,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,X2) )
        | ord_less(nat,huffma410068972_depth(X0,X1,X2),huffma945805758height(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_190])]) ).

tff(f980,plain,
    ( ! [X0: $tType,X2: X0,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,X2) )
        | ord_less(nat,huffma410068972_depth(X0,X1,X2),huffma945805758height(X0,X1)) )
    | ~ spl18_58
    | ~ spl18_74 ),
    inference(resolution,[],[f947,f849]) ).

tff(f2545,plain,
    ( spl18_189
    | ~ spl18_29
    | ~ spl18_132 ),
    inference(avatar_split_clause,[],[f1789,f1770,f715,f2543]) ).

tff(f1789,plain,
    ( ! [X2: huffma1450048681e_tree(a1),X3: huffma1450048681e_tree(a1),X0: nat,X1: nat] : ( huffma1401021291ibling(a1,t_1,a) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,huffma1146269203erNode(a1,X1,X2,X3)),a) )
    | ~ spl18_29
    | ~ spl18_132 ),
    inference(resolution,[],[f1771,f717]) ).

tff(f2482,plain,
    ( spl18_188
    | ~ spl18_61
    | ~ spl18_104 ),
    inference(avatar_split_clause,[],[f1419,f1278,f880,f2480]) ).

tff(f1419,plain,
    ( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
        ( ~ ord_less_eq(X0,X1,X2)
        | ord_less_eq(X0,X3,X2)
        | ~ preorder(X0)
        | ord_less_eq(X0,X1,X3)
        | ~ linorder(X0) )
    | ~ spl18_61
    | ~ spl18_104 ),
    inference(resolution,[],[f1279,f881]) ).

tff(f2468,plain,
    ( spl18_187
    | ~ spl18_61
    | ~ spl18_102 ),
    inference(avatar_split_clause,[],[f1371,f1270,f880,f2466]) ).

tff(f1371,plain,
    ( ! [X2: $tType,X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ~ linordered_semidom(X2)
        | ord_less_eq(X2,semiring_1_of_nat(X2,X1),semiring_1_of_nat(X2,X0))
        | ~ linorder(X2) )
    | ~ spl18_61
    | ~ spl18_102 ),
    inference(resolution,[],[f1271,f881]) ).

tff(f2432,plain,
    ( spl18_186
    | ~ spl18_53
    | ~ spl18_104 ),
    inference(avatar_split_clause,[],[f1421,f1278,f827,f2430]) ).

tff(f1421,plain,
    ( ! [X0: $tType,X2: X0,X1: nat] :
        ( ~ ord_less_eq(X0,semiring_1_of_nat(X0,X1),X2)
        | ord_less_eq(X0,zero_zero(X0),X2)
        | ~ preorder(X0)
        | ~ linordered_semidom(X0) )
    | ~ spl18_53
    | ~ spl18_104 ),
    inference(resolution,[],[f1279,f828]) ).

tff(f2422,plain,
    ( ~ spl18_16
    | spl18_185
    | ~ spl18_41
    | ~ spl18_92 ),
    inference(avatar_split_clause,[],[f1232,f1203,f770,f2420,f655]) ).

tff(f1232,plain,
    ( ! [X0: nat] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int))
        | ( zero_zero(int) = semiring_1_of_nat(int,X0) )
        | ~ order(int) )
    | ~ spl18_41
    | ~ spl18_92 ),
    inference(resolution,[],[f1204,f771]) ).

tff(f2418,plain,
    ( spl18_184
    | ~ spl18_70
    | ~ spl18_80 ),
    inference(avatar_split_clause,[],[f1164,f1012,f930,f2416]) ).

tff(f1012,plain,
    ( spl18_80
  <=> ! [X0: nat] :
        ( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0))
        | ~ ord_less(nat,zero_zero(nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_80])]) ).

tff(f1164,plain,
    ( ! [X0: nat] :
        ( ~ ord_less(nat,zero_zero(nat),X0)
        | ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,sK1(semiring_1_of_nat(int,X0))) ) )
    | ~ spl18_70
    | ~ spl18_80 ),
    inference(resolution,[],[f1013,f931]) ).

tff(f1013,plain,
    ( ! [X0: nat] :
        ( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0))
        | ~ ord_less(nat,zero_zero(nat),X0) )
    | ~ spl18_80 ),
    inference(avatar_component_clause,[],[f1012]) ).

tff(f2414,plain,
    ( ~ spl18_182
    | spl18_183
    | ~ spl18_31
    | ~ spl18_78 ),
    inference(avatar_split_clause,[],[f1055,f1004,f725,f2412,f2408]) ).

tff(f2408,plain,
    ( spl18_182
  <=> semiring_char_0(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_182])]) ).

tff(f2412,plain,
    ( spl18_183
  <=> ! [X0: nat,X1: nat] :
        ( ( fTrue != semiring_1_of_nat(bool,X1) )
        | ( fFalse = semiring_1_of_nat(bool,X0) )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_183])]) ).

tff(f1055,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( fTrue != semiring_1_of_nat(bool,X1) )
        | ( X0 = X1 )
        | ~ semiring_char_0(bool)
        | ( fFalse = semiring_1_of_nat(bool,X0) ) )
    | ~ spl18_31
    | ~ spl18_78 ),
    inference(superposition,[],[f1005,f726]) ).

tff(f2398,plain,
    ( spl18_181
    | ~ spl18_81
    | spl18_165 ),
    inference(avatar_split_clause,[],[f2254,f2189,f1016,f2396]) ).

tff(f2254,plain,
    ( ! [X0: bool] :
        ( ( zero_zero(bool) = X0 )
        | ( fFalse = X0 ) )
    | ~ spl18_81
    | spl18_165 ),
    inference(trivial_inequality_removal,[],[f2248]) ).

tff(f2248,plain,
    ( ! [X0: bool] :
        ( ( fFalse != fFalse )
        | ( zero_zero(bool) = X0 )
        | ( fFalse = X0 ) )
    | ~ spl18_81
    | spl18_165 ),
    inference(superposition,[],[f2190,f1017]) ).

tff(f2190,plain,
    ( ( fFalse != zero_zero(bool) )
    | spl18_165 ),
    inference(avatar_component_clause,[],[f2189]) ).

tff(f2364,plain,
    ( spl18_180
    | ~ spl18_113
    | ~ spl18_128 ),
    inference(avatar_split_clause,[],[f1714,f1647,f1483,f2362]) ).

tff(f1714,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),fun(bool,fun(bool,bool))))),X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( ~ pp(huffma1280178957ee_rec(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ~ sP0(X2,X1,X0) )
    | ~ spl18_113
    | ~ spl18_128 ),
    inference(superposition,[],[f1484,f1648]) ).

tff(f2360,plain,
    ( spl18_179
    | ~ spl18_113
    | ~ spl18_127 ),
    inference(avatar_split_clause,[],[f1683,f1643,f1483,f2358]) ).

tff(f1683,plain,
    ( ! [X2: nat,X3: fun(nat,fun(huffma1450048681e_tree(nat),fun(huffma1450048681e_tree(nat),bool))),X0: fun(nat,fun(nat,bool)),X1: nat] :
        ( ~ pp(huffma107959123e_case(nat,bool,X0,X3,huffma2021818691e_Leaf(nat,X1,X2)))
        | ~ sP0(X2,X1,X0) )
    | ~ spl18_113
    | ~ spl18_127 ),
    inference(superposition,[],[f1484,f1644]) ).

tff(f2356,plain,
    ( spl18_178
    | ~ spl18_65
    | ~ spl18_113 ),
    inference(avatar_split_clause,[],[f1506,f1483,f896,f2354]) ).

tff(f1506,plain,
    ( ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( ~ sP0(X0,X1,X2)
        | ~ member(nat,X0,aa(nat,fun(nat,bool),X2,X1)) )
    | ~ spl18_65
    | ~ spl18_113 ),
    inference(resolution,[],[f1484,f897]) ).

tff(f2352,plain,
    ( spl18_177
    | ~ spl18_39
    | ~ spl18_110 ),
    inference(avatar_split_clause,[],[f1471,f1452,f761,f2350]) ).

tff(f1471,plain,
    ( ! [X0: fun(int,bool)] :
        ( ~ pp(aa(int,bool,X0,zero_zero(int)))
        | pp(aa(int,bool,X0,sK4(X0))) )
    | ~ spl18_39
    | ~ spl18_110 ),
    inference(superposition,[],[f1453,f763]) ).

tff(f2339,plain,
    ( ~ spl18_9
    | spl18_176
    | ~ spl18_44
    | ~ spl18_102 ),
    inference(avatar_split_clause,[],[f1366,f1270,f788,f2337,f620]) ).

tff(f1366,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ~ linordered_semidom(nat)
        | ord_less_eq(nat,semiring_1_of_nat(nat,X1),semiring_1_of_nat(nat,X0)) )
    | ~ spl18_44
    | ~ spl18_102 ),
    inference(resolution,[],[f1271,f789]) ).

tff(f2321,plain,
    ( ~ spl18_9
    | spl18_175
    | ~ spl18_45
    | ~ spl18_100 ),
    inference(avatar_split_clause,[],[f1330,f1262,f792,f2319,f620]) ).

tff(f1262,plain,
    ( spl18_100
  <=> ! [X0: $tType,X2: nat,X1: nat] :
        ( ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
        | ~ ord_less(nat,X2,X1)
        | ~ linordered_semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_100])]) ).

tff(f1330,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,X1)
        | ~ linordered_semidom(nat)
        | ord_less_eq(nat,semiring_1_of_nat(nat,X0),semiring_1_of_nat(nat,X1)) )
    | ~ spl18_45
    | ~ spl18_100 ),
    inference(resolution,[],[f1263,f793]) ).

tff(f1263,plain,
    ( ! [X0: $tType,X2: nat,X1: nat] :
        ( ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
        | ~ ord_less(nat,X2,X1)
        | ~ linordered_semidom(X0) )
    | ~ spl18_100 ),
    inference(avatar_component_clause,[],[f1262]) ).

tff(f2309,plain,
    ( ~ spl18_11
    | spl18_174
    | ~ spl18_61
    | ~ spl18_85 ),
    inference(avatar_split_clause,[],[f1178,f1032,f880,f2307,f630]) ).

tff(f1178,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ord_less_eq(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
        | ~ linorder(int) )
    | ~ spl18_61
    | ~ spl18_85 ),
    inference(resolution,[],[f1033,f881]) ).

tff(f2305,plain,
    ( spl18_173
    | ~ spl18_31
    | ~ spl18_73 ),
    inference(avatar_split_clause,[],[f975,f942,f725,f2303]) ).

tff(f975,plain,
    ( ! [X0: huffma1450048681e_tree(bool)] :
        ( member(bool,fTrue,huffma675207370phabet(bool,X0))
        | ~ huffma1518433673istent(bool,X0)
        | ( fFalse = sK6(bool,X0) ) )
    | ~ spl18_31
    | ~ spl18_73 ),
    inference(superposition,[],[f943,f726]) ).

tff(f2234,plain,
    ( spl18_172
    | ~ spl18_65
    | ~ spl18_110 ),
    inference(avatar_split_clause,[],[f1468,f1452,f896,f2232]) ).

tff(f1468,plain,
    ( ! [X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,sK4(X0)))
        | ~ member(int,semiring_1_of_nat(int,X1),X0) )
    | ~ spl18_65
    | ~ spl18_110 ),
    inference(resolution,[],[f1453,f897]) ).

tff(f2230,plain,
    ( spl18_171
    | ~ spl18_106
    | ~ spl18_110 ),
    inference(avatar_split_clause,[],[f1467,f1452,f1286,f2228]) ).

tff(f1467,plain,
    ( ! [X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,sK4(X0)))
        | ord_less_eq(int,zero_zero(int),sK3(X0)) )
    | ~ spl18_106
    | ~ spl18_110 ),
    inference(resolution,[],[f1453,f1287]) ).

tff(f2226,plain,
    ( spl18_170
    | ~ spl18_65
    | ~ spl18_109 ),
    inference(avatar_split_clause,[],[f1459,f1448,f896,f2224]) ).

tff(f1459,plain,
    ( ! [X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,X1)))
        | ~ member(int,sK3(X0),X0) )
    | ~ spl18_65
    | ~ spl18_109 ),
    inference(resolution,[],[f1449,f897]) ).

tff(f2222,plain,
    ( spl18_169
    | ~ spl18_39
    | ~ spl18_107 ),
    inference(avatar_split_clause,[],[f1441,f1290,f761,f2220]) ).

tff(f1441,plain,
    ( ! [X0: fun(int,bool)] :
        ( ~ pp(aa(int,bool,X0,zero_zero(int)))
        | ord_less_eq(int,zero_zero(int),sK4(X0)) )
    | ~ spl18_39
    | ~ spl18_107 ),
    inference(superposition,[],[f1291,f763]) ).

tff(f2218,plain,
    ( spl18_168
    | ~ spl18_39
    | ~ spl18_106 ),
    inference(avatar_split_clause,[],[f1427,f1286,f761,f2216]) ).

tff(f1427,plain,
    ( ! [X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,zero_zero(int)))
        | ord_less_eq(int,zero_zero(int),sK3(X0)) )
    | ~ spl18_39
    | ~ spl18_106 ),
    inference(superposition,[],[f1287,f763]) ).

tff(f2204,plain,
    ( ~ spl18_15
    | spl18_167
    | ~ spl18_41
    | ~ spl18_104 ),
    inference(avatar_split_clause,[],[f1415,f1278,f770,f2202,f650]) ).

tff(f1415,plain,
    ( ! [X0: nat,X1: int] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X0),X1)
        | ord_less_eq(int,zero_zero(int),X1)
        | ~ preorder(int) )
    | ~ spl18_41
    | ~ spl18_104 ),
    inference(resolution,[],[f1279,f771]) ).

tff(f2196,plain,
    ( spl18_165
    | ~ spl18_166
    | ~ spl18_31
    | spl18_150 ),
    inference(avatar_split_clause,[],[f2046,f2033,f725,f2193,f2189]) ).

tff(f2046,plain,
    ( ~ ord_less(bool,fTrue,fTrue)
    | ( fFalse = zero_zero(bool) )
    | ~ spl18_31
    | spl18_150 ),
    inference(superposition,[],[f2035,f726]) ).

tff(f2187,plain,
    ( ~ spl18_9
    | spl18_164
    | ~ spl18_54
    | ~ spl18_98 ),
    inference(avatar_split_clause,[],[f1293,f1254,f832,f2185,f620]) ).

tff(f1293,plain,
    ( ! [X0: nat] :
        ( ord_less(nat,zero_zero(nat),X0)
        | ~ linordered_semidom(nat)
        | ( zero_zero(nat) = semiring_1_of_nat(nat,X0) ) )
    | ~ spl18_54
    | ~ spl18_98 ),
    inference(resolution,[],[f1255,f833]) ).

tff(f2183,plain,
    ( spl18_163
    | ~ spl18_58
    | ~ spl18_87 ),
    inference(avatar_split_clause,[],[f1190,f1040,f848,f2181]) ).

tff(f1190,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: huffma1450048681e_tree(X0)] :
        ( ~ ord_less_eq(nat,huffma945805758height(X0,X1),X2)
        | ord_less_eq(nat,huffma410068972_depth(X0,X1,X3),X2) )
    | ~ spl18_58
    | ~ spl18_87 ),
    inference(resolution,[],[f1041,f849]) ).

tff(f2170,plain,
    ( ~ spl18_11
    | spl18_162
    | ~ spl18_61
    | ~ spl18_76 ),
    inference(avatar_split_clause,[],[f1000,f954,f880,f2168,f630]) ).

tff(f1000,plain,
    ( ! [X0: int,X1: int] :
        ( ( X0 = X1 )
        | ord_less(int,X1,X0)
        | ord_less_eq(int,X0,X1)
        | ~ linorder(int) )
    | ~ spl18_61
    | ~ spl18_76 ),
    inference(resolution,[],[f955,f881]) ).

tff(f2166,plain,
    ( spl18_161
    | ~ spl18_41
    | ~ spl18_76 ),
    inference(avatar_split_clause,[],[f997,f954,f770,f2164]) ).

tff(f997,plain,
    ( ! [X0: nat] :
        ( ( zero_zero(int) = semiring_1_of_nat(int,X0) )
        | ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) )
    | ~ spl18_41
    | ~ spl18_76 ),
    inference(resolution,[],[f955,f771]) ).

tff(f2119,plain,
    ( spl18_160
    | ~ spl18_31
    | ~ spl18_150 ),
    inference(avatar_split_clause,[],[f2063,f2033,f725,f2117]) ).

tff(f2063,plain,
    ( ! [X0: bool] :
        ( ord_less(bool,X0,zero_zero(bool))
        | ( fFalse = X0 ) )
    | ~ spl18_31
    | ~ spl18_150 ),
    inference(superposition,[],[f2034,f726]) ).

tff(f2034,plain,
    ( ord_less(bool,fTrue,zero_zero(bool))
    | ~ spl18_150 ),
    inference(avatar_component_clause,[],[f2033]) ).

tff(f2092,plain,
    ( spl18_159
    | ~ spl18_65
    | ~ spl18_107 ),
    inference(avatar_split_clause,[],[f1438,f1290,f896,f2090]) ).

tff(f1438,plain,
    ( ! [X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK4(X0))
        | ~ member(int,semiring_1_of_nat(int,X1),X0) )
    | ~ spl18_65
    | ~ spl18_107 ),
    inference(resolution,[],[f1291,f897]) ).

tff(f2088,plain,
    ( spl18_158
    | ~ spl18_106
    | ~ spl18_107 ),
    inference(avatar_split_clause,[],[f1437,f1290,f1286,f2086]) ).

tff(f1437,plain,
    ( ! [X0: fun(int,bool)] :
        ( ord_less_eq(int,zero_zero(int),sK4(X0))
        | ord_less_eq(int,zero_zero(int),sK3(X0)) )
    | ~ spl18_106
    | ~ spl18_107 ),
    inference(resolution,[],[f1291,f1287]) ).

tff(f2084,plain,
    ( spl18_157
    | ~ spl18_66
    | ~ spl18_106 ),
    inference(avatar_split_clause,[],[f1424,f1286,f902,f2082]) ).

tff(f1424,plain,
    ( ! [X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK3(X0))
        | member(int,semiring_1_of_nat(int,X1),X0) )
    | ~ spl18_66
    | ~ spl18_106 ),
    inference(resolution,[],[f1287,f903]) ).

tff(f2080,plain,
    ( spl18_156
    | ~ spl18_44
    | ~ spl18_87 ),
    inference(avatar_split_clause,[],[f1188,f1040,f788,f2078]) ).

tff(f1188,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less_eq(nat,X2,X1)
        | ord_less_eq(nat,X0,X2) )
    | ~ spl18_44
    | ~ spl18_87 ),
    inference(resolution,[],[f1041,f789]) ).

tff(f2076,plain,
    ( spl18_155
    | ~ spl18_39
    | ~ spl18_86 ),
    inference(avatar_split_clause,[],[f1185,f1036,f761,f2074]) ).

tff(f1185,plain,
    ( ! [X0: nat] :
        ( ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int))
        | ~ ord_less_eq(nat,X0,zero_zero(nat)) )
    | ~ spl18_39
    | ~ spl18_86 ),
    inference(superposition,[],[f1037,f763]) ).

tff(f2062,plain,
    ( spl18_154
    | ~ spl18_31
    | spl18_150 ),
    inference(avatar_split_clause,[],[f2037,f2033,f725,f2060]) ).

tff(f2037,plain,
    ( ! [X0: bool] :
        ( ~ ord_less(bool,X0,zero_zero(bool))
        | ( fFalse = X0 ) )
    | ~ spl18_31
    | spl18_150 ),
    inference(superposition,[],[f2035,f726]) ).

tff(f2058,plain,
    ( spl18_153
    | ~ spl18_39
    | ~ spl18_85 ),
    inference(avatar_split_clause,[],[f1181,f1032,f761,f2056]) ).

tff(f2056,plain,
    ( spl18_153
  <=> ! [X0: nat] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int))
        | ord_less_eq(nat,X0,zero_zero(nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_153])]) ).

tff(f1181,plain,
    ( ! [X0: nat] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int))
        | ord_less_eq(nat,X0,zero_zero(nat)) )
    | ~ spl18_39
    | ~ spl18_85 ),
    inference(superposition,[],[f1033,f763]) ).

tff(f2054,plain,
    ( spl18_152
    | ~ spl18_46
    | ~ spl18_84 ),
    inference(avatar_split_clause,[],[f1173,f1028,f796,f2052]) ).

tff(f796,plain,
    ( spl18_46
  <=> ! [X0: int,X1: int] :
        ( ord_less_eq(int,X1,X0)
        | ~ ord_less(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_46])]) ).

tff(f1028,plain,
    ( spl18_84
  <=> ! [X0: nat,X1: nat] :
        ( ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
        | ~ ord_less(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_84])]) ).

tff(f1173,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,X1)
        | ord_less_eq(int,semiring_1_of_nat(int,X0),semiring_1_of_nat(int,X1)) )
    | ~ spl18_46
    | ~ spl18_84 ),
    inference(resolution,[],[f1029,f797]) ).

tff(f797,plain,
    ( ! [X0: int,X1: int] :
        ( ~ ord_less(int,X1,X0)
        | ord_less_eq(int,X1,X0) )
    | ~ spl18_46 ),
    inference(avatar_component_clause,[],[f796]) ).

tff(f1029,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
        | ~ ord_less(nat,X1,X0) )
    | ~ spl18_84 ),
    inference(avatar_component_clause,[],[f1028]) ).

tff(f2050,plain,
    ( spl18_151
    | ~ spl18_31
    | ~ spl18_59 ),
    inference(avatar_split_clause,[],[f878,f852,f725,f2048]) ).

tff(f2048,plain,
    ( spl18_151
  <=> ! [X2: bool,X0: nat,X1: bool] :
        ( ( fTrue = X2 )
        | ( fFalse = huffma1401021291ibling(bool,huffma2021818691e_Leaf(bool,X0,X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_151])]) ).

tff(f878,plain,
    ( ! [X2: bool,X0: nat,X1: bool] :
        ( ( fTrue = X2 )
        | ( fFalse = huffma1401021291ibling(bool,huffma2021818691e_Leaf(bool,X0,X1),X2) ) )
    | ~ spl18_31
    | ~ spl18_59 ),
    inference(superposition,[],[f853,f726]) ).

tff(f2036,plain,
    ( spl18_148
    | ~ spl18_149
    | ~ spl18_150
    | ~ spl18_31
    | ~ spl18_52 ),
    inference(avatar_split_clause,[],[f857,f823,f725,f2033,f2029,f2026]) ).

tff(f2026,plain,
    ( spl18_148
  <=> ! [X0: nat] : ( fFalse = semiring_1_of_nat(bool,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_148])]) ).

tff(f2029,plain,
    ( spl18_149
  <=> linordered_semidom(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_149])]) ).

tff(f823,plain,
    ( spl18_52
  <=> ! [X0: $tType,X1: nat] :
        ( ~ ord_less(X0,semiring_1_of_nat(X0,X1),zero_zero(X0))
        | ~ linordered_semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_52])]) ).

tff(f857,plain,
    ( ! [X0: nat] :
        ( ~ ord_less(bool,fTrue,zero_zero(bool))
        | ~ linordered_semidom(bool)
        | ( fFalse = semiring_1_of_nat(bool,X0) ) )
    | ~ spl18_31
    | ~ spl18_52 ),
    inference(superposition,[],[f824,f726]) ).

tff(f824,plain,
    ( ! [X0: $tType,X1: nat] :
        ( ~ ord_less(X0,semiring_1_of_nat(X0,X1),zero_zero(X0))
        | ~ linordered_semidom(X0) )
    | ~ spl18_52 ),
    inference(avatar_component_clause,[],[f823]) ).

tff(f1981,plain,
    spl18_147,
    inference(avatar_split_clause,[],[f533,f1979]) ).

tff(f533,plain,
    ! [X1: $tType,X0: $tType,X2: huffma1450048681e_tree(X1),X3: huffma1450048681e_tree(X1),X6: fun(nat,fun(X1,X0)),X4: nat,X5: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0)))))] : ( huffma1280178957ee_rec(X1,X0,X6,X5,huffma1146269203erNode(X1,X4,X3,X2)) = aa(X0,X0,aa(X0,fun(X0,X0),aa(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0)),aa(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))),aa(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0)))),X5,X4),X3),X2),huffma1280178957ee_rec(X1,X0,X6,X5,X3)),huffma1280178957ee_rec(X1,X0,X6,X5,X2)) ),
    inference(cnf_transformation,[],[f229]) ).

tff(f229,plain,
    ! [X0: $tType,X1: $tType,X2: huffma1450048681e_tree(X1),X3: huffma1450048681e_tree(X1),X4: nat,X5: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))))),X6: fun(nat,fun(X1,X0))] : ( huffma1280178957ee_rec(X1,X0,X6,X5,huffma1146269203erNode(X1,X4,X3,X2)) = aa(X0,X0,aa(X0,fun(X0,X0),aa(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0)),aa(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))),aa(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0)))),X5,X4),X3),X2),huffma1280178957ee_rec(X1,X0,X6,X5,X3)),huffma1280178957ee_rec(X1,X0,X6,X5,X2)) ),
    inference(rectify,[],[f48]) ).

tff(f48,axiom,
    ! [X2: $tType,X23: $tType,X6: huffma1450048681e_tree(X23),X7: huffma1450048681e_tree(X23),X8: nat,X24: fun(nat,fun(huffma1450048681e_tree(X23),fun(huffma1450048681e_tree(X23),fun(X2,fun(X2,X2))))),X25: fun(nat,fun(X23,X2))] : ( huffma1280178957ee_rec(X23,X2,X25,X24,huffma1146269203erNode(X23,X8,X7,X6)) = aa(X2,X2,aa(X2,fun(X2,X2),aa(huffma1450048681e_tree(X23),fun(X2,fun(X2,X2)),aa(huffma1450048681e_tree(X23),fun(huffma1450048681e_tree(X23),fun(X2,fun(X2,X2))),aa(nat,fun(huffma1450048681e_tree(X23),fun(huffma1450048681e_tree(X23),fun(X2,fun(X2,X2)))),X24,X8),X7),X6),huffma1280178957ee_rec(X23,X2,X25,X24,X7)),huffma1280178957ee_rec(X23,X2,X25,X24,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_tree_Orecs_I2_J) ).

tff(f1959,plain,
    spl18_146,
    inference(avatar_split_clause,[],[f538,f1957]) ).

tff(f538,plain,
    ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X6: X0,X4: nat,X5: huffma1450048681e_tree(X0)] :
      ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X5,huffma1146269203erNode(X0,X3,X2,X1)),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X2,X1),X6) )
      | ~ member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X3,X2,X1)))
      | member(X0,X6,huffma675207370phabet(X0,X5)) ),
    inference(cnf_transformation,[],[f298]) ).

tff(f298,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat,X4: nat,X5: huffma1450048681e_tree(X0),X6: X0] :
      ( ( ( ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X5,huffma1146269203erNode(X0,X3,X2,X1)),X6) = X6 )
            | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X3,X2,X1))) )
          & ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X5,huffma1146269203erNode(X0,X3,X2,X1)),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X2,X1),X6) )
            | ~ member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X3,X2,X1))) ) )
        | member(X0,X6,huffma675207370phabet(X0,X5)) )
      & ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X5,huffma1146269203erNode(X0,X3,X2,X1)),X6) = huffma1401021291ibling(X0,X5,X6) )
        | ~ member(X0,X6,huffma675207370phabet(X0,X5)) ) ),
    inference(ennf_transformation,[],[f231]) ).

tff(f231,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat,X4: nat,X5: huffma1450048681e_tree(X0),X6: X0] :
      ( ( ~ member(X0,X6,huffma675207370phabet(X0,X5))
       => ( ( ~ member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X3,X2,X1)))
           => ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X5,huffma1146269203erNode(X0,X3,X2,X1)),X6) = X6 ) )
          & ( member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X3,X2,X1)))
           => ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X5,huffma1146269203erNode(X0,X3,X2,X1)),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X2,X1),X6) ) ) ) )
      & ( member(X0,X6,huffma675207370phabet(X0,X5))
       => ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X5,huffma1146269203erNode(X0,X3,X2,X1)),X6) = huffma1401021291ibling(X0,X5,X6) ) ) ),
    inference(rectify,[],[f2]) ).

tff(f2,axiom,
    ! [X2: $tType,X9: huffma1450048681e_tree(X2),X10: huffma1450048681e_tree(X2),X11: nat,X12: nat,X13: huffma1450048681e_tree(X2),X14: X2] :
      ( ( ~ member(X2,X14,huffma675207370phabet(X2,X13))
       => ( ( ~ member(X2,X14,huffma675207370phabet(X2,huffma1146269203erNode(X2,X11,X10,X9)))
           => ( huffma1401021291ibling(X2,huffma1146269203erNode(X2,X12,X13,huffma1146269203erNode(X2,X11,X10,X9)),X14) = X14 ) )
          & ( member(X2,X14,huffma675207370phabet(X2,huffma1146269203erNode(X2,X11,X10,X9)))
           => ( huffma1401021291ibling(X2,huffma1146269203erNode(X2,X12,X13,huffma1146269203erNode(X2,X11,X10,X9)),X14) = huffma1401021291ibling(X2,huffma1146269203erNode(X2,X11,X10,X9),X14) ) ) ) )
      & ( member(X2,X14,huffma675207370phabet(X2,X13))
       => ( huffma1401021291ibling(X2,huffma1146269203erNode(X2,X12,X13,huffma1146269203erNode(X2,X11,X10,X9)),X14) = huffma1401021291ibling(X2,X13,X14) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_sibling_Osimps_I4_J) ).

tff(f1933,plain,
    spl18_145,
    inference(avatar_split_clause,[],[f532,f1931]) ).

tff(f532,plain,
    ! [X1: $tType,X0: $tType,X2: huffma1450048681e_tree(X1),X3: huffma1450048681e_tree(X1),X6: fun(nat,fun(X1,X0)),X4: nat,X5: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),X0)))] : ( huffma107959123e_case(X1,X0,X6,X5,huffma1146269203erNode(X1,X4,X3,X2)) = aa(huffma1450048681e_tree(X1),X0,aa(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),X0),aa(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),X0)),X5,X4),X3),X2) ),
    inference(cnf_transformation,[],[f228]) ).

tff(f228,plain,
    ! [X0: $tType,X1: $tType,X2: huffma1450048681e_tree(X1),X3: huffma1450048681e_tree(X1),X4: nat,X5: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),X0))),X6: fun(nat,fun(X1,X0))] : ( huffma107959123e_case(X1,X0,X6,X5,huffma1146269203erNode(X1,X4,X3,X2)) = aa(huffma1450048681e_tree(X1),X0,aa(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),X0),aa(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),X0)),X5,X4),X3),X2) ),
    inference(rectify,[],[f13]) ).

tff(f13,axiom,
    ! [X2: $tType,X23: $tType,X6: huffma1450048681e_tree(X23),X7: huffma1450048681e_tree(X23),X8: nat,X24: fun(nat,fun(huffma1450048681e_tree(X23),fun(huffma1450048681e_tree(X23),X2))),X25: fun(nat,fun(X23,X2))] : ( huffma107959123e_case(X23,X2,X25,X24,huffma1146269203erNode(X23,X8,X7,X6)) = aa(huffma1450048681e_tree(X23),X2,aa(huffma1450048681e_tree(X23),fun(huffma1450048681e_tree(X23),X2),aa(nat,fun(huffma1450048681e_tree(X23),fun(huffma1450048681e_tree(X23),X2)),X24,X8),X7),X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_tree_Osimps_I6_J) ).

tff(f1920,plain,
    spl18_144,
    inference(avatar_split_clause,[],[f541,f1918]) ).

tff(f541,plain,
    ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0),X6: X0,X4: huffma1450048681e_tree(X0),X5: nat] :
      ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,huffma1146269203erNode(X0,X5,X4,X3),X1),X6) = huffma1401021291ibling(X0,X1,X6) )
      | ~ member(X0,X6,huffma675207370phabet(X0,X1))
      | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X5,X4,X3))) ),
    inference(cnf_transformation,[],[f299]) ).

tff(f299,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: nat,X3: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X5: nat,X6: X0] :
      ( ( ( ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,huffma1146269203erNode(X0,X5,X4,X3),X1),X6) = X6 )
            | member(X0,X6,huffma675207370phabet(X0,X1)) )
          & ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,huffma1146269203erNode(X0,X5,X4,X3),X1),X6) = huffma1401021291ibling(X0,X1,X6) )
            | ~ member(X0,X6,huffma675207370phabet(X0,X1)) ) )
        | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X5,X4,X3))) )
      & ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,huffma1146269203erNode(X0,X5,X4,X3),X1),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X5,X4,X3),X6) )
        | ~ member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X5,X4,X3))) ) ),
    inference(ennf_transformation,[],[f232]) ).

tff(f232,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: nat,X3: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X5: nat,X6: X0] :
      ( ( ~ member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X5,X4,X3)))
       => ( ( ~ member(X0,X6,huffma675207370phabet(X0,X1))
           => ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,huffma1146269203erNode(X0,X5,X4,X3),X1),X6) = X6 ) )
          & ( member(X0,X6,huffma675207370phabet(X0,X1))
           => ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,huffma1146269203erNode(X0,X5,X4,X3),X1),X6) = huffma1401021291ibling(X0,X1,X6) ) ) ) )
      & ( member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X5,X4,X3)))
       => ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,huffma1146269203erNode(X0,X5,X4,X3),X1),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X5,X4,X3),X6) ) ) ),
    inference(rectify,[],[f3]) ).

tff(f3,axiom,
    ! [X2: $tType,X15: huffma1450048681e_tree(X2),X12: nat,X9: huffma1450048681e_tree(X2),X10: huffma1450048681e_tree(X2),X11: nat,X14: X2] :
      ( ( ~ member(X2,X14,huffma675207370phabet(X2,huffma1146269203erNode(X2,X11,X10,X9)))
       => ( ( ~ member(X2,X14,huffma675207370phabet(X2,X15))
           => ( huffma1401021291ibling(X2,huffma1146269203erNode(X2,X12,huffma1146269203erNode(X2,X11,X10,X9),X15),X14) = X14 ) )
          & ( member(X2,X14,huffma675207370phabet(X2,X15))
           => ( huffma1401021291ibling(X2,huffma1146269203erNode(X2,X12,huffma1146269203erNode(X2,X11,X10,X9),X15),X14) = huffma1401021291ibling(X2,X15,X14) ) ) ) )
      & ( member(X2,X14,huffma675207370phabet(X2,huffma1146269203erNode(X2,X11,X10,X9)))
       => ( huffma1401021291ibling(X2,huffma1146269203erNode(X2,X11,X10,X9),X14) = huffma1401021291ibling(X2,huffma1146269203erNode(X2,X12,huffma1146269203erNode(X2,X11,X10,X9),X15),X14) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_sibling_Osimps_I3_J) ).

tff(f1907,plain,
    spl18_143,
    inference(avatar_split_clause,[],[f540,f1905]) ).

tff(f540,plain,
    ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0),X6: X0,X4: huffma1450048681e_tree(X0),X5: nat] :
      ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,huffma1146269203erNode(X0,X5,X4,X3),X1),X6) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X5,X4,X3),X6) )
      | ~ member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X5,X4,X3))) ),
    inference(cnf_transformation,[],[f299]) ).

tff(f1887,plain,
    ( spl18_142
    | ~ spl18_45
    | ~ spl18_72 ),
    inference(avatar_split_clause,[],[f968,f938,f792,f1885]) ).

tff(f968,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less(nat,X1,X0)
        | ( X0 = X1 )
        | ord_less_eq(nat,X0,X1) )
    | ~ spl18_45
    | ~ spl18_72 ),
    inference(resolution,[],[f939,f793]) ).

tff(f1883,plain,
    spl18_141,
    inference(avatar_split_clause,[],[f542,f1881]) ).

tff(f542,plain,
    ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0),X6: X0,X4: huffma1450048681e_tree(X0),X5: nat] :
      ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,huffma1146269203erNode(X0,X5,X4,X3),X1),X6) = X6 )
      | member(X0,X6,huffma675207370phabet(X0,X1))
      | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X5,X4,X3))) ),
    inference(cnf_transformation,[],[f299]) ).

tff(f1879,plain,
    spl18_140,
    inference(avatar_split_clause,[],[f539,f1877]) ).

tff(f539,plain,
    ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X6: X0,X4: nat,X5: huffma1450048681e_tree(X0)] :
      ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X5,huffma1146269203erNode(X0,X3,X2,X1)),X6) = X6 )
      | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X3,X2,X1)))
      | member(X0,X6,huffma675207370phabet(X0,X5)) ),
    inference(cnf_transformation,[],[f298]) ).

tff(f1875,plain,
    spl18_139,
    inference(avatar_split_clause,[],[f517,f1873]) ).

tff(f517,plain,
    ! [X2: fun(nat,nat),X0: nat,X1: nat] :
      ( ord_less_eq(nat,aa(nat,nat,X2,X1),aa(nat,nat,X2,X0))
      | ~ ord_less_eq(nat,X1,X0)
      | ~ ord_less(nat,aa(nat,nat,X2,sK15(X2)),aa(nat,nat,X2,sK16(X2))) ),
    inference(cnf_transformation,[],[f354]) ).

tff(f354,plain,
    ! [X0: nat,X1: nat,X2: fun(nat,nat)] :
      ( ord_less_eq(nat,aa(nat,nat,X2,X1),aa(nat,nat,X2,X0))
      | ~ ord_less_eq(nat,X1,X0)
      | ( ~ ord_less(nat,aa(nat,nat,X2,sK15(X2)),aa(nat,nat,X2,sK16(X2)))
        & ord_less(nat,sK15(X2),sK16(X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f294,f353]) ).

tff(f353,plain,
    ! [X2: fun(nat,nat)] :
      ( ? [X3: nat,X4: nat] :
          ( ~ ord_less(nat,aa(nat,nat,X2,X3),aa(nat,nat,X2,X4))
          & ord_less(nat,X3,X4) )
     => ( ~ ord_less(nat,aa(nat,nat,X2,sK15(X2)),aa(nat,nat,X2,sK16(X2)))
        & ord_less(nat,sK15(X2),sK16(X2)) ) ),
    introduced(choice_axiom,[]) ).

tff(f294,plain,
    ! [X0: nat,X1: nat,X2: fun(nat,nat)] :
      ( ord_less_eq(nat,aa(nat,nat,X2,X1),aa(nat,nat,X2,X0))
      | ~ ord_less_eq(nat,X1,X0)
      | ? [X3: nat,X4: nat] :
          ( ~ ord_less(nat,aa(nat,nat,X2,X3),aa(nat,nat,X2,X4))
          & ord_less(nat,X3,X4) ) ),
    inference(flattening,[],[f293]) ).

tff(f293,plain,
    ! [X0: nat,X1: nat,X2: fun(nat,nat)] :
      ( ord_less_eq(nat,aa(nat,nat,X2,X1),aa(nat,nat,X2,X0))
      | ~ ord_less_eq(nat,X1,X0)
      | ? [X3: nat,X4: nat] :
          ( ~ ord_less(nat,aa(nat,nat,X2,X3),aa(nat,nat,X2,X4))
          & ord_less(nat,X3,X4) ) ),
    inference(ennf_transformation,[],[f217]) ).

tff(f217,plain,
    ! [X0: nat,X1: nat,X2: fun(nat,nat)] :
      ( ! [X3: nat,X4: nat] :
          ( ord_less(nat,X3,X4)
         => ord_less(nat,aa(nat,nat,X2,X3),aa(nat,nat,X2,X4)) )
     => ( ord_less_eq(nat,X1,X0)
       => ord_less_eq(nat,aa(nat,nat,X2,X1),aa(nat,nat,X2,X0)) ) ),
    inference(rectify,[],[f81]) ).

tff(f81,axiom,
    ! [X60: nat,X61: nat,X56: fun(nat,nat)] :
      ( ! [X62: nat,X63: nat] :
          ( ord_less(nat,X62,X63)
         => ord_less(nat,aa(nat,nat,X56,X62),aa(nat,nat,X56,X63)) )
     => ( ord_less_eq(nat,X61,X60)
       => ord_less_eq(nat,aa(nat,nat,X56,X61),aa(nat,nat,X56,X60)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_less__mono__imp__le__mono) ).

tff(f1870,plain,
    spl18_138,
    inference(avatar_split_clause,[],[f509,f1868]) ).

tff(f1868,plain,
    ( spl18_138
  <=> ! [X0: $tType,X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
        ( ord_less(nat,zero_zero(nat),huffma945805758height(X0,X1))
        | ( huffma675207370phabet(X0,X1) != huffma675207370phabet(X0,X2) )
        | ~ huffma1518433673istent(X0,X2)
        | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_138])]) ).

tff(f509,plain,
    ! [X0: $tType,X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
      ( ord_less(nat,zero_zero(nat),huffma945805758height(X0,X1))
      | ( huffma675207370phabet(X0,X1) != huffma675207370phabet(X0,X2) )
      | ~ huffma1518433673istent(X0,X2)
      | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X2)) ),
    inference(cnf_transformation,[],[f290]) ).

tff(f290,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0)] :
      ( ord_less(nat,zero_zero(nat),huffma945805758height(X0,X1))
      | ( huffma675207370phabet(X0,X1) != huffma675207370phabet(X0,X2) )
      | ~ huffma1518433673istent(X0,X2)
      | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X2)) ),
    inference(flattening,[],[f289]) ).

tff(f289,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0)] :
      ( ord_less(nat,zero_zero(nat),huffma945805758height(X0,X1))
      | ( huffma675207370phabet(X0,X1) != huffma675207370phabet(X0,X2) )
      | ~ huffma1518433673istent(X0,X2)
      | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X2)) ),
    inference(ennf_transformation,[],[f215]) ).

tff(f215,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0)] :
      ( ord_less(nat,zero_zero(nat),huffma945805758height(X0,X2))
     => ( huffma1518433673istent(X0,X2)
       => ( ( huffma675207370phabet(X0,X1) = huffma675207370phabet(X0,X2) )
         => ord_less(nat,zero_zero(nat),huffma945805758height(X0,X1)) ) ) ),
    inference(rectify,[],[f9]) ).

tff(f9,axiom,
    ! [X2: $tType,X21: huffma1450048681e_tree(X2),X16: huffma1450048681e_tree(X2)] :
      ( ord_less(nat,zero_zero(nat),huffma945805758height(X2,X16))
     => ( huffma1518433673istent(X2,X16)
       => ( ( huffma675207370phabet(X2,X16) = huffma675207370phabet(X2,X21) )
         => ord_less(nat,zero_zero(nat),huffma945805758height(X2,X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_height__gt__0__alphabet__eq__imp__height__gt__0) ).

tff(f1846,plain,
    spl18_137,
    inference(avatar_split_clause,[],[f470,f1844]) ).

tff(f470,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ( huffma1146269203erNode(X0,sK9(X0,X1),sK10(X0,X1),sK11(X0,X1)) = X1 )
      | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) ),
    inference(cnf_transformation,[],[f334]) ).

tff(f334,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ( huffma1146269203erNode(X0,sK9(X0,X1),sK10(X0,X1),sK11(X0,X1)) = X1 )
      | ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13])],[f331,f333,f332]) ).

tff(f332,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ? [X2: nat,X3: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0)] : ( huffma1146269203erNode(X0,X2,X3,X4) = X1 )
     => ( huffma1146269203erNode(X0,sK9(X0,X1),sK10(X0,X1),sK11(X0,X1)) = X1 ) ),
    introduced(choice_axiom,[]) ).

tff(f333,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ? [X5: nat,X6: X0] : ( huffma2021818691e_Leaf(X0,X5,X6) = X1 )
     => ( huffma2021818691e_Leaf(X0,sK12(X0,X1),sK13(X0,X1)) = X1 ) ),
    introduced(choice_axiom,[]) ).

tff(f331,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ? [X2: nat,X3: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0)] : ( huffma1146269203erNode(X0,X2,X3,X4) = X1 )
      | ? [X5: nat,X6: X0] : ( huffma2021818691e_Leaf(X0,X5,X6) = X1 ) ),
    inference(rectify,[],[f282]) ).

tff(f282,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ? [X4: nat,X5: huffma1450048681e_tree(X0),X6: huffma1450048681e_tree(X0)] : ( huffma1146269203erNode(X0,X4,X5,X6) = X1 )
      | ? [X2: nat,X3: X0] : ( huffma2021818691e_Leaf(X0,X2,X3) = X1 ) ),
    inference(ennf_transformation,[],[f190]) ).

tff(f190,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ! [X2: nat,X3: X0] : ( huffma2021818691e_Leaf(X0,X2,X3) != X1 )
     => ~ ! [X4: nat,X5: huffma1450048681e_tree(X0),X6: huffma1450048681e_tree(X0)] : ( huffma1146269203erNode(X0,X4,X5,X6) != X1 ) ),
    inference(rectify,[],[f36]) ).

tff(f36,axiom,
    ! [X0: $tType,X41: huffma1450048681e_tree(X0)] :
      ( ! [X43: nat,X26: X0] : ( huffma2021818691e_Leaf(X0,X43,X26) != X41 )
     => ~ ! [X43: nat,X44: huffma1450048681e_tree(X0),X45: huffma1450048681e_tree(X0)] : ( huffma1146269203erNode(X0,X43,X44,X45) != X41 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_tree_Oexhaust) ).

tff(f1842,plain,
    spl18_136,
    inference(avatar_split_clause,[],[f463,f1840]) ).

tff(f463,plain,
    ! [X3: nat,X0: nat,X1: fun(nat,bool)] :
      ( ~ pp(aa(nat,bool,X1,X3))
      | ~ ord_less(nat,X3,sK7(X0,X1))
      | ~ pp(aa(nat,bool,X1,X0))
      | pp(aa(nat,bool,X1,zero_zero(nat))) ),
    inference(cnf_transformation,[],[f328]) ).

tff(f328,plain,
    ! [X0: nat,X1: fun(nat,bool)] :
      ( ( pp(aa(nat,bool,X1,sK7(X0,X1)))
        & ! [X3: nat] :
            ( ~ pp(aa(nat,bool,X1,X3))
            | ~ ord_less(nat,X3,sK7(X0,X1)) )
        & ord_less_eq(nat,sK7(X0,X1),X0) )
      | ~ pp(aa(nat,bool,X1,X0))
      | pp(aa(nat,bool,X1,zero_zero(nat))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f278,f327]) ).

tff(f327,plain,
    ! [X0: nat,X1: fun(nat,bool)] :
      ( ? [X2: nat] :
          ( pp(aa(nat,bool,X1,X2))
          & ! [X3: nat] :
              ( ~ pp(aa(nat,bool,X1,X3))
              | ~ ord_less(nat,X3,X2) )
          & ord_less_eq(nat,X2,X0) )
     => ( pp(aa(nat,bool,X1,sK7(X0,X1)))
        & ! [X3: nat] :
            ( ~ pp(aa(nat,bool,X1,X3))
            | ~ ord_less(nat,X3,sK7(X0,X1)) )
        & ord_less_eq(nat,sK7(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

tff(f278,plain,
    ! [X0: nat,X1: fun(nat,bool)] :
      ( ? [X2: nat] :
          ( pp(aa(nat,bool,X1,X2))
          & ! [X3: nat] :
              ( ~ pp(aa(nat,bool,X1,X3))
              | ~ ord_less(nat,X3,X2) )
          & ord_less_eq(nat,X2,X0) )
      | ~ pp(aa(nat,bool,X1,X0))
      | pp(aa(nat,bool,X1,zero_zero(nat))) ),
    inference(flattening,[],[f277]) ).

tff(f277,plain,
    ! [X0: nat,X1: fun(nat,bool)] :
      ( ? [X2: nat] :
          ( pp(aa(nat,bool,X1,X2))
          & ! [X3: nat] :
              ( ~ pp(aa(nat,bool,X1,X3))
              | ~ ord_less(nat,X3,X2) )
          & ord_less_eq(nat,X2,X0) )
      | ~ pp(aa(nat,bool,X1,X0))
      | pp(aa(nat,bool,X1,zero_zero(nat))) ),
    inference(ennf_transformation,[],[f187]) ).

tff(f187,plain,
    ! [X0: nat,X1: fun(nat,bool)] :
      ( ~ pp(aa(nat,bool,X1,zero_zero(nat)))
     => ( pp(aa(nat,bool,X1,X0))
       => ? [X2: nat] :
            ( pp(aa(nat,bool,X1,X2))
            & ! [X3: nat] :
                ( ord_less(nat,X3,X2)
               => ~ pp(aa(nat,bool,X1,X3)) )
            & ord_less_eq(nat,X2,X0) ) ) ),
    inference(rectify,[],[f80]) ).

tff(f80,axiom,
    ! [X19: nat,X38: fun(nat,bool)] :
      ( ~ pp(aa(nat,bool,X38,zero_zero(nat)))
     => ( pp(aa(nat,bool,X38,X19))
       => ? [X58: nat] :
            ( pp(aa(nat,bool,X38,X58))
            & ! [X59: nat] :
                ( ord_less(nat,X59,X58)
               => ~ pp(aa(nat,bool,X38,X59)) )
            & ord_less_eq(nat,X58,X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_ex__least__nat__le) ).

tff(f1816,plain,
    ( spl18_135
    | ~ spl18_31
    | ~ spl18_49 ),
    inference(avatar_split_clause,[],[f817,f808,f725,f1814]) ).

tff(f817,plain,
    ( ! [X0: huffma1450048681e_tree(bool)] :
        ( member(bool,fTrue,huffma675207370phabet(bool,X0))
        | ( fFalse = sK14(bool,X0) ) )
    | ~ spl18_31
    | ~ spl18_49 ),
    inference(superposition,[],[f809,f726]) ).

tff(f1801,plain,
    spl18_134,
    inference(avatar_split_clause,[],[f524,f1799]) ).

tff(f524,plain,
    ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
      ( ( X2 = X3 )
      | ( aa(X1,X0,X3,sK17(X0,X1,X2,X3)) != aa(X1,X0,X2,sK17(X0,X1,X2,X3)) ) ),
    inference(cnf_transformation,[],[f357]) ).

tff(f357,plain,
    ! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
      ( ( X2 = X3 )
      | ( aa(X1,X0,X3,sK17(X0,X1,X2,X3)) != aa(X1,X0,X2,sK17(X0,X1,X2,X3)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f296,f356]) ).

tff(f356,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,sK17(X0,X1,X2,X3)) != aa(X1,X0,X2,sK17(X0,X1,X2,X3)) ) ),
    introduced(choice_axiom,[]) ).

tff(f296,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,[],[f222]) ).

tff(f222,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,[],[f75]) ).

tff(f75,axiom,
    ! [X23: $tType,X2: $tType,X55: fun(X2,X23),X56: fun(X2,X23)] :
      ( ! [X47: X2] : ( aa(X2,X23,X56,X47) = aa(X2,X23,X55,X47) )
     => ( X55 = X56 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).

tff(f1797,plain,
    spl18_133,
    inference(avatar_split_clause,[],[f467,f1795]) ).

tff(f467,plain,
    ! [X3: nat,X0: nat,X1: fun(nat,bool)] :
      ( pp(aa(nat,bool,X1,X0))
      | pp(aa(nat,bool,X1,X3))
      | ~ ord_less(nat,X3,sK8(X1))
      | ~ pp(aa(nat,bool,X1,zero_zero(nat))) ),
    inference(cnf_transformation,[],[f330]) ).

tff(f330,plain,
    ! [X0: nat,X1: fun(nat,bool)] :
      ( pp(aa(nat,bool,X1,X0))
      | ( ! [X3: nat] :
            ( pp(aa(nat,bool,X1,X3))
            | ~ ord_less(nat,X3,sK8(X1)) )
        & ~ pp(aa(nat,bool,X1,sK8(X1)))
        & ord_less(nat,zero_zero(nat),sK8(X1)) )
      | ~ pp(aa(nat,bool,X1,zero_zero(nat))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f280,f329]) ).

tff(f329,plain,
    ! [X1: fun(nat,bool)] :
      ( ? [X2: nat] :
          ( ! [X3: nat] :
              ( pp(aa(nat,bool,X1,X3))
              | ~ ord_less(nat,X3,X2) )
          & ~ pp(aa(nat,bool,X1,X2))
          & ord_less(nat,zero_zero(nat),X2) )
     => ( ! [X3: nat] :
            ( pp(aa(nat,bool,X1,X3))
            | ~ ord_less(nat,X3,sK8(X1)) )
        & ~ pp(aa(nat,bool,X1,sK8(X1)))
        & ord_less(nat,zero_zero(nat),sK8(X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f280,plain,
    ! [X0: nat,X1: fun(nat,bool)] :
      ( pp(aa(nat,bool,X1,X0))
      | ? [X2: nat] :
          ( ! [X3: nat] :
              ( pp(aa(nat,bool,X1,X3))
              | ~ ord_less(nat,X3,X2) )
          & ~ pp(aa(nat,bool,X1,X2))
          & ord_less(nat,zero_zero(nat),X2) )
      | ~ pp(aa(nat,bool,X1,zero_zero(nat))) ),
    inference(flattening,[],[f279]) ).

tff(f279,plain,
    ! [X0: nat,X1: fun(nat,bool)] :
      ( pp(aa(nat,bool,X1,X0))
      | ? [X2: nat] :
          ( ! [X3: nat] :
              ( pp(aa(nat,bool,X1,X3))
              | ~ ord_less(nat,X3,X2) )
          & ~ pp(aa(nat,bool,X1,X2))
          & ord_less(nat,zero_zero(nat),X2) )
      | ~ pp(aa(nat,bool,X1,zero_zero(nat))) ),
    inference(ennf_transformation,[],[f188]) ).

tff(f188,plain,
    ! [X0: nat,X1: fun(nat,bool)] :
      ( pp(aa(nat,bool,X1,zero_zero(nat)))
     => ( ! [X2: nat] :
            ( ord_less(nat,zero_zero(nat),X2)
           => ( ~ pp(aa(nat,bool,X1,X2))
             => ? [X3: nat] :
                  ( ~ pp(aa(nat,bool,X1,X3))
                  & ord_less(nat,X3,X2) ) ) )
       => pp(aa(nat,bool,X1,X0)) ) ),
    inference(rectify,[],[f39]) ).

tff(f39,axiom,
    ! [X19: nat,X38: fun(nat,bool)] :
      ( pp(aa(nat,bool,X38,zero_zero(nat)))
     => ( ! [X48: nat] :
            ( ord_less(nat,zero_zero(nat),X48)
           => ( ~ pp(aa(nat,bool,X38,X48))
             => ? [X49: nat] :
                  ( ~ pp(aa(nat,bool,X38,X49))
                  & ord_less(nat,X49,X48) ) ) )
       => pp(aa(nat,bool,X38,X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_infinite__descent0) ).

tff(f1772,plain,
    spl18_132,
    inference(avatar_split_clause,[],[f537,f1770]) ).

tff(f537,plain,
    ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X6: X0,X4: nat,X5: huffma1450048681e_tree(X0)] :
      ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X5,huffma1146269203erNode(X0,X3,X2,X1)),X6) = huffma1401021291ibling(X0,X5,X6) )
      | ~ member(X0,X6,huffma675207370phabet(X0,X5)) ),
    inference(cnf_transformation,[],[f298]) ).

tff(f1768,plain,
    spl18_131,
    inference(avatar_split_clause,[],[f512,f1766]) ).

tff(f512,plain,
    ! [X2: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
      ( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
      | ord_less(nat,X1,X2)
      | ( X1 = X2 )
      | sP0(X2,X1,X0) ),
    inference(cnf_transformation,[],[f301]) ).

tff(f301,plain,
    ! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
      ( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
      | ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ord_less(nat,X1,X2) )
      | ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ( X1 = X2 ) )
      | sP0(X2,X1,X0) ),
    inference(definition_folding,[],[f292,f300]) ).

tff(f300,plain,
    ! [X2: nat,X1: nat,X0: fun(nat,fun(nat,bool))] :
      ( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ord_less(nat,X2,X1) )
      | ~ sP0(X2,X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f292,plain,
    ! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
      ( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
      | ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ord_less(nat,X1,X2) )
      | ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ( X1 = X2 ) )
      | ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ord_less(nat,X2,X1) ) ),
    inference(flattening,[],[f291]) ).

tff(f291,plain,
    ! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
      ( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
      | ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ord_less(nat,X1,X2) )
      | ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ( X1 = X2 ) )
      | ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ord_less(nat,X2,X1) ) ),
    inference(ennf_transformation,[],[f216]) ).

tff(f216,plain,
    ! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
      ( ( ord_less(nat,X2,X1)
       => pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) )
     => ( ( ( X1 = X2 )
         => pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) )
       => ( ( ord_less(nat,X1,X2)
           => pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) )
         => pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) ) ) ),
    inference(rectify,[],[f26]) ).

tff(f26,axiom,
    ! [X38: fun(nat,fun(nat,bool)),X19: nat,X39: nat] :
      ( ( ord_less(nat,X39,X19)
       => pp(aa(nat,bool,aa(nat,fun(nat,bool),X38,X19),X39)) )
     => ( ( ( X19 = X39 )
         => pp(aa(nat,bool,aa(nat,fun(nat,bool),X38,X19),X39)) )
       => ( ( ord_less(nat,X19,X39)
           => pp(aa(nat,bool,aa(nat,fun(nat,bool),X38,X19),X39)) )
         => pp(aa(nat,bool,aa(nat,fun(nat,bool),X38,X19),X39)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_nat__less__cases) ).

tff(f1742,plain,
    spl18_130,
    inference(avatar_split_clause,[],[f536,f1740]) ).

tff(f536,plain,
    ! [X0: $tType,X2: nat,X3: nat,X1: X0,X6: X0,X4: nat,X5: X0] :
      ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,huffma2021818691e_Leaf(X0,X3,X5),huffma2021818691e_Leaf(X0,X2,X1)),X6) = X6 )
      | ( X1 = X6 )
      | ( X5 = X6 ) ),
    inference(cnf_transformation,[],[f297]) ).

tff(f297,plain,
    ! [X0: $tType,X1: X0,X2: nat,X3: nat,X4: nat,X5: X0,X6: X0] :
      ( ( ( ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,huffma2021818691e_Leaf(X0,X3,X5),huffma2021818691e_Leaf(X0,X2,X1)),X6) = X6 )
            | ( X1 = X6 ) )
          & ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,huffma2021818691e_Leaf(X0,X3,X5),huffma2021818691e_Leaf(X0,X2,X1)),X6) = X5 )
            | ( X1 != X6 ) ) )
        | ( X5 = X6 ) )
      & ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,huffma2021818691e_Leaf(X0,X3,X5),huffma2021818691e_Leaf(X0,X2,X1)),X6) = X1 )
        | ( X5 != X6 ) ) ),
    inference(ennf_transformation,[],[f230]) ).

tff(f230,plain,
    ! [X0: $tType,X1: X0,X2: nat,X3: nat,X4: nat,X5: X0,X6: X0] :
      ( ( ( X5 != X6 )
       => ( ( ( X1 != X6 )
           => ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,huffma2021818691e_Leaf(X0,X3,X5),huffma2021818691e_Leaf(X0,X2,X1)),X6) = X6 ) )
          & ( ( X1 = X6 )
           => ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,huffma2021818691e_Leaf(X0,X3,X5),huffma2021818691e_Leaf(X0,X2,X1)),X6) = X5 ) ) ) )
      & ( ( X5 = X6 )
       => ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,huffma2021818691e_Leaf(X0,X3,X5),huffma2021818691e_Leaf(X0,X2,X1)),X6) = X1 ) ) ),
    inference(rectify,[],[f15]) ).

tff(f15,axiom,
    ! [X0: $tType,X27: X0,X28: nat,X29: nat,X30: nat,X31: X0,X17: X0] :
      ( ( ( X17 != X31 )
       => ( ( ( X17 != X27 )
           => ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X30,huffma2021818691e_Leaf(X0,X29,X31),huffma2021818691e_Leaf(X0,X28,X27)),X17) = X17 ) )
          & ( ( X17 = X27 )
           => ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X30,huffma2021818691e_Leaf(X0,X29,X31),huffma2021818691e_Leaf(X0,X28,X27)),X17) = X31 ) ) ) )
      & ( ( X17 = X31 )
       => ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X30,huffma2021818691e_Leaf(X0,X29,X31),huffma2021818691e_Leaf(X0,X28,X27)),X17) = X27 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_sibling_Osimps_I2_J) ).

tff(f1724,plain,
    spl18_129,
    inference(avatar_split_clause,[],[f516,f1722]) ).

tff(f516,plain,
    ! [X2: fun(nat,nat),X0: nat,X1: nat] :
      ( ord_less_eq(nat,aa(nat,nat,X2,X1),aa(nat,nat,X2,X0))
      | ~ ord_less_eq(nat,X1,X0)
      | ord_less(nat,sK15(X2),sK16(X2)) ),
    inference(cnf_transformation,[],[f354]) ).

tff(f1649,plain,
    spl18_128,
    inference(avatar_split_clause,[],[f531,f1647]) ).

tff(f531,plain,
    ! [X1: $tType,X0: $tType,X2: X1,X3: nat,X4: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))))),X5: fun(nat,fun(X1,X0))] : ( aa(X1,X0,aa(nat,fun(X1,X0),X5,X3),X2) = huffma1280178957ee_rec(X1,X0,X5,X4,huffma2021818691e_Leaf(X1,X3,X2)) ),
    inference(cnf_transformation,[],[f227]) ).

tff(f227,plain,
    ! [X0: $tType,X1: $tType,X2: X1,X3: nat,X4: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))))),X5: fun(nat,fun(X1,X0))] : ( aa(X1,X0,aa(nat,fun(X1,X0),X5,X3),X2) = huffma1280178957ee_rec(X1,X0,X5,X4,huffma2021818691e_Leaf(X1,X3,X2)) ),
    inference(rectify,[],[f40]) ).

tff(f40,axiom,
    ! [X2: $tType,X23: $tType,X14: X23,X8: nat,X24: fun(nat,fun(huffma1450048681e_tree(X23),fun(huffma1450048681e_tree(X23),fun(X2,fun(X2,X2))))),X25: fun(nat,fun(X23,X2))] : ( aa(X23,X2,aa(nat,fun(X23,X2),X25,X8),X14) = huffma1280178957ee_rec(X23,X2,X25,X24,huffma2021818691e_Leaf(X23,X8,X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_tree_Orecs_I1_J) ).

tff(f1645,plain,
    spl18_127,
    inference(avatar_split_clause,[],[f530,f1643]) ).

tff(f530,plain,
    ! [X1: $tType,X0: $tType,X2: X1,X3: nat,X4: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),X0))),X5: fun(nat,fun(X1,X0))] : ( huffma107959123e_case(X1,X0,X5,X4,huffma2021818691e_Leaf(X1,X3,X2)) = aa(X1,X0,aa(nat,fun(X1,X0),X5,X3),X2) ),
    inference(cnf_transformation,[],[f226]) ).

tff(f226,plain,
    ! [X0: $tType,X1: $tType,X2: X1,X3: nat,X4: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),X0))),X5: fun(nat,fun(X1,X0))] : ( huffma107959123e_case(X1,X0,X5,X4,huffma2021818691e_Leaf(X1,X3,X2)) = aa(X1,X0,aa(nat,fun(X1,X0),X5,X3),X2) ),
    inference(rectify,[],[f21]) ).

tff(f21,axiom,
    ! [X2: $tType,X23: $tType,X14: X23,X8: nat,X24: fun(nat,fun(huffma1450048681e_tree(X23),fun(huffma1450048681e_tree(X23),X2))),X25: fun(nat,fun(X23,X2))] : ( huffma107959123e_case(X23,X2,X25,X24,huffma2021818691e_Leaf(X23,X8,X14)) = aa(X23,X2,aa(nat,fun(X23,X2),X25,X8),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_tree_Osimps_I5_J) ).

tff(f1641,plain,
    spl18_126,
    inference(avatar_split_clause,[],[f464,f1639]) ).

tff(f464,plain,
    ! [X0: nat,X1: fun(nat,bool)] :
      ( pp(aa(nat,bool,X1,sK7(X0,X1)))
      | ~ pp(aa(nat,bool,X1,X0))
      | pp(aa(nat,bool,X1,zero_zero(nat))) ),
    inference(cnf_transformation,[],[f328]) ).

tff(f1582,plain,
    spl18_125,
    inference(avatar_split_clause,[],[f466,f1580]) ).

tff(f466,plain,
    ! [X0: nat,X1: fun(nat,bool)] :
      ( pp(aa(nat,bool,X1,X0))
      | ~ pp(aa(nat,bool,X1,sK8(X1)))
      | ~ pp(aa(nat,bool,X1,zero_zero(nat))) ),
    inference(cnf_transformation,[],[f330]) ).

tff(f1578,plain,
    spl18_124,
    inference(avatar_split_clause,[],[f449,f1576]) ).

tff(f449,plain,
    ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X1,X0),X4: fun(X1,X0)] :
      ( ord_less_eq(X0,aa(X1,X0,X4,X2),aa(X1,X0,X3,X2))
      | ~ ord_less_eq(fun(X1,X0),X4,X3)
      | ~ ord(X0) ),
    inference(cnf_transformation,[],[f262]) ).

tff(f262,plain,
    ! [X0: $tType,X1: $tType] :
      ( ! [X2: X1,X3: fun(X1,X0),X4: fun(X1,X0)] :
          ( ord_less_eq(X0,aa(X1,X0,X4,X2),aa(X1,X0,X3,X2))
          | ~ ord_less_eq(fun(X1,X0),X4,X3) )
      | ~ ord(X0) ),
    inference(ennf_transformation,[],[f175]) ).

tff(f175,plain,
    ! [X0: $tType,X1: $tType] :
      ( ord(X0)
     => ! [X2: X1,X3: fun(X1,X0),X4: fun(X1,X0)] :
          ( ord_less_eq(fun(X1,X0),X4,X3)
         => ord_less_eq(X0,aa(X1,X0,X4,X2),aa(X1,X0,X3,X2)) ) ),
    inference(rectify,[],[f94]) ).

tff(f94,axiom,
    ! [X23: $tType,X2: $tType] :
      ( ord(X23)
     => ! [X37: X2,X55: fun(X2,X23),X56: fun(X2,X23)] :
          ( ord_less_eq(fun(X2,X23),X56,X55)
         => ord_less_eq(X23,aa(X2,X23,X56,X37),aa(X2,X23,X55,X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_le__funE) ).

tff(f1574,plain,
    spl18_123,
    inference(avatar_split_clause,[],[f442,f1572]) ).

tff(f442,plain,
    ! [X0: fun(int,bool),X4: int] :
      ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
      | ~ pp(aa(int,bool,X0,X4))
      | ~ ord_less_eq(int,zero_zero(int),X4) ),
    inference(cnf_transformation,[],[f324]) ).

tff(f324,plain,
    ! [X0: fun(int,bool)] :
      ( ( ( pp(aa(int,bool,X0,sK4(X0)))
          & ord_less_eq(int,zero_zero(int),sK4(X0)) )
        | ! [X2: nat] : ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,X2))) )
      & ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0))))
        | ! [X4: int] :
            ( ~ pp(aa(int,bool,X0,X4))
            | ~ ord_less_eq(int,zero_zero(int),X4) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f321,f323,f322]) ).

tff(f322,plain,
    ! [X0: fun(int,bool)] :
      ( ? [X1: int] :
          ( pp(aa(int,bool,X0,X1))
          & ord_less_eq(int,zero_zero(int),X1) )
     => ( pp(aa(int,bool,X0,sK4(X0)))
        & ord_less_eq(int,zero_zero(int),sK4(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f323,plain,
    ! [X0: fun(int,bool)] :
      ( ? [X3: nat] : pp(aa(int,bool,X0,semiring_1_of_nat(int,X3)))
     => pp(aa(int,bool,X0,semiring_1_of_nat(int,sK5(X0)))) ),
    introduced(choice_axiom,[]) ).

tff(f321,plain,
    ! [X0: fun(int,bool)] :
      ( ( ? [X1: int] :
            ( pp(aa(int,bool,X0,X1))
            & ord_less_eq(int,zero_zero(int),X1) )
        | ! [X2: nat] : ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,X2))) )
      & ( ? [X3: nat] : pp(aa(int,bool,X0,semiring_1_of_nat(int,X3)))
        | ! [X4: int] :
            ( ~ pp(aa(int,bool,X0,X4))
            | ~ ord_less_eq(int,zero_zero(int),X4) ) ) ),
    inference(rectify,[],[f320]) ).

tff(f320,plain,
    ! [X0: fun(int,bool)] :
      ( ( ? [X1: int] :
            ( pp(aa(int,bool,X0,X1))
            & ord_less_eq(int,zero_zero(int),X1) )
        | ! [X2: nat] : ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,X2))) )
      & ( ? [X2: nat] : pp(aa(int,bool,X0,semiring_1_of_nat(int,X2)))
        | ! [X1: int] :
            ( ~ pp(aa(int,bool,X0,X1))
            | ~ ord_less_eq(int,zero_zero(int),X1) ) ) ),
    inference(nnf_transformation,[],[f170]) ).

tff(f170,plain,
    ! [X0: fun(int,bool)] :
      ( ? [X1: int] :
          ( pp(aa(int,bool,X0,X1))
          & ord_less_eq(int,zero_zero(int),X1) )
    <=> ? [X2: nat] : pp(aa(int,bool,X0,semiring_1_of_nat(int,X2))) ),
    inference(rectify,[],[f87]) ).

tff(f87,axiom,
    ! [X38: fun(int,bool)] :
      ( ? [X65: int] :
          ( pp(aa(int,bool,X38,X65))
          & ord_less_eq(int,zero_zero(int),X65) )
    <=> ? [X65: nat] : pp(aa(int,bool,X38,semiring_1_of_nat(int,X65))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_transfer__int__nat__quantifiers_I2_J) ).

tff(f1570,plain,
    spl18_122,
    inference(avatar_split_clause,[],[f441,f1568]) ).

tff(f441,plain,
    ! [X0: fun(int,bool),X1: int] :
      ( pp(aa(int,bool,X0,X1))
      | ~ ord_less_eq(int,zero_zero(int),X1)
      | ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,sK2(X0)))) ),
    inference(cnf_transformation,[],[f319]) ).

tff(f319,plain,
    ! [X0: fun(int,bool)] :
      ( ( ! [X1: int] :
            ( pp(aa(int,bool,X0,X1))
            | ~ ord_less_eq(int,zero_zero(int),X1) )
        | ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,sK2(X0)))) )
      & ( ! [X3: nat] : pp(aa(int,bool,X0,semiring_1_of_nat(int,X3)))
        | ( ~ pp(aa(int,bool,X0,sK3(X0)))
          & ord_less_eq(int,zero_zero(int),sK3(X0)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f316,f318,f317]) ).

tff(f317,plain,
    ! [X0: fun(int,bool)] :
      ( ? [X2: nat] : ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,X2)))
     => ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,sK2(X0)))) ),
    introduced(choice_axiom,[]) ).

tff(f318,plain,
    ! [X0: fun(int,bool)] :
      ( ? [X4: int] :
          ( ~ pp(aa(int,bool,X0,X4))
          & ord_less_eq(int,zero_zero(int),X4) )
     => ( ~ pp(aa(int,bool,X0,sK3(X0)))
        & ord_less_eq(int,zero_zero(int),sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f316,plain,
    ! [X0: fun(int,bool)] :
      ( ( ! [X1: int] :
            ( pp(aa(int,bool,X0,X1))
            | ~ ord_less_eq(int,zero_zero(int),X1) )
        | ? [X2: nat] : ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,X2))) )
      & ( ! [X3: nat] : pp(aa(int,bool,X0,semiring_1_of_nat(int,X3)))
        | ? [X4: int] :
            ( ~ pp(aa(int,bool,X0,X4))
            & ord_less_eq(int,zero_zero(int),X4) ) ) ),
    inference(rectify,[],[f315]) ).

tff(f315,plain,
    ! [X0: fun(int,bool)] :
      ( ( ! [X1: int] :
            ( pp(aa(int,bool,X0,X1))
            | ~ ord_less_eq(int,zero_zero(int),X1) )
        | ? [X2: nat] : ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,X2))) )
      & ( ! [X2: nat] : pp(aa(int,bool,X0,semiring_1_of_nat(int,X2)))
        | ? [X1: int] :
            ( ~ pp(aa(int,bool,X0,X1))
            & ord_less_eq(int,zero_zero(int),X1) ) ) ),
    inference(nnf_transformation,[],[f258]) ).

tff(f258,plain,
    ! [X0: fun(int,bool)] :
      ( ! [X1: int] :
          ( pp(aa(int,bool,X0,X1))
          | ~ ord_less_eq(int,zero_zero(int),X1) )
    <=> ! [X2: nat] : pp(aa(int,bool,X0,semiring_1_of_nat(int,X2))) ),
    inference(ennf_transformation,[],[f169]) ).

tff(f169,plain,
    ! [X0: fun(int,bool)] :
      ( ! [X1: int] :
          ( ord_less_eq(int,zero_zero(int),X1)
         => pp(aa(int,bool,X0,X1)) )
    <=> ! [X2: nat] : pp(aa(int,bool,X0,semiring_1_of_nat(int,X2))) ),
    inference(rectify,[],[f86]) ).

tff(f86,axiom,
    ! [X38: fun(int,bool)] :
      ( ! [X65: int] :
          ( ord_less_eq(int,zero_zero(int),X65)
         => pp(aa(int,bool,X38,X65)) )
    <=> ! [X65: nat] : pp(aa(int,bool,X38,semiring_1_of_nat(int,X65))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_transfer__int__nat__quantifiers_I1_J) ).

tff(f1545,plain,
    spl18_121,
    inference(avatar_split_clause,[],[f572,f1543]) ).

tff(f572,plain,
    ! [X0: $tType,X2: nat,X3: nat,X6: X0,X4: nat,X5: X0] :
      ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,huffma2021818691e_Leaf(X0,X3,X5),huffma2021818691e_Leaf(X0,X2,X6)),X6) = X5 )
      | ( X5 = X6 ) ),
    inference(equality_resolution,[],[f535]) ).

tff(f535,plain,
    ! [X0: $tType,X2: nat,X3: nat,X1: X0,X6: X0,X4: nat,X5: X0] :
      ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,huffma2021818691e_Leaf(X0,X3,X5),huffma2021818691e_Leaf(X0,X2,X1)),X6) = X5 )
      | ( X1 != X6 )
      | ( X5 = X6 ) ),
    inference(cnf_transformation,[],[f297]) ).

tff(f1541,plain,
    spl18_120,
    inference(avatar_split_clause,[],[f465,f1539]) ).

tff(f465,plain,
    ! [X0: nat,X1: fun(nat,bool)] :
      ( pp(aa(nat,bool,X1,X0))
      | ord_less(nat,zero_zero(nat),sK8(X1))
      | ~ pp(aa(nat,bool,X1,zero_zero(nat))) ),
    inference(cnf_transformation,[],[f330]) ).

tff(f1526,plain,
    spl18_119,
    inference(avatar_split_clause,[],[f462,f1524]) ).

tff(f462,plain,
    ! [X0: nat,X1: fun(nat,bool)] :
      ( ord_less_eq(nat,sK7(X0,X1),X0)
      | ~ pp(aa(nat,bool,X1,X0))
      | pp(aa(nat,bool,X1,zero_zero(nat))) ),
    inference(cnf_transformation,[],[f328]) ).

tff(f1505,plain,
    spl18_118,
    inference(avatar_split_clause,[],[f573,f1503]) ).

tff(f573,plain,
    ! [X0: $tType,X2: nat,X3: nat,X1: X0,X6: X0,X4: nat] : ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,huffma2021818691e_Leaf(X0,X3,X6),huffma2021818691e_Leaf(X0,X2,X1)),X6) = X1 ),
    inference(equality_resolution,[],[f534]) ).

tff(f534,plain,
    ! [X0: $tType,X2: nat,X3: nat,X1: X0,X6: X0,X4: nat,X5: X0] :
      ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,huffma2021818691e_Leaf(X0,X3,X5),huffma2021818691e_Leaf(X0,X2,X1)),X6) = X1 )
      | ( X5 != X6 ) ),
    inference(cnf_transformation,[],[f297]) ).

tff(f1501,plain,
    spl18_117,
    inference(avatar_split_clause,[],[f545,f1499]) ).

tff(f545,plain,
    ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X6: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
      ( ( X1 = X4 )
      | ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ),
    inference(cnf_transformation,[],[f361]) ).

tff(f361,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0),X6: nat] :
      ( ( ( huffma1146269203erNode(X0,X3,X2,X1) = huffma1146269203erNode(X0,X6,X5,X4) )
        | ( X1 != X4 )
        | ( X2 != X5 )
        | ( X3 != X6 ) )
      & ( ( ( X1 = X4 )
          & ( X2 = X5 )
          & ( X3 = X6 ) )
        | ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ) ),
    inference(flattening,[],[f360]) ).

tff(f360,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0),X6: nat] :
      ( ( ( huffma1146269203erNode(X0,X3,X2,X1) = huffma1146269203erNode(X0,X6,X5,X4) )
        | ( X1 != X4 )
        | ( X2 != X5 )
        | ( X3 != X6 ) )
      & ( ( ( X1 = X4 )
          & ( X2 = X5 )
          & ( X3 = X6 ) )
        | ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ) ),
    inference(nnf_transformation,[],[f233]) ).

tff(f233,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0),X6: nat] :
      ( ( huffma1146269203erNode(X0,X3,X2,X1) = huffma1146269203erNode(X0,X6,X5,X4) )
    <=> ( ( X1 = X4 )
        & ( X2 = X5 )
        & ( X3 = X6 ) ) ),
    inference(rectify,[],[f1]) ).

tff(f1,axiom,
    ! [X2: $tType,X3: huffma1450048681e_tree(X2),X4: huffma1450048681e_tree(X2),X5: nat,X6: huffma1450048681e_tree(X2),X7: huffma1450048681e_tree(X2),X8: nat] :
      ( ( huffma1146269203erNode(X2,X8,X7,X6) = huffma1146269203erNode(X2,X5,X4,X3) )
    <=> ( ( X3 = X6 )
        & ( X4 = X7 )
        & ( X5 = X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tree_Osimps_I2_J) ).

tff(f1497,plain,
    spl18_116,
    inference(avatar_split_clause,[],[f544,f1495]) ).

tff(f544,plain,
    ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X6: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
      ( ( X2 = X5 )
      | ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ),
    inference(cnf_transformation,[],[f361]) ).

tff(f1493,plain,
    ( spl18_115
    | ~ spl18_31
    | ~ spl18_43 ),
    inference(avatar_split_clause,[],[f786,f779,f725,f1491]) ).

tff(f786,plain,
    ( ! [X0: bool,X1: bool] :
        ( ( fTrue = X0 )
        | ( fFalse = if(bool,fTrue,X0,X1) ) )
    | ~ spl18_31
    | ~ spl18_43 ),
    inference(superposition,[],[f780,f726]) ).

tff(f1489,plain,
    spl18_114,
    inference(avatar_split_clause,[],[f523,f1487]) ).

tff(f523,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: nat] :
      ( ( zero_zero(nat) = aa(X0,nat,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3) )
      | ( X2 = X3 ) ),
    inference(cnf_transformation,[],[f295]) ).

tff(f295,plain,
    ! [X0: $tType,X1: nat,X2: X0,X3: X0] :
      ( ( ( zero_zero(nat) = aa(X0,nat,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3) )
        | ( X2 = X3 ) )
      & ( ( aa(X0,nat,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3) = X1 )
        | ( X2 != X3 ) ) ),
    inference(ennf_transformation,[],[f221]) ).

tff(f221,plain,
    ! [X0: $tType,X1: nat,X2: X0,X3: X0] :
      ( ( ( X2 != X3 )
       => ( zero_zero(nat) = aa(X0,nat,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3) ) )
      & ( ( X2 = X3 )
       => ( aa(X0,nat,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3) = X1 ) ) ),
    inference(rectify,[],[f37]) ).

tff(f37,axiom,
    ! [X0: $tType,X30: nat,X17: X0,X46: X0] :
      ( ( ( X17 != X46 )
       => ( zero_zero(nat) = aa(X0,nat,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X30,X17)),X46) ) )
      & ( ( X17 = X46 )
       => ( aa(X0,nat,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X30,X17)),X46) = X30 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_freq_Osimps_I1_J) ).

tff(f1485,plain,
    spl18_113,
    inference(avatar_split_clause,[],[f511,f1483]) ).

tff(f511,plain,
    ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
      ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f352]) ).

tff(f352,plain,
    ! [X0: nat,X1: nat,X2: fun(nat,fun(nat,bool))] :
      ( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
        & ord_less(nat,X0,X1) )
      | ~ sP0(X0,X1,X2) ),
    inference(rectify,[],[f351]) ).

tff(f351,plain,
    ! [X2: nat,X1: nat,X0: fun(nat,fun(nat,bool))] :
      ( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
        & ord_less(nat,X2,X1) )
      | ~ sP0(X2,X1,X0) ),
    inference(nnf_transformation,[],[f300]) ).

tff(f1481,plain,
    spl18_112,
    inference(avatar_split_clause,[],[f507,f1479]) ).

tff(f507,plain,
    ! [X0: $tType,X2: X0,X1: huffma1450048681e_tree(X0)] :
      ( ( zero_zero(nat) = aa(X0,nat,huffma1352802255e_freq(X0,X1),X2) )
      | member(X0,X2,huffma675207370phabet(X0,X1)) ),
    inference(cnf_transformation,[],[f287]) ).

tff(f287,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: X0] :
      ( ( zero_zero(nat) = aa(X0,nat,huffma1352802255e_freq(X0,X1),X2) )
      | member(X0,X2,huffma675207370phabet(X0,X1)) ),
    inference(ennf_transformation,[],[f213]) ).

tff(f213,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: X0] :
      ( ~ member(X0,X2,huffma675207370phabet(X0,X1))
     => ( zero_zero(nat) = aa(X0,nat,huffma1352802255e_freq(X0,X1),X2) ) ),
    inference(rectify,[],[f47]) ).

tff(f47,axiom,
    ! [X2: $tType,X16: huffma1450048681e_tree(X2),X14: X2] :
      ( ~ member(X2,X14,huffma675207370phabet(X2,X16))
     => ( zero_zero(nat) = aa(X2,nat,huffma1352802255e_freq(X2,X16),X14) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_notin__alphabet__imp__freq__0) ).

tff(f1458,plain,
    spl18_111,
    inference(avatar_split_clause,[],[f543,f1456]) ).

tff(f543,plain,
    ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X6: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
      ( ( X3 = X6 )
      | ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ),
    inference(cnf_transformation,[],[f361]) ).

tff(f1454,plain,
    spl18_110,
    inference(avatar_split_clause,[],[f444,f1452]) ).

tff(f444,plain,
    ! [X2: nat,X0: fun(int,bool)] :
      ( pp(aa(int,bool,X0,sK4(X0)))
      | ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,X2))) ),
    inference(cnf_transformation,[],[f324]) ).

tff(f1450,plain,
    spl18_109,
    inference(avatar_split_clause,[],[f440,f1448]) ).

tff(f440,plain,
    ! [X3: nat,X0: fun(int,bool)] :
      ( pp(aa(int,bool,X0,semiring_1_of_nat(int,X3)))
      | ~ pp(aa(int,bool,X0,sK3(X0))) ),
    inference(cnf_transformation,[],[f319]) ).

tff(f1436,plain,
    ( spl18_108
    | ~ spl18_31
    | ~ spl18_43 ),
    inference(avatar_split_clause,[],[f785,f779,f725,f1434]) ).

tff(f785,plain,
    ( ! [X1: $tType,X2: X1,X3: X1,X0: bool] :
        ( ( if(X1,X0,X2,X3) = X2 )
        | ( fFalse = X0 ) )
    | ~ spl18_31
    | ~ spl18_43 ),
    inference(superposition,[],[f780,f726]) ).

tff(f1292,plain,
    spl18_107,
    inference(avatar_split_clause,[],[f443,f1290]) ).

tff(f443,plain,
    ! [X2: nat,X0: fun(int,bool)] :
      ( ord_less_eq(int,zero_zero(int),sK4(X0))
      | ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,X2))) ),
    inference(cnf_transformation,[],[f324]) ).

tff(f1288,plain,
    spl18_106,
    inference(avatar_split_clause,[],[f439,f1286]) ).

tff(f439,plain,
    ! [X3: nat,X0: fun(int,bool)] :
      ( pp(aa(int,bool,X0,semiring_1_of_nat(int,X3)))
      | ord_less_eq(int,zero_zero(int),sK3(X0)) ),
    inference(cnf_transformation,[],[f319]) ).

tff(f1284,plain,
    ( spl18_105
    | ~ spl18_31
    | ~ spl18_42 ),
    inference(avatar_split_clause,[],[f784,f775,f725,f1282]) ).

tff(f784,plain,
    ( ! [X0: bool,X1: bool] :
        ( ( fTrue = X1 )
        | ( fFalse = if(bool,fFalse,X0,X1) ) )
    | ~ spl18_31
    | ~ spl18_42 ),
    inference(superposition,[],[f776,f726]) ).

tff(f1280,plain,
    spl18_104,
    inference(avatar_split_clause,[],[f423,f1278]) ).

tff(f423,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( ord_less_eq(X0,X3,X1)
      | ~ ord_less_eq(X0,X2,X1)
      | ~ ord_less_eq(X0,X3,X2)
      | ~ preorder(X0) ),
    inference(cnf_transformation,[],[f251]) ).

tff(f251,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less_eq(X0,X3,X1)
          | ~ ord_less_eq(X0,X2,X1)
          | ~ ord_less_eq(X0,X3,X2) )
      | ~ preorder(X0) ),
    inference(flattening,[],[f250]) ).

tff(f250,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less_eq(X0,X3,X1)
          | ~ ord_less_eq(X0,X2,X1)
          | ~ ord_less_eq(X0,X3,X2) )
      | ~ preorder(X0) ),
    inference(ennf_transformation,[],[f159]) ).

tff(f159,plain,
    ! [X0: $tType] :
      ( preorder(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less_eq(X0,X3,X2)
         => ( ord_less_eq(X0,X2,X1)
           => ord_less_eq(X0,X3,X1) ) ) ),
    inference(rectify,[],[f95]) ).

tff(f95,axiom,
    ! [X0: $tType] :
      ( preorder(X0)
     => ! [X66: X0,X41: X0,X42: X0] :
          ( ord_less_eq(X0,X42,X41)
         => ( ord_less_eq(X0,X41,X66)
           => ord_less_eq(X0,X42,X66) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_order__trans) ).

tff(f1276,plain,
    spl18_103,
    inference(avatar_split_clause,[],[f417,f1274]) ).

tff(f417,plain,
    ! [X0: $tType,X2: nat,X1: nat] :
      ( ord_less_eq(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
      | ~ ord_less_eq(nat,X2,X1)
      | ~ linordered_semidom(X0) ),
    inference(cnf_transformation,[],[f306]) ).

tff(f306,plain,
    ! [X0: $tType] :
      ( ! [X1: nat,X2: nat] :
          ( ( ord_less_eq(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
            | ~ ord_less_eq(nat,X2,X1) )
          & ( ord_less_eq(nat,X2,X1)
            | ~ ord_less_eq(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1)) ) )
      | ~ linordered_semidom(X0) ),
    inference(nnf_transformation,[],[f244]) ).

tff(f244,plain,
    ! [X0: $tType] :
      ( ! [X1: nat,X2: nat] :
          ( ord_less_eq(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
        <=> ord_less_eq(nat,X2,X1) )
      | ~ linordered_semidom(X0) ),
    inference(ennf_transformation,[],[f154]) ).

tff(f154,plain,
    ! [X0: $tType] :
      ( linordered_semidom(X0)
     => ! [X1: nat,X2: nat] :
          ( ord_less_eq(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
        <=> ord_less_eq(nat,X2,X1) ) ),
    inference(rectify,[],[f57]) ).

tff(f57,axiom,
    ! [X2: $tType] :
      ( linordered_semidom(X2)
     => ! [X19: nat,X39: nat] :
          ( ord_less_eq(X2,semiring_1_of_nat(X2,X39),semiring_1_of_nat(X2,X19))
        <=> ord_less_eq(nat,X39,X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_of__nat__le__iff) ).

tff(f1272,plain,
    spl18_102,
    inference(avatar_split_clause,[],[f416,f1270]) ).

tff(f416,plain,
    ! [X0: $tType,X2: nat,X1: nat] :
      ( ord_less_eq(nat,X2,X1)
      | ~ ord_less_eq(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
      | ~ linordered_semidom(X0) ),
    inference(cnf_transformation,[],[f306]) ).

tff(f1268,plain,
    spl18_101,
    inference(avatar_split_clause,[],[f413,f1266]) ).

tff(f413,plain,
    ! [X0: $tType,X2: nat,X1: nat] :
      ( ord_less(nat,X2,X1)
      | ~ ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
      | ~ linordered_semidom(X0) ),
    inference(cnf_transformation,[],[f242]) ).

tff(f242,plain,
    ! [X0: $tType] :
      ( ! [X1: nat,X2: nat] :
          ( ord_less(nat,X2,X1)
          | ~ ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1)) )
      | ~ linordered_semidom(X0) ),
    inference(ennf_transformation,[],[f152]) ).

tff(f152,plain,
    ! [X0: $tType] :
      ( linordered_semidom(X0)
     => ! [X1: nat,X2: nat] :
          ( ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
         => ord_less(nat,X2,X1) ) ),
    inference(rectify,[],[f46]) ).

tff(f46,axiom,
    ! [X0: $tType] :
      ( linordered_semidom(X0)
     => ! [X20: nat,X22: nat] :
          ( ord_less(X0,semiring_1_of_nat(X0,X22),semiring_1_of_nat(X0,X20))
         => ord_less(nat,X22,X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_of__nat__less__imp__less) ).

tff(f1264,plain,
    spl18_100,
    inference(avatar_split_clause,[],[f412,f1262]) ).

tff(f412,plain,
    ! [X0: $tType,X2: nat,X1: nat] :
      ( ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
      | ~ ord_less(nat,X2,X1)
      | ~ linordered_semidom(X0) ),
    inference(cnf_transformation,[],[f241]) ).

tff(f241,plain,
    ! [X0: $tType] :
      ( ! [X1: nat,X2: nat] :
          ( ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
          | ~ ord_less(nat,X2,X1) )
      | ~ linordered_semidom(X0) ),
    inference(ennf_transformation,[],[f151]) ).

tff(f151,plain,
    ! [X0: $tType] :
      ( linordered_semidom(X0)
     => ! [X1: nat,X2: nat] :
          ( ord_less(nat,X2,X1)
         => ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1)) ) ),
    inference(rectify,[],[f45]) ).

tff(f45,axiom,
    ! [X0: $tType] :
      ( linordered_semidom(X0)
     => ! [X20: nat,X22: nat] :
          ( ord_less(nat,X22,X20)
         => ord_less(X0,semiring_1_of_nat(X0,X22),semiring_1_of_nat(X0,X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_less__imp__of__nat__less) ).

tff(f1260,plain,
    spl18_99,
    inference(avatar_split_clause,[],[f411,f1258]) ).

tff(f411,plain,
    ! [X0: $tType,X1: nat] :
      ( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
      | ~ ord_less(nat,zero_zero(nat),X1)
      | ~ linordered_semidom(X0) ),
    inference(cnf_transformation,[],[f304]) ).

tff(f304,plain,
    ! [X0: $tType] :
      ( ! [X1: nat] :
          ( ( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
            | ~ ord_less(nat,zero_zero(nat),X1) )
          & ( ord_less(nat,zero_zero(nat),X1)
            | ~ ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1)) ) )
      | ~ linordered_semidom(X0) ),
    inference(nnf_transformation,[],[f240]) ).

tff(f240,plain,
    ! [X0: $tType] :
      ( ! [X1: nat] :
          ( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
        <=> ord_less(nat,zero_zero(nat),X1) )
      | ~ linordered_semidom(X0) ),
    inference(ennf_transformation,[],[f150]) ).

tff(f150,plain,
    ! [X0: $tType] :
      ( linordered_semidom(X0)
     => ! [X1: nat] :
          ( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
        <=> ord_less(nat,zero_zero(nat),X1) ) ),
    inference(rectify,[],[f35]) ).

tff(f35,axiom,
    ! [X2: $tType] :
      ( linordered_semidom(X2)
     => ! [X19: nat] :
          ( ord_less(X2,zero_zero(X2),semiring_1_of_nat(X2,X19))
        <=> ord_less(nat,zero_zero(nat),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_of__nat__0__less__iff) ).

tff(f1256,plain,
    spl18_98,
    inference(avatar_split_clause,[],[f410,f1254]) ).

tff(f410,plain,
    ! [X0: $tType,X1: nat] :
      ( ord_less(nat,zero_zero(nat),X1)
      | ~ ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
      | ~ linordered_semidom(X0) ),
    inference(cnf_transformation,[],[f304]) ).

tff(f1225,plain,
    spl18_97,
    inference(avatar_split_clause,[],[f526,f1223]) ).

tff(f1223,plain,
    ( spl18_97
  <=> ! [X0: $tType,X2: nat,X4: nat,X3: X0,X1: X0] :
        ( ( X1 = X3 )
        | ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_97])]) ).

tff(f526,plain,
    ! [X0: $tType,X2: nat,X3: X0,X1: X0,X4: nat] :
      ( ( X1 = X3 )
      | ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ),
    inference(cnf_transformation,[],[f359]) ).

tff(f359,plain,
    ! [X0: $tType,X1: X0,X2: nat,X3: X0,X4: nat] :
      ( ( ( huffma2021818691e_Leaf(X0,X2,X1) = huffma2021818691e_Leaf(X0,X4,X3) )
        | ( X1 != X3 )
        | ( X2 != X4 ) )
      & ( ( ( X1 = X3 )
          & ( X2 = X4 ) )
        | ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ) ),
    inference(flattening,[],[f358]) ).

tff(f358,plain,
    ! [X0: $tType,X1: X0,X2: nat,X3: X0,X4: nat] :
      ( ( ( huffma2021818691e_Leaf(X0,X2,X1) = huffma2021818691e_Leaf(X0,X4,X3) )
        | ( X1 != X3 )
        | ( X2 != X4 ) )
      & ( ( ( X1 = X3 )
          & ( X2 = X4 ) )
        | ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ) ),
    inference(nnf_transformation,[],[f223]) ).

tff(f223,plain,
    ! [X0: $tType,X1: X0,X2: nat,X3: X0,X4: nat] :
      ( ( huffma2021818691e_Leaf(X0,X2,X1) = huffma2021818691e_Leaf(X0,X4,X3) )
    <=> ( ( X1 = X3 )
        & ( X2 = X4 ) ) ),
    inference(rectify,[],[f17]) ).

tff(f17,axiom,
    ! [X2: $tType,X32: X2,X5: nat,X14: X2,X8: nat] :
      ( ( huffma2021818691e_Leaf(X2,X8,X14) = huffma2021818691e_Leaf(X2,X5,X32) )
    <=> ( ( X14 = X32 )
        & ( X5 = X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_tree_Osimps_I1_J) ).

tff(f1221,plain,
    spl18_96,
    inference(avatar_split_clause,[],[f525,f1219]) ).

tff(f1219,plain,
    ( spl18_96
  <=> ! [X0: $tType,X4: nat,X3: X0,X2: nat,X1: X0] :
        ( ( X2 = X4 )
        | ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_96])]) ).

tff(f525,plain,
    ! [X0: $tType,X2: nat,X3: X0,X1: X0,X4: nat] :
      ( ( X2 = X4 )
      | ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ),
    inference(cnf_transformation,[],[f359]) ).

tff(f1217,plain,
    spl18_95,
    inference(avatar_split_clause,[],[f504,f1215]) ).

tff(f504,plain,
    ! [X2: bool,X0: nat,X1: nat] :
      ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) )
      | pp(X2) ),
    inference(cnf_transformation,[],[f283]) ).

tff(f283,plain,
    ! [X0: nat,X1: nat,X2: bool] :
      ( ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) )
        | pp(X2) )
      & ( ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) )
        | ~ pp(X2) ) ),
    inference(ennf_transformation,[],[f210]) ).

tff(f210,plain,
    ! [X0: nat,X1: nat,X2: bool] :
      ( ( ~ pp(X2)
       => ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) ) )
      & ( pp(X2)
       => ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) ) ) ),
    inference(rectify,[],[f59]) ).

tff(f59,axiom,
    ! [X51: nat,X37: nat,X38: bool] :
      ( ( ~ pp(X38)
       => ( semiring_1_of_nat(int,X51) = semiring_1_of_nat(int,if(nat,X38,X37,X51)) ) )
      & ( pp(X38)
       => ( semiring_1_of_nat(int,X37) = semiring_1_of_nat(int,if(nat,X38,X37,X51)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_int__if__cong) ).

tff(f1213,plain,
    spl18_94,
    inference(avatar_split_clause,[],[f503,f1211]) ).

tff(f503,plain,
    ! [X2: bool,X0: nat,X1: nat] :
      ( ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) )
      | ~ pp(X2) ),
    inference(cnf_transformation,[],[f283]) ).

tff(f1209,plain,
    spl18_93,
    inference(avatar_split_clause,[],[f453,f1207]) ).

tff(f1207,plain,
    ( spl18_93
  <=> ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,sK6(X0,X1)) )
        | ~ huffma1518433673istent(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_93])]) ).

tff(f453,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,sK6(X0,X1)) )
      | ~ huffma1518433673istent(X0,X1) ),
    inference(cnf_transformation,[],[f326]) ).

tff(f326,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,sK6(X0,X1)) )
        & member(X0,sK6(X0,X1),huffma675207370phabet(X0,X1)) )
      | ~ huffma1518433673istent(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f266,f325]) ).

tff(f325,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ? [X2: X0] :
          ( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,X2) )
          & member(X0,X2,huffma675207370phabet(X0,X1)) )
     => ( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,sK6(X0,X1)) )
        & member(X0,sK6(X0,X1),huffma675207370phabet(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f266,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ? [X2: X0] :
          ( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,X2) )
          & member(X0,X2,huffma675207370phabet(X0,X1)) )
      | ~ huffma1518433673istent(X0,X1) ),
    inference(ennf_transformation,[],[f178]) ).

tff(f178,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( huffma1518433673istent(X0,X1)
     => ? [X2: X0] :
          ( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,X2) )
          & member(X0,X2,huffma675207370phabet(X0,X1)) ) ),
    inference(rectify,[],[f38]) ).

tff(f38,axiom,
    ! [X2: $tType,X16: huffma1450048681e_tree(X2)] :
      ( huffma1518433673istent(X2,X16)
     => ? [X47: X2] :
          ( ( huffma945805758height(X2,X16) = huffma410068972_depth(X2,X16,X47) )
          & member(X2,X47,huffma675207370phabet(X2,X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_exists__at__height) ).

tff(f1205,plain,
    spl18_92,
    inference(avatar_split_clause,[],[f420,f1203]) ).

tff(f420,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( X1 = X2 )
      | ~ ord_less_eq(X0,X1,X2)
      | ~ ord_less_eq(X0,X2,X1)
      | ~ order(X0) ),
    inference(cnf_transformation,[],[f248]) ).

tff(f248,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ( X1 = X2 )
          | ~ ord_less_eq(X0,X1,X2)
          | ~ ord_less_eq(X0,X2,X1) )
      | ~ order(X0) ),
    inference(flattening,[],[f247]) ).

tff(f247,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ( X1 = X2 )
          | ~ ord_less_eq(X0,X1,X2)
          | ~ ord_less_eq(X0,X2,X1) )
      | ~ order(X0) ),
    inference(ennf_transformation,[],[f157]) ).

tff(f157,plain,
    ! [X0: $tType] :
      ( order(X0)
     => ! [X1: X0,X2: X0] :
          ( ord_less_eq(X0,X2,X1)
         => ( ord_less_eq(X0,X1,X2)
           => ( X1 = X2 ) ) ) ),
    inference(rectify,[],[f96]) ).

tff(f96,axiom,
    ! [X0: $tType] :
      ( order(X0)
     => ! [X41: X0,X42: X0] :
          ( ord_less_eq(X0,X42,X41)
         => ( ord_less_eq(X0,X41,X42)
           => ( X41 = X42 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_order__antisym) ).

tff(f1201,plain,
    ( spl18_91
    | spl18_1
    | ~ spl18_81 ),
    inference(avatar_split_clause,[],[f1109,f1016,f580,f1199]) ).

tff(f1199,plain,
    ( spl18_91
  <=> ! [X0: bool,X1: bool] :
        ( ~ pp(X0)
        | ( X0 = X1 )
        | ( fFalse = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_91])]) ).

tff(f1109,plain,
    ( ! [X0: bool,X1: bool] :
        ( ~ pp(X0)
        | ( X0 = X1 )
        | ( fFalse = X1 ) )
    | spl18_1
    | ~ spl18_81 ),
    inference(superposition,[],[f582,f1017]) ).

tff(f1054,plain,
    spl18_90,
    inference(avatar_split_clause,[],[f569,f1052]) ).

tff(f569,plain,
    ! [X0: $tType,X3: X0,X1: nat] : ( aa(X0,nat,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X3)),X3) = X1 ),
    inference(equality_resolution,[],[f522]) ).

tff(f522,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: nat] :
      ( ( aa(X0,nat,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3) = X1 )
      | ( X2 != X3 ) ),
    inference(cnf_transformation,[],[f295]) ).

tff(f1050,plain,
    spl18_89,
    inference(avatar_split_clause,[],[f508,f1048]) ).

tff(f1048,plain,
    ( spl18_89
  <=> ! [X0: $tType,X2: huffma1450048681e_tree(X0),X1: X0] :
        ( ( huffma1401021291ibling(X0,X2,X1) = X1 )
        | ( zero_zero(nat) != huffma945805758height(X0,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_89])]) ).

tff(f508,plain,
    ! [X0: $tType,X2: huffma1450048681e_tree(X0),X1: X0] :
      ( ( huffma1401021291ibling(X0,X2,X1) = X1 )
      | ( zero_zero(nat) != huffma945805758height(X0,X2) ) ),
    inference(cnf_transformation,[],[f288]) ).

tff(f288,plain,
    ! [X0: $tType,X1: X0,X2: huffma1450048681e_tree(X0)] :
      ( ( huffma1401021291ibling(X0,X2,X1) = X1 )
      | ( zero_zero(nat) != huffma945805758height(X0,X2) ) ),
    inference(ennf_transformation,[],[f214]) ).

tff(f214,plain,
    ! [X0: $tType,X1: X0,X2: huffma1450048681e_tree(X0)] :
      ( ( zero_zero(nat) = huffma945805758height(X0,X2) )
     => ( huffma1401021291ibling(X0,X2,X1) = X1 ) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X0: $tType,X17: X0,X18: huffma1450048681e_tree(X0)] :
      ( ( huffma945805758height(X0,X18) = zero_zero(nat) )
     => ( huffma1401021291ibling(X0,X18,X17) = X17 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_height__0__imp__sibling__id) ).

tff(f1046,plain,
    spl18_88,
    inference(avatar_split_clause,[],[f506,f1044]) ).

tff(f506,plain,
    ! [X0: $tType,X2: X0,X1: huffma1450048681e_tree(X0)] :
      ( ( huffma1401021291ibling(X0,X1,X2) = X2 )
      | member(X0,X2,huffma675207370phabet(X0,X1)) ),
    inference(cnf_transformation,[],[f286]) ).

tff(f286,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: X0] :
      ( ( huffma1401021291ibling(X0,X1,X2) = X2 )
      | member(X0,X2,huffma675207370phabet(X0,X1)) ),
    inference(ennf_transformation,[],[f212]) ).

tff(f212,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: X0] :
      ( ~ member(X0,X2,huffma675207370phabet(X0,X1))
     => ( huffma1401021291ibling(X0,X1,X2) = X2 ) ),
    inference(rectify,[],[f4]) ).

tff(f4,axiom,
    ! [X2: $tType,X16: huffma1450048681e_tree(X2),X14: X2] :
      ( ~ member(X2,X14,huffma675207370phabet(X2,X16))
     => ( huffma1401021291ibling(X2,X16,X14) = X14 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_notin__alphabet__imp__sibling__id) ).

tff(f1042,plain,
    spl18_87,
    inference(avatar_split_clause,[],[f505,f1040]) ).

tff(f505,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ord_less_eq(nat,X2,X0)
      | ~ ord_less_eq(nat,X1,X0)
      | ~ ord_less_eq(nat,X2,X1) ),
    inference(cnf_transformation,[],[f285]) ).

tff(f285,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ord_less_eq(nat,X2,X0)
      | ~ ord_less_eq(nat,X1,X0)
      | ~ ord_less_eq(nat,X2,X1) ),
    inference(flattening,[],[f284]) ).

tff(f284,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ord_less_eq(nat,X2,X0)
      | ~ ord_less_eq(nat,X1,X0)
      | ~ ord_less_eq(nat,X2,X1) ),
    inference(ennf_transformation,[],[f211]) ).

tff(f211,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ord_less_eq(nat,X2,X1)
     => ( ord_less_eq(nat,X1,X0)
       => ord_less_eq(nat,X2,X0) ) ),
    inference(rectify,[],[f68]) ).

tff(f68,axiom,
    ! [X52: nat,X53: nat,X54: nat] :
      ( ord_less_eq(nat,X54,X53)
     => ( ord_less_eq(nat,X53,X52)
       => ord_less_eq(nat,X54,X52) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_le__trans) ).

tff(f1038,plain,
    spl18_86,
    inference(avatar_split_clause,[],[f492,f1036]) ).

tff(f492,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less_eq(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
      | ~ ord_less_eq(nat,X1,X0) ),
    inference(cnf_transformation,[],[f347]) ).

tff(f347,plain,
    ! [X0: nat,X1: nat] :
      ( ( ord_less_eq(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
        | ~ ord_less_eq(nat,X1,X0) )
      & ( ord_less_eq(nat,X1,X0)
        | ~ ord_less_eq(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ) ),
    inference(nnf_transformation,[],[f200]) ).

tff(f200,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less_eq(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
    <=> ord_less_eq(nat,X1,X0) ),
    inference(rectify,[],[f90]) ).

tff(f90,axiom,
    ! [X19: nat,X39: nat] :
      ( ord_less_eq(int,semiring_1_of_nat(int,X39),semiring_1_of_nat(int,X19))
    <=> ord_less_eq(nat,X39,X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_zle__int) ).

tff(f1034,plain,
    spl18_85,
    inference(avatar_split_clause,[],[f491,f1032]) ).

tff(f491,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less_eq(nat,X1,X0)
      | ~ ord_less_eq(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ),
    inference(cnf_transformation,[],[f347]) ).

tff(f1030,plain,
    spl18_84,
    inference(avatar_split_clause,[],[f488,f1028]) ).

tff(f488,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
      | ~ ord_less(nat,X1,X0) ),
    inference(cnf_transformation,[],[f345]) ).

tff(f345,plain,
    ! [X0: nat,X1: nat] :
      ( ( ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
        | ~ ord_less(nat,X1,X0) )
      & ( ord_less(nat,X1,X0)
        | ~ ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ) ),
    inference(nnf_transformation,[],[f198]) ).

tff(f198,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
    <=> ord_less(nat,X1,X0) ),
    inference(rectify,[],[f52]) ).

tff(f52,axiom,
    ! [X19: nat,X39: nat] :
      ( ord_less(int,semiring_1_of_nat(int,X39),semiring_1_of_nat(int,X19))
    <=> ord_less(nat,X39,X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_zless__int) ).

tff(f1026,plain,
    spl18_83,
    inference(avatar_split_clause,[],[f487,f1024]) ).

tff(f487,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,X1,X0)
      | ~ ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ),
    inference(cnf_transformation,[],[f345]) ).

tff(f1022,plain,
    spl18_82,
    inference(avatar_split_clause,[],[f461,f1020]) ).

tff(f1020,plain,
    ( spl18_82
  <=> ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
        ( ( zero_zero(nat) = huffma1134658180e_cost(X0,X1) )
        | ( zero_zero(nat) != huffma945805758height(X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_82])]) ).

tff(f461,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ( zero_zero(nat) = huffma1134658180e_cost(X0,X1) )
      | ( zero_zero(nat) != huffma945805758height(X0,X1) ) ),
    inference(cnf_transformation,[],[f276]) ).

tff(f276,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ( zero_zero(nat) = huffma1134658180e_cost(X0,X1) )
      | ( zero_zero(nat) != huffma945805758height(X0,X1) ) ),
    inference(ennf_transformation,[],[f186]) ).

tff(f186,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ( zero_zero(nat) = huffma945805758height(X0,X1) )
     => ( zero_zero(nat) = huffma1134658180e_cost(X0,X1) ) ),
    inference(rectify,[],[f16]) ).

tff(f16,axiom,
    ! [X0: $tType,X18: huffma1450048681e_tree(X0)] :
      ( ( huffma945805758height(X0,X18) = zero_zero(nat) )
     => ( zero_zero(nat) = huffma1134658180e_cost(X0,X18) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_height__0__imp__cost__0) ).

tff(f1018,plain,
    ( spl18_81
    | ~ spl18_31 ),
    inference(avatar_split_clause,[],[f748,f725,f1016]) ).

tff(f748,plain,
    ( ! [X0: bool,X1: bool] :
        ( ( X0 = X1 )
        | ( fFalse = X1 )
        | ( fFalse = X0 ) )
    | ~ spl18_31 ),
    inference(superposition,[],[f726,f726]) ).

tff(f1014,plain,
    spl18_80,
    inference(avatar_split_clause,[],[f436,f1012]) ).

tff(f436,plain,
    ! [X0: nat] :
      ( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0))
      | ~ ord_less(nat,zero_zero(nat),X0) ),
    inference(cnf_transformation,[],[f313]) ).

tff(f313,plain,
    ! [X0: nat] :
      ( ( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0))
        | ~ ord_less(nat,zero_zero(nat),X0) )
      & ( ord_less(nat,zero_zero(nat),X0)
        | ~ ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) ) ),
    inference(nnf_transformation,[],[f167]) ).

tff(f167,plain,
    ! [X0: nat] :
      ( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0))
    <=> ord_less(nat,zero_zero(nat),X0) ),
    inference(rectify,[],[f49]) ).

tff(f49,axiom,
    ! [X19: nat] :
      ( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X19))
    <=> ord_less(nat,zero_zero(nat),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_zero__less__int__conv) ).

tff(f1010,plain,
    spl18_79,
    inference(avatar_split_clause,[],[f435,f1008]) ).

tff(f435,plain,
    ! [X0: nat] :
      ( ord_less(nat,zero_zero(nat),X0)
      | ~ ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) ),
    inference(cnf_transformation,[],[f313]) ).

tff(f1006,plain,
    spl18_78,
    inference(avatar_split_clause,[],[f405,f1004]) ).

tff(f405,plain,
    ! [X0: $tType,X2: nat,X1: nat] :
      ( ( X1 = X2 )
      | ( semiring_1_of_nat(X0,X1) != semiring_1_of_nat(X0,X2) )
      | ~ semiring_char_0(X0) ),
    inference(cnf_transformation,[],[f303]) ).

tff(f303,plain,
    ! [X0: $tType] :
      ( ! [X1: nat,X2: nat] :
          ( ( ( semiring_1_of_nat(X0,X1) = semiring_1_of_nat(X0,X2) )
            | ( X1 != X2 ) )
          & ( ( X1 = X2 )
            | ( semiring_1_of_nat(X0,X1) != semiring_1_of_nat(X0,X2) ) ) )
      | ~ semiring_char_0(X0) ),
    inference(nnf_transformation,[],[f236]) ).

tff(f236,plain,
    ! [X0: $tType] :
      ( ! [X1: nat,X2: nat] :
          ( ( semiring_1_of_nat(X0,X1) = semiring_1_of_nat(X0,X2) )
        <=> ( X1 = X2 ) )
      | ~ semiring_char_0(X0) ),
    inference(ennf_transformation,[],[f146]) ).

tff(f146,plain,
    ! [X0: $tType] :
      ( semiring_char_0(X0)
     => ! [X1: nat,X2: nat] :
          ( ( semiring_1_of_nat(X0,X1) = semiring_1_of_nat(X0,X2) )
        <=> ( X1 = X2 ) ) ),
    inference(rectify,[],[f41]) ).

tff(f41,axiom,
    ! [X2: $tType] :
      ( semiring_char_0(X2)
     => ! [X19: nat,X39: nat] :
          ( ( semiring_1_of_nat(X2,X19) = semiring_1_of_nat(X2,X39) )
        <=> ( X19 = X39 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_of__nat__eq__iff) ).

tff(f960,plain,
    spl18_77,
    inference(avatar_split_clause,[],[f528,f958]) ).

tff(f528,plain,
    ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X4: X0,X5: nat] : ( huffma1146269203erNode(X0,X3,X2,X1) != huffma2021818691e_Leaf(X0,X5,X4) ),
    inference(cnf_transformation,[],[f224]) ).

tff(f224,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat,X4: X0,X5: nat] : ( huffma1146269203erNode(X0,X3,X2,X1) != huffma2021818691e_Leaf(X0,X5,X4) ),
    inference(rectify,[],[f23]) ).

tff(f23,axiom,
    ! [X0: $tType,X34: huffma1450048681e_tree(X0),X35: huffma1450048681e_tree(X0),X36: nat,X17: X0,X33: nat] : ( huffma1146269203erNode(X0,X36,X35,X34) != huffma2021818691e_Leaf(X0,X33,X17) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_tree_Osimps_I3_J) ).

tff(f956,plain,
    spl18_76,
    inference(avatar_split_clause,[],[f476,f954]) ).

tff(f476,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,X0)
      | ( X0 = X1 )
      | ~ ord_less_eq(int,X1,X0) ),
    inference(cnf_transformation,[],[f338]) ).

tff(f338,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less(int,X1,X0)
        | ( X0 = X1 )
        | ~ ord_less_eq(int,X1,X0) )
      & ( ( ( X0 != X1 )
          & ord_less_eq(int,X1,X0) )
        | ~ ord_less(int,X1,X0) ) ),
    inference(flattening,[],[f337]) ).

tff(f337,plain,
    ! [X0: int,X1: int] :
      ( ( ord_less(int,X1,X0)
        | ( X0 = X1 )
        | ~ ord_less_eq(int,X1,X0) )
      & ( ( ( X0 != X1 )
          & ord_less_eq(int,X1,X0) )
        | ~ ord_less(int,X1,X0) ) ),
    inference(nnf_transformation,[],[f193]) ).

tff(f193,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,X0)
    <=> ( ( X0 != X1 )
        & ord_less_eq(int,X1,X0) ) ),
    inference(rectify,[],[f84]) ).

tff(f84,axiom,
    ! [X12: int,X64: int] :
      ( ord_less(int,X64,X12)
    <=> ( ( X12 != X64 )
        & ord_less_eq(int,X64,X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_less__int__def) ).

tff(f952,plain,
    spl18_75,
    inference(avatar_split_clause,[],[f460,f950]) ).

tff(f460,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ ord_less_eq(nat,X0,X1)
      | ~ ord_less_eq(nat,X1,X0) ),
    inference(cnf_transformation,[],[f275]) ).

tff(f275,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ ord_less_eq(nat,X0,X1)
      | ~ ord_less_eq(nat,X1,X0) ),
    inference(flattening,[],[f274]) ).

tff(f274,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ ord_less_eq(nat,X0,X1)
      | ~ ord_less_eq(nat,X1,X0) ),
    inference(ennf_transformation,[],[f185]) ).

tff(f185,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less_eq(nat,X1,X0)
     => ( ord_less_eq(nat,X0,X1)
       => ( X0 = X1 ) ) ),
    inference(rectify,[],[f67]) ).

tff(f67,axiom,
    ! [X20: nat,X22: nat] :
      ( ord_less_eq(nat,X22,X20)
     => ( ord_less_eq(nat,X20,X22)
       => ( X20 = X22 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_le__antisym) ).

tff(f948,plain,
    spl18_74,
    inference(avatar_split_clause,[],[f459,f946]) ).

tff(f459,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,X1,X0)
      | ( X0 = X1 )
      | ~ ord_less_eq(nat,X1,X0) ),
    inference(cnf_transformation,[],[f273]) ).

tff(f273,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,X1,X0)
      | ( X0 = X1 )
      | ~ ord_less_eq(nat,X1,X0) ),
    inference(flattening,[],[f272]) ).

tff(f272,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,X1,X0)
      | ( X0 = X1 )
      | ~ ord_less_eq(nat,X1,X0) ),
    inference(ennf_transformation,[],[f184]) ).

tff(f184,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less_eq(nat,X1,X0)
     => ( ( X0 != X1 )
       => ord_less(nat,X1,X0) ) ),
    inference(rectify,[],[f65]) ).

tff(f65,axiom,
    ! [X20: nat,X22: nat] :
      ( ord_less_eq(nat,X22,X20)
     => ( ( X20 != X22 )
       => ord_less(nat,X22,X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_le__neq__implies__less) ).

tff(f944,plain,
    spl18_73,
    inference(avatar_split_clause,[],[f452,f942]) ).

tff(f452,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( member(X0,sK6(X0,X1),huffma675207370phabet(X0,X1))
      | ~ huffma1518433673istent(X0,X1) ),
    inference(cnf_transformation,[],[f326]) ).

tff(f940,plain,
    spl18_72,
    inference(avatar_split_clause,[],[f450,f938]) ).

tff(f450,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,X0,X1)
      | ord_less(nat,X1,X0)
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f264]) ).

tff(f264,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,X0,X1)
      | ord_less(nat,X1,X0)
      | ( X0 = X1 ) ),
    inference(flattening,[],[f263]) ).

tff(f263,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,X0,X1)
      | ord_less(nat,X1,X0)
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f176]) ).

tff(f176,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 != X1 )
     => ( ~ ord_less(nat,X1,X0)
       => ord_less(nat,X0,X1) ) ),
    inference(rectify,[],[f30]) ).

tff(f30,axiom,
    ! [X41: nat,X42: nat] :
      ( ( X41 != X42 )
     => ( ~ ord_less(nat,X42,X41)
       => ord_less(nat,X41,X42) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_linorder__neqE__nat) ).

tff(f936,plain,
    spl18_71,
    inference(avatar_split_clause,[],[f437,f934]) ).

tff(f437,plain,
    ! [X0: nat] :
      ( ( zero_zero(nat) = X0 )
      | ~ ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int)) ),
    inference(cnf_transformation,[],[f314]) ).

tff(f314,plain,
    ! [X0: nat] :
      ( ( ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int))
        | ( zero_zero(nat) != X0 ) )
      & ( ( zero_zero(nat) = X0 )
        | ~ ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int)) ) ),
    inference(nnf_transformation,[],[f168]) ).

tff(f168,plain,
    ! [X0: nat] :
      ( ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int))
    <=> ( zero_zero(nat) = X0 ) ),
    inference(rectify,[],[f92]) ).

tff(f92,axiom,
    ! [X19: nat] :
      ( ord_less_eq(int,semiring_1_of_nat(int,X19),zero_zero(int))
    <=> ( zero_zero(nat) = X19 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_int__le__0__conv) ).

tff(f932,plain,
    spl18_70,
    inference(avatar_split_clause,[],[f428,f930]) ).

tff(f428,plain,
    ! [X0: int] :
      ( ( semiring_1_of_nat(int,sK1(X0)) = X0 )
      | ~ ord_less(int,zero_zero(int),X0) ),
    inference(cnf_transformation,[],[f309]) ).

tff(f309,plain,
    ! [X0: int] :
      ( ( ( semiring_1_of_nat(int,sK1(X0)) = X0 )
        & ord_less(nat,zero_zero(nat),sK1(X0)) )
      | ~ ord_less(int,zero_zero(int),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f257,f308]) ).

tff(f308,plain,
    ! [X0: int] :
      ( ? [X1: nat] :
          ( ( semiring_1_of_nat(int,X1) = X0 )
          & ord_less(nat,zero_zero(nat),X1) )
     => ( ( semiring_1_of_nat(int,sK1(X0)) = X0 )
        & ord_less(nat,zero_zero(nat),sK1(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f257,plain,
    ! [X0: int] :
      ( ? [X1: nat] :
          ( ( semiring_1_of_nat(int,X1) = X0 )
          & ord_less(nat,zero_zero(nat),X1) )
      | ~ ord_less(int,zero_zero(int),X0) ),
    inference(ennf_transformation,[],[f163]) ).

tff(f163,plain,
    ! [X0: int] :
      ( ord_less(int,zero_zero(int),X0)
     => ? [X1: nat] :
          ( ( semiring_1_of_nat(int,X1) = X0 )
          & ord_less(nat,zero_zero(nat),X1) ) ),
    inference(rectify,[],[f53]) ).

tff(f53,axiom,
    ! [X52: int] :
      ( ord_less(int,zero_zero(int),X52)
     => ? [X48: nat] :
          ( ( semiring_1_of_nat(int,X48) = X52 )
          & ord_less(nat,zero_zero(nat),X48) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_zero__less__imp__eq__int) ).

tff(f928,plain,
    ( spl18_69
    | ~ spl18_61 ),
    inference(avatar_split_clause,[],[f911,f880,f926]) ).

tff(f911,plain,
    ( ! [X0: $tType,X1: X0] :
        ( ord_less_eq(X0,X1,X1)
        | ~ linorder(X0) )
    | ~ spl18_61 ),
    inference(factoring,[],[f881]) ).

tff(f924,plain,
    spl18_68,
    inference(avatar_split_clause,[],[f427,f922]) ).

tff(f427,plain,
    ! [X0: int] :
      ( ord_less(nat,zero_zero(nat),sK1(X0))
      | ~ ord_less(int,zero_zero(int),X0) ),
    inference(cnf_transformation,[],[f309]) ).

tff(f908,plain,
    spl18_67,
    inference(avatar_split_clause,[],[f521,f906]) ).

tff(f906,plain,
    ( spl18_67
  <=> ! [X0: $tType,X3: nat,X2: X0,X1: X0] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_67])]) ).

tff(f521,plain,
    ! [X0: $tType,X2: X0,X3: nat,X1: X0] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) ),
    inference(cnf_transformation,[],[f220]) ).

tff(f220,plain,
    ! [X0: $tType,X1: X0,X2: X0,X3: nat] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) ),
    inference(rectify,[],[f34]) ).

tff(f34,axiom,
    ! [X0: $tType,X17: X0,X31: X0,X30: nat] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X30,X31),X17) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_depth_Osimps_I1_J) ).

tff(f904,plain,
    spl18_66,
    inference(avatar_split_clause,[],[f519,f902]) ).

tff(f519,plain,
    ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
      ( member(X0,X2,X1)
      | ~ pp(aa(X0,bool,X1,X2)) ),
    inference(cnf_transformation,[],[f355]) ).

tff(f355,plain,
    ! [X0: $tType,X1: fun(X0,bool),X2: X0] :
      ( ( member(X0,X2,X1)
        | ~ pp(aa(X0,bool,X1,X2)) )
      & ( pp(aa(X0,bool,X1,X2))
        | ~ member(X0,X2,X1) ) ),
    inference(nnf_transformation,[],[f218]) ).

tff(f218,plain,
    ! [X0: $tType,X1: fun(X0,bool),X2: X0] :
      ( member(X0,X2,X1)
    <=> pp(aa(X0,bool,X1,X2)) ),
    inference(rectify,[],[f76]) ).

tff(f76,axiom,
    ! [X2: $tType,X57: fun(X2,bool),X37: X2] :
      ( member(X2,X37,X57)
    <=> pp(aa(X2,bool,X57,X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).

tff(f898,plain,
    spl18_65,
    inference(avatar_split_clause,[],[f518,f896]) ).

tff(f518,plain,
    ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
      ( pp(aa(X0,bool,X1,X2))
      | ~ member(X0,X2,X1) ),
    inference(cnf_transformation,[],[f355]) ).

tff(f894,plain,
    spl18_64,
    inference(avatar_split_clause,[],[f502,f892]) ).

tff(f892,plain,
    ( spl18_64
  <=> ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_64])]) ).

tff(f502,plain,
    ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X2,X1)) ),
    inference(cnf_transformation,[],[f209]) ).

tff(f209,plain,
    ! [X0: $tType,X1: X0,X2: nat] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X2,X1)) ),
    inference(rectify,[],[f33]) ).

tff(f33,axiom,
    ! [X0: $tType,X17: X0,X33: nat] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X33,X17)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_tree_Osize_I3_J) ).

tff(f890,plain,
    spl18_63,
    inference(avatar_split_clause,[],[f483,f888]) ).

tff(f483,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) ) ),
    inference(cnf_transformation,[],[f343]) ).

tff(f343,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) ) ) ),
    inference(nnf_transformation,[],[f196]) ).

tff(f196,plain,
    ! [X0: nat,X1: nat] :
      ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
    <=> ( X0 = X1 ) ),
    inference(rectify,[],[f61]) ).

tff(f61,axiom,
    ! [X19: nat,X39: nat] :
      ( ( semiring_1_of_nat(int,X19) = semiring_1_of_nat(int,X39) )
    <=> ( X19 = X39 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_int__int__eq) ).

tff(f886,plain,
    spl18_62,
    inference(avatar_split_clause,[],[f433,f884]) ).

tff(f433,plain,
    ! [X0: nat] :
      ( ( zero_zero(nat) = X0 )
      | ( zero_zero(int) != semiring_1_of_nat(int,X0) ) ),
    inference(cnf_transformation,[],[f312]) ).

tff(f312,plain,
    ! [X0: nat] :
      ( ( ( zero_zero(int) = semiring_1_of_nat(int,X0) )
        | ( zero_zero(nat) != X0 ) )
      & ( ( zero_zero(nat) = X0 )
        | ( zero_zero(int) != semiring_1_of_nat(int,X0) ) ) ),
    inference(nnf_transformation,[],[f166]) ).

tff(f166,plain,
    ! [X0: nat] :
      ( ( zero_zero(int) = semiring_1_of_nat(int,X0) )
    <=> ( zero_zero(nat) = X0 ) ),
    inference(rectify,[],[f77]) ).

tff(f77,axiom,
    ! [X19: nat] :
      ( ( zero_zero(int) = semiring_1_of_nat(int,X19) )
    <=> ( zero_zero(nat) = X19 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_int__eq__0__conv) ).

tff(f882,plain,
    spl18_61,
    inference(avatar_split_clause,[],[f418,f880]) ).

tff(f418,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ord_less_eq(X0,X1,X2)
      | ord_less_eq(X0,X2,X1)
      | ~ linorder(X0) ),
    inference(cnf_transformation,[],[f245]) ).

tff(f245,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ord_less_eq(X0,X1,X2)
          | ord_less_eq(X0,X2,X1) )
      | ~ linorder(X0) ),
    inference(ennf_transformation,[],[f155]) ).

tff(f155,plain,
    ! [X0: $tType] :
      ( linorder(X0)
     => ! [X1: X0,X2: X0] :
          ( ~ ord_less_eq(X0,X2,X1)
         => ord_less_eq(X0,X1,X2) ) ),
    inference(rectify,[],[f93]) ).

tff(f93,axiom,
    ! [X0: $tType] :
      ( linorder(X0)
     => ! [X41: X0,X42: X0] :
          ( ~ ord_less_eq(X0,X42,X41)
         => ord_less_eq(X0,X41,X42) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_linorder__le__cases) ).

tff(f870,plain,
    ( spl18_60
    | ~ spl18_7
    | ~ spl18_51 ),
    inference(avatar_split_clause,[],[f856,f819,f610,f867]) ).

tff(f610,plain,
    ( spl18_7
  <=> semiring_1(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_7])]) ).

tff(f819,plain,
    ( spl18_51
  <=> ! [X0: $tType] :
        ( ( semiring_1_of_nat(X0,zero_zero(nat)) = zero_zero(X0) )
        | ~ semiring_1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_51])]) ).

tff(f856,plain,
    ( ( zero_zero(nat) = semiring_1_of_nat(nat,zero_zero(nat)) )
    | ~ spl18_7
    | ~ spl18_51 ),
    inference(resolution,[],[f820,f612]) ).

tff(f612,plain,
    ( semiring_1(nat)
    | ~ spl18_7 ),
    inference(avatar_component_clause,[],[f610]) ).

tff(f820,plain,
    ( ! [X0: $tType] :
        ( ~ semiring_1(X0)
        | ( semiring_1_of_nat(X0,zero_zero(nat)) = zero_zero(X0) ) )
    | ~ spl18_51 ),
    inference(avatar_component_clause,[],[f819]) ).

tff(f854,plain,
    spl18_59,
    inference(avatar_split_clause,[],[f520,f852]) ).

tff(f520,plain,
    ! [X0: $tType,X2: X0,X3: nat,X1: X0] : ( huffma1401021291ibling(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) = X1 ),
    inference(cnf_transformation,[],[f219]) ).

tff(f219,plain,
    ! [X0: $tType,X1: X0,X2: X0,X3: nat] : ( huffma1401021291ibling(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) = X1 ),
    inference(rectify,[],[f24]) ).

tff(f24,axiom,
    ! [X0: $tType,X17: X0,X31: X0,X29: nat] : ( huffma1401021291ibling(X0,huffma2021818691e_Leaf(X0,X29,X31),X17) = X17 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_sibling_Osimps_I1_J) ).

tff(f850,plain,
    spl18_58,
    inference(avatar_split_clause,[],[f501,f848]) ).

tff(f501,plain,
    ! [X0: $tType,X2: huffma1450048681e_tree(X0),X1: X0] : ord_less_eq(nat,huffma410068972_depth(X0,X2,X1),huffma945805758height(X0,X2)),
    inference(cnf_transformation,[],[f208]) ).

tff(f208,plain,
    ! [X0: $tType,X1: X0,X2: huffma1450048681e_tree(X0)] : ord_less_eq(nat,huffma410068972_depth(X0,X2,X1),huffma945805758height(X0,X2)),
    inference(rectify,[],[f74]) ).

tff(f74,axiom,
    ! [X0: $tType,X17: X0,X18: huffma1450048681e_tree(X0)] : ord_less_eq(nat,huffma410068972_depth(X0,X18,X17),huffma945805758height(X0,X18)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_depth__le__height) ).

tff(f846,plain,
    spl18_57,
    inference(avatar_split_clause,[],[f500,f844]) ).

tff(f500,plain,
    ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
    inference(cnf_transformation,[],[f207]) ).

tff(f207,plain,
    ! [X0: $tType,X1: X0,X2: nat] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
    inference(rectify,[],[f19]) ).

tff(f19,axiom,
    ! [X0: $tType,X17: X0,X30: nat] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X30,X17)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_height_Osimps_I1_J) ).

tff(f842,plain,
    spl18_56,
    inference(avatar_split_clause,[],[f499,f840]) ).

tff(f499,plain,
    ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma1134658180e_cost(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
    inference(cnf_transformation,[],[f206]) ).

tff(f206,plain,
    ! [X0: $tType,X1: X0,X2: nat] : ( zero_zero(nat) = huffma1134658180e_cost(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
    inference(rectify,[],[f20]) ).

tff(f20,axiom,
    ! [X0: $tType,X17: X0,X30: nat] : ( zero_zero(nat) = huffma1134658180e_cost(X0,huffma2021818691e_Leaf(X0,X30,X17)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_cost_Osimps_I1_J) ).

tff(f838,plain,
    spl18_55,
    inference(avatar_split_clause,[],[f431,f836]) ).

tff(f431,plain,
    ! [X0: nat] :
      ( ( zero_zero(nat) = X0 )
      | ~ ord_less_eq(nat,X0,zero_zero(nat)) ),
    inference(cnf_transformation,[],[f311]) ).

tff(f311,plain,
    ! [X0: nat] :
      ( ( ord_less_eq(nat,X0,zero_zero(nat))
        | ( zero_zero(nat) != X0 ) )
      & ( ( zero_zero(nat) = X0 )
        | ~ ord_less_eq(nat,X0,zero_zero(nat)) ) ),
    inference(nnf_transformation,[],[f165]) ).

tff(f165,plain,
    ! [X0: nat] :
      ( ord_less_eq(nat,X0,zero_zero(nat))
    <=> ( zero_zero(nat) = X0 ) ),
    inference(rectify,[],[f54]) ).

tff(f54,axiom,
    ! [X19: nat] :
      ( ord_less_eq(nat,X19,zero_zero(nat))
    <=> ( zero_zero(nat) = X19 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_le__0__eq) ).

tff(f834,plain,
    spl18_54,
    inference(avatar_split_clause,[],[f426,f832]) ).

tff(f426,plain,
    ! [X0: nat] :
      ( ord_less(nat,zero_zero(nat),X0)
      | ( zero_zero(nat) = X0 ) ),
    inference(cnf_transformation,[],[f256]) ).

tff(f256,plain,
    ! [X0: nat] :
      ( ord_less(nat,zero_zero(nat),X0)
      | ( zero_zero(nat) = X0 ) ),
    inference(ennf_transformation,[],[f162]) ).

tff(f162,plain,
    ! [X0: nat] :
      ( ( zero_zero(nat) != X0 )
     => ord_less(nat,zero_zero(nat),X0) ),
    inference(rectify,[],[f12]) ).

tff(f12,axiom,
    ! [X20: nat] :
      ( ( zero_zero(nat) != X20 )
     => ord_less(nat,zero_zero(nat),X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_gr0I) ).

tff(f829,plain,
    spl18_53,
    inference(avatar_split_clause,[],[f408,f827]) ).

tff(f408,plain,
    ! [X0: $tType,X1: nat] :
      ( ord_less_eq(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
      | ~ linordered_semidom(X0) ),
    inference(cnf_transformation,[],[f238]) ).

tff(f238,plain,
    ! [X0: $tType] :
      ( ! [X1: nat] : ord_less_eq(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
      | ~ linordered_semidom(X0) ),
    inference(ennf_transformation,[],[f148]) ).

tff(f148,plain,
    ! [X0: $tType] :
      ( linordered_semidom(X0)
     => ! [X1: nat] : ord_less_eq(X0,zero_zero(X0),semiring_1_of_nat(X0,X1)) ),
    inference(rectify,[],[f73]) ).

tff(f73,axiom,
    ! [X0: $tType] :
      ( linordered_semidom(X0)
     => ! [X22: nat] : ord_less_eq(X0,zero_zero(X0),semiring_1_of_nat(X0,X22)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_zero__le__imp__of__nat) ).

tff(f825,plain,
    spl18_52,
    inference(avatar_split_clause,[],[f407,f823]) ).

tff(f407,plain,
    ! [X0: $tType,X1: nat] :
      ( ~ ord_less(X0,semiring_1_of_nat(X0,X1),zero_zero(X0))
      | ~ linordered_semidom(X0) ),
    inference(cnf_transformation,[],[f237]) ).

tff(f237,plain,
    ! [X0: $tType] :
      ( ! [X1: nat] : ~ ord_less(X0,semiring_1_of_nat(X0,X1),zero_zero(X0))
      | ~ linordered_semidom(X0) ),
    inference(ennf_transformation,[],[f147]) ).

tff(f147,plain,
    ! [X0: $tType] :
      ( linordered_semidom(X0)
     => ! [X1: nat] : ~ ord_less(X0,semiring_1_of_nat(X0,X1),zero_zero(X0)) ),
    inference(rectify,[],[f44]) ).

tff(f44,axiom,
    ! [X0: $tType] :
      ( linordered_semidom(X0)
     => ! [X22: nat] : ~ ord_less(X0,semiring_1_of_nat(X0,X22),zero_zero(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_of__nat__less__0__iff) ).

tff(f821,plain,
    spl18_51,
    inference(avatar_split_clause,[],[f402,f819]) ).

tff(f402,plain,
    ! [X0: $tType] :
      ( ( semiring_1_of_nat(X0,zero_zero(nat)) = zero_zero(X0) )
      | ~ semiring_1(X0) ),
    inference(cnf_transformation,[],[f234]) ).

tff(f234,plain,
    ! [X0: $tType] :
      ( ( semiring_1_of_nat(X0,zero_zero(nat)) = zero_zero(X0) )
      | ~ semiring_1(X0) ),
    inference(ennf_transformation,[],[f42]) ).

tff(f42,axiom,
    ! [X0: $tType] :
      ( semiring_1(X0)
     => ( semiring_1_of_nat(X0,zero_zero(nat)) = zero_zero(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_of__nat__0) ).

tff(f814,plain,
    spl18_50,
    inference(avatar_split_clause,[],[f510,f812]) ).

tff(f812,plain,
    ( spl18_50
  <=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
        ( ord_less(nat,X0,X1)
        | ~ sP0(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_50])]) ).

tff(f510,plain,
    ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
      ( ord_less(nat,X0,X1)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f352]) ).

tff(f810,plain,
    spl18_49,
    inference(avatar_split_clause,[],[f495,f808]) ).

tff(f495,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] : member(X0,sK14(X0,X1),huffma675207370phabet(X0,X1)),
    inference(cnf_transformation,[],[f350]) ).

tff(f350,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] : member(X0,sK14(X0,X1),huffma675207370phabet(X0,X1)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f202,f349]) ).

tff(f349,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ? [X2: X0] : member(X0,X2,huffma675207370phabet(X0,X1))
     => member(X0,sK14(X0,X1),huffma675207370phabet(X0,X1)) ),
    introduced(choice_axiom,[]) ).

tff(f202,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
    ? [X2: X0] : member(X0,X2,huffma675207370phabet(X0,X1)),
    inference(rectify,[],[f14]) ).

tff(f14,axiom,
    ! [X2: $tType,X16: huffma1450048681e_tree(X2)] :
    ? [X26: X2] : member(X2,X26,huffma675207370phabet(X2,X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_exists__in__alphabet) ).

tff(f806,plain,
    ( spl18_47
    | ~ spl18_48
    | ~ spl18_31 ),
    inference(avatar_split_clause,[],[f750,f725,f803,f800]) ).

tff(f800,plain,
    ( spl18_47
  <=> ! [X0: bool] : ( fFalse = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_47])]) ).

tff(f750,plain,
    ( ! [X0: bool] :
        ( ( fTrue != fFalse )
        | ( fFalse = X0 ) )
    | ~ spl18_31 ),
    inference(equality_factoring,[],[f726]) ).

tff(f798,plain,
    spl18_46,
    inference(avatar_split_clause,[],[f474,f796]) ).

tff(f474,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,X1,X0)
      | ~ ord_less(int,X1,X0) ),
    inference(cnf_transformation,[],[f338]) ).

tff(f794,plain,
    spl18_45,
    inference(avatar_split_clause,[],[f457,f792]) ).

tff(f457,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less_eq(nat,X1,X0)
      | ~ ord_less(nat,X1,X0) ),
    inference(cnf_transformation,[],[f270]) ).

tff(f270,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less_eq(nat,X1,X0)
      | ~ ord_less(nat,X1,X0) ),
    inference(ennf_transformation,[],[f182]) ).

tff(f182,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,X1,X0)
     => ord_less_eq(nat,X1,X0) ),
    inference(rectify,[],[f64]) ).

tff(f64,axiom,
    ! [X20: nat,X22: nat] :
      ( ord_less(nat,X22,X20)
     => ord_less_eq(nat,X22,X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_less__imp__le__nat) ).

tff(f790,plain,
    spl18_44,
    inference(avatar_split_clause,[],[f445,f788]) ).

tff(f445,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less_eq(nat,X0,X1)
      | ord_less_eq(nat,X1,X0) ),
    inference(cnf_transformation,[],[f171]) ).

tff(f171,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less_eq(nat,X0,X1)
      | ord_less_eq(nat,X1,X0) ),
    inference(rectify,[],[f70]) ).

tff(f70,axiom,
    ! [X20: nat,X22: nat] :
      ( ord_less_eq(nat,X20,X22)
      | ord_less_eq(nat,X22,X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_nat__le__linear) ).

tff(f781,plain,
    spl18_43,
    inference(avatar_split_clause,[],[f498,f779]) ).

tff(f498,plain,
    ! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fTrue,X2,X1) = X2 ),
    inference(cnf_transformation,[],[f205]) ).

tff(f205,plain,
    ! [X0: $tType,X1: X0,X2: X0] : ( if(X0,fTrue,X2,X1) = X2 ),
    inference(rectify,[],[f123]) ).

tff(f123,axiom,
    ! [X0: $tType,X41: X0,X42: X0] : ( if(X0,fTrue,X42,X41) = X42 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).

tff(f777,plain,
    spl18_42,
    inference(avatar_split_clause,[],[f497,f775]) ).

tff(f497,plain,
    ! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fFalse,X2,X1) = X1 ),
    inference(cnf_transformation,[],[f204]) ).

tff(f204,plain,
    ! [X0: $tType,X1: X0,X2: X0] : ( if(X0,fFalse,X2,X1) = X1 ),
    inference(rectify,[],[f124]) ).

tff(f124,axiom,
    ! [X0: $tType,X41: X0,X42: X0] : ( if(X0,fFalse,X42,X41) = X41 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).

tff(f772,plain,
    spl18_41,
    inference(avatar_split_clause,[],[f399,f770]) ).

tff(f399,plain,
    ! [X0: nat] : ord_less_eq(int,zero_zero(int),semiring_1_of_nat(int,X0)),
    inference(cnf_transformation,[],[f142]) ).

tff(f142,plain,
    ! [X0: nat] : ord_less_eq(int,zero_zero(int),semiring_1_of_nat(int,X0)),
    inference(rectify,[],[f89]) ).

tff(f89,axiom,
    ! [X20: nat] : ord_less_eq(int,zero_zero(int),semiring_1_of_nat(int,X20)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_zero__zle__int) ).

tff(f768,plain,
    spl18_40,
    inference(avatar_split_clause,[],[f398,f766]) ).

tff(f766,plain,
    ( spl18_40
  <=> ! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_40])]) ).

tff(f398,plain,
    ! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)),
    inference(cnf_transformation,[],[f141]) ).

tff(f141,plain,
    ! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)),
    inference(rectify,[],[f58]) ).

tff(f58,axiom,
    ! [X52: nat] : ~ ord_less(int,semiring_1_of_nat(int,X52),zero_zero(int)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_int__less__0__conv) ).

tff(f764,plain,
    spl18_39,
    inference(avatar_split_clause,[],[f388,f761]) ).

tff(f388,plain,
    zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)),
    inference(cnf_transformation,[],[f79]) ).

tff(f79,axiom,
    zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_transfer__int__nat__numerals_I1_J) ).

tff(f759,plain,
    spl18_38,
    inference(avatar_split_clause,[],[f364,f756]) ).

tff(f364,plain,
    ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_1)),
    inference(cnf_transformation,[],[f128]) ).

tff(f128,axiom,
    ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

tff(f754,plain,
    ( spl18_37
    | ~ spl18_22
    | ~ spl18_31 ),
    inference(avatar_split_clause,[],[f749,f725,f685,f752]) ).

tff(f749,plain,
    ( ! [X0: bool] :
        ( pp(X0)
        | ( fFalse = X0 ) )
    | ~ spl18_22
    | ~ spl18_31 ),
    inference(superposition,[],[f687,f726]) ).

tff(f747,plain,
    spl18_36,
    inference(avatar_split_clause,[],[f496,f745]) ).

tff(f496,plain,
    ! [X0: $tType,X2: nat,X1: X0] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1)),
    inference(cnf_transformation,[],[f203]) ).

tff(f203,plain,
    ! [X0: $tType,X1: X0,X2: nat] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1)),
    inference(rectify,[],[f18]) ).

tff(f18,axiom,
    ! [X0: $tType,X17: X0,X30: nat] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X30,X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_consistent_Osimps_I1_J) ).

tff(f743,plain,
    spl18_35,
    inference(avatar_split_clause,[],[f448,f741]) ).

tff(f741,plain,
    ( spl18_35
  <=> ! [X1: $tType,X0: $tType] :
        ( ord(fun(X0,X1))
        | ~ ord(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_35])]) ).

tff(f448,plain,
    ! [X1: $tType,X0: $tType] :
      ( ord(fun(X0,X1))
      | ~ ord(X1) ),
    inference(cnf_transformation,[],[f261]) ).

tff(f261,plain,
    ! [X0: $tType,X1: $tType] :
      ( ord(fun(X0,X1))
      | ~ ord(X1) ),
    inference(ennf_transformation,[],[f174]) ).

tff(f174,plain,
    ! [X0: $tType,X1: $tType] :
      ( ord(X1)
     => ord(fun(X0,X1)) ),
    inference(rectify,[],[f102]) ).

tff(f102,axiom,
    ! [X67: $tType,X68: $tType] :
      ( ord(X68)
     => ord(fun(X67,X68)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).

tff(f739,plain,
    spl18_34,
    inference(avatar_split_clause,[],[f447,f737]) ).

tff(f737,plain,
    ( spl18_34
  <=> ! [X1: $tType,X0: $tType] :
        ( order(fun(X0,X1))
        | ~ order(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_34])]) ).

tff(f447,plain,
    ! [X1: $tType,X0: $tType] :
      ( order(fun(X0,X1))
      | ~ order(X1) ),
    inference(cnf_transformation,[],[f260]) ).

tff(f260,plain,
    ! [X0: $tType,X1: $tType] :
      ( order(fun(X0,X1))
      | ~ order(X1) ),
    inference(ennf_transformation,[],[f173]) ).

tff(f173,plain,
    ! [X0: $tType,X1: $tType] :
      ( order(X1)
     => order(fun(X0,X1)) ),
    inference(rectify,[],[f101]) ).

tff(f101,axiom,
    ! [X67: $tType,X68: $tType] :
      ( order(X68)
     => order(fun(X67,X68)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).

tff(f735,plain,
    spl18_33,
    inference(avatar_split_clause,[],[f446,f733]) ).

tff(f733,plain,
    ( spl18_33
  <=> ! [X1: $tType,X0: $tType] :
        ( preorder(fun(X0,X1))
        | ~ preorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_33])]) ).

tff(f446,plain,
    ! [X1: $tType,X0: $tType] :
      ( preorder(fun(X0,X1))
      | ~ preorder(X1) ),
    inference(cnf_transformation,[],[f259]) ).

tff(f259,plain,
    ! [X0: $tType,X1: $tType] :
      ( preorder(fun(X0,X1))
      | ~ preorder(X1) ),
    inference(ennf_transformation,[],[f172]) ).

tff(f172,plain,
    ! [X0: $tType,X1: $tType] :
      ( preorder(X1)
     => preorder(fun(X0,X1)) ),
    inference(rectify,[],[f100]) ).

tff(f100,axiom,
    ! [X67: $tType,X68: $tType] :
      ( preorder(X68)
     => preorder(fun(X67,X68)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).

tff(f731,plain,
    spl18_32,
    inference(avatar_split_clause,[],[f419,f729]) ).

tff(f419,plain,
    ! [X0: $tType,X1: X0] :
      ( ord_less_eq(X0,X1,X1)
      | ~ preorder(X0) ),
    inference(cnf_transformation,[],[f246]) ).

tff(f246,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ord_less_eq(X0,X1,X1)
      | ~ preorder(X0) ),
    inference(ennf_transformation,[],[f156]) ).

tff(f156,plain,
    ! [X0: $tType] :
      ( preorder(X0)
     => ! [X1: X0] : ord_less_eq(X0,X1,X1) ),
    inference(rectify,[],[f82]) ).

tff(f82,axiom,
    ! [X0: $tType] :
      ( preorder(X0)
     => ! [X42: X0] : ord_less_eq(X0,X42,X42) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_order__refl) ).

tff(f727,plain,
    spl18_31,
    inference(avatar_split_clause,[],[f401,f725]) ).

tff(f401,plain,
    ! [X0: bool] :
      ( ( fFalse = X0 )
      | ( fTrue = X0 ) ),
    inference(cnf_transformation,[],[f144]) ).

tff(f144,plain,
    ! [X0: bool] :
      ( ( fFalse = X0 )
      | ( fTrue = X0 ) ),
    inference(rectify,[],[f125]) ).

tff(f125,axiom,
    ! [X69: bool] :
      ( ( fFalse = X69 )
      | ( fTrue = X69 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).

tff(f723,plain,
    spl18_30,
    inference(avatar_split_clause,[],[f387,f720]) ).

tff(f387,plain,
    ord_less_eq(int,zero_zero(int),zero_zero(int)),
    inference(cnf_transformation,[],[f85]) ).

tff(f85,axiom,
    ord_less_eq(int,zero_zero(int),zero_zero(int)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).

tff(f718,plain,
    spl18_29,
    inference(avatar_split_clause,[],[f363,f715]) ).

tff(f363,plain,
    member(a1,a,huffma675207370phabet(a1,t_1)),
    inference(cnf_transformation,[],[f129]) ).

tff(f129,axiom,
    member(a1,a,huffma675207370phabet(a1,t_1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

tff(f713,plain,
    spl18_28,
    inference(avatar_split_clause,[],[f396,f711]) ).

tff(f396,plain,
    ! [X0: nat] : ord_less_eq(nat,zero_zero(nat),X0),
    inference(cnf_transformation,[],[f139]) ).

tff(f139,plain,
    ! [X0: nat] : ord_less_eq(nat,zero_zero(nat),X0),
    inference(rectify,[],[f55]) ).

tff(f55,axiom,
    ! [X20: nat] : ord_less_eq(nat,zero_zero(nat),X20),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_less__eq__nat_Osimps_I1_J) ).

tff(f709,plain,
    spl18_27,
    inference(avatar_split_clause,[],[f393,f707]) ).

tff(f393,plain,
    ! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
    inference(cnf_transformation,[],[f136]) ).

tff(f136,plain,
    ! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
    inference(rectify,[],[f10]) ).

tff(f10,axiom,
    ! [X20: nat] : ~ ord_less(nat,X20,zero_zero(nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_not__less0) ).

tff(f705,plain,
    spl18_26,
    inference(avatar_split_clause,[],[f564,f703]) ).

tff(f703,plain,
    ( spl18_26
  <=> ! [X1: int] : ~ ord_less(int,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_26])]) ).

tff(f564,plain,
    ! [X1: int] : ~ ord_less(int,X1,X1),
    inference(equality_resolution,[],[f475]) ).

tff(f475,plain,
    ! [X0: int,X1: int] :
      ( ( X0 != X1 )
      | ~ ord_less(int,X1,X0) ),
    inference(cnf_transformation,[],[f338]) ).

tff(f701,plain,
    spl18_25,
    inference(avatar_split_clause,[],[f392,f699]) ).

tff(f392,plain,
    ! [X0: nat] : ord_less_eq(nat,X0,X0),
    inference(cnf_transformation,[],[f135]) ).

tff(f135,plain,
    ! [X0: nat] : ord_less_eq(nat,X0,X0),
    inference(rectify,[],[f71]) ).

tff(f71,axiom,
    ! [X20: nat] : ord_less_eq(nat,X20,X20),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_le__refl) ).

tff(f697,plain,
    spl18_24,
    inference(avatar_split_clause,[],[f390,f695]) ).

tff(f390,plain,
    ! [X0: nat] : ~ ord_less(nat,X0,X0),
    inference(cnf_transformation,[],[f133]) ).

tff(f133,plain,
    ! [X0: nat] : ~ ord_less(nat,X0,X0),
    inference(rectify,[],[f29]) ).

tff(f29,axiom,
    ! [X20: nat] : ~ ord_less(nat,X20,X20),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_less__irrefl__nat) ).

tff(f693,plain,
    ~ spl18_23,
    inference(avatar_split_clause,[],[f362,f690]) ).

tff(f362,plain,
    huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) != huffma1401021291ibling(a1,t_1,a),
    inference(cnf_transformation,[],[f132]) ).

tff(f132,plain,
    huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) != huffma1401021291ibling(a1,t_1,a),
    inference(flattening,[],[f131]) ).

tff(f131,negated_conjecture,
    ( ~ huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) = huffma1401021291ibling(a1,t_1,a) ),
    inference(negated_conjecture,[],[f130]) ).

tff(f130,conjecture,
    huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) = huffma1401021291ibling(a1,t_1,a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).

tff(f688,plain,
    spl18_22,
    inference(avatar_split_clause,[],[f386,f685]) ).

tff(f386,plain,
    pp(fTrue),
    inference(cnf_transformation,[],[f127]) ).

tff(f127,axiom,
    pp(fTrue),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).

tff(f683,plain,
    spl18_21,
    inference(avatar_split_clause,[],[f385,f680]) ).

tff(f385,plain,
    ord(nat),
    inference(cnf_transformation,[],[f117]) ).

tff(f117,axiom,
    ord(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).

tff(f678,plain,
    spl18_20,
    inference(avatar_split_clause,[],[f384,f675]) ).

tff(f384,plain,
    ord(int),
    inference(cnf_transformation,[],[f109]) ).

tff(f109,axiom,
    ord(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oord) ).

tff(f673,plain,
    spl18_19,
    inference(avatar_split_clause,[],[f383,f670]) ).

tff(f383,plain,
    ord(bool),
    inference(cnf_transformation,[],[f122]) ).

tff(f122,axiom,
    ord(bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).

tff(f668,plain,
    spl18_18,
    inference(avatar_split_clause,[],[f382,f665]) ).

tff(f665,plain,
    ( spl18_18
  <=> preorder(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_18])]) ).

tff(f382,plain,
    preorder(nat),
    inference(cnf_transformation,[],[f113]) ).

tff(f113,axiom,
    preorder(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).

tff(f663,plain,
    spl18_17,
    inference(avatar_split_clause,[],[f381,f660]) ).

tff(f660,plain,
    ( spl18_17
  <=> order(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_17])]) ).

tff(f381,plain,
    order(nat),
    inference(cnf_transformation,[],[f116]) ).

tff(f116,axiom,
    order(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).

tff(f658,plain,
    spl18_16,
    inference(avatar_split_clause,[],[f380,f655]) ).

tff(f380,plain,
    order(int),
    inference(cnf_transformation,[],[f108]) ).

tff(f108,axiom,
    order(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oorder) ).

tff(f653,plain,
    spl18_15,
    inference(avatar_split_clause,[],[f379,f650]) ).

tff(f379,plain,
    preorder(int),
    inference(cnf_transformation,[],[f105]) ).

tff(f105,axiom,
    preorder(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Opreorder) ).

tff(f648,plain,
    spl18_14,
    inference(avatar_split_clause,[],[f378,f645]) ).

tff(f645,plain,
    ( spl18_14
  <=> preorder(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_14])]) ).

tff(f378,plain,
    preorder(bool),
    inference(cnf_transformation,[],[f119]) ).

tff(f119,axiom,
    preorder(bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).

tff(f643,plain,
    spl18_13,
    inference(avatar_split_clause,[],[f377,f640]) ).

tff(f640,plain,
    ( spl18_13
  <=> order(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_13])]) ).

tff(f377,plain,
    order(bool),
    inference(cnf_transformation,[],[f121]) ).

tff(f121,axiom,
    order(bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).

tff(f638,plain,
    spl18_12,
    inference(avatar_split_clause,[],[f376,f635]) ).

tff(f635,plain,
    ( spl18_12
  <=> linorder(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_12])]) ).

tff(f376,plain,
    linorder(nat),
    inference(cnf_transformation,[],[f114]) ).

tff(f114,axiom,
    linorder(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).

tff(f633,plain,
    spl18_11,
    inference(avatar_split_clause,[],[f375,f630]) ).

tff(f375,plain,
    linorder(int),
    inference(cnf_transformation,[],[f106]) ).

tff(f106,axiom,
    linorder(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).

tff(f628,plain,
    spl18_10,
    inference(avatar_split_clause,[],[f374,f625]) ).

tff(f625,plain,
    ( spl18_10
  <=> linorder(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_10])]) ).

tff(f374,plain,
    linorder(bool),
    inference(cnf_transformation,[],[f120]) ).

tff(f120,axiom,
    linorder(bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).

tff(f623,plain,
    spl18_9,
    inference(avatar_split_clause,[],[f373,f620]) ).

tff(f373,plain,
    linordered_semidom(nat),
    inference(cnf_transformation,[],[f111]) ).

tff(f111,axiom,
    linordered_semidom(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).

tff(f618,plain,
    spl18_8,
    inference(avatar_split_clause,[],[f372,f615]) ).

tff(f615,plain,
    ( spl18_8
  <=> linordered_semidom(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_8])]) ).

tff(f372,plain,
    linordered_semidom(int),
    inference(cnf_transformation,[],[f103]) ).

tff(f103,axiom,
    linordered_semidom(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).

tff(f613,plain,
    spl18_7,
    inference(avatar_split_clause,[],[f371,f610]) ).

tff(f371,plain,
    semiring_1(nat),
    inference(cnf_transformation,[],[f115]) ).

tff(f115,axiom,
    semiring_1(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).

tff(f608,plain,
    spl18_6,
    inference(avatar_split_clause,[],[f370,f605]) ).

tff(f605,plain,
    ( spl18_6
  <=> zero(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_6])]) ).

tff(f370,plain,
    zero(nat),
    inference(cnf_transformation,[],[f118]) ).

tff(f118,axiom,
    zero(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).

tff(f603,plain,
    spl18_5,
    inference(avatar_split_clause,[],[f369,f600]) ).

tff(f369,plain,
    semiring_char_0(nat),
    inference(cnf_transformation,[],[f112]) ).

tff(f112,axiom,
    semiring_char_0(nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).

tff(f598,plain,
    spl18_4,
    inference(avatar_split_clause,[],[f368,f595]) ).

tff(f595,plain,
    ( spl18_4
  <=> semiring_char_0(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_4])]) ).

tff(f368,plain,
    semiring_char_0(int),
    inference(cnf_transformation,[],[f104]) ).

tff(f104,axiom,
    semiring_char_0(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).

tff(f593,plain,
    spl18_3,
    inference(avatar_split_clause,[],[f367,f590]) ).

tff(f590,plain,
    ( spl18_3
  <=> zero(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_3])]) ).

tff(f367,plain,
    zero(int),
    inference(cnf_transformation,[],[f110]) ).

tff(f110,axiom,
    zero(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).

tff(f588,plain,
    spl18_2,
    inference(avatar_split_clause,[],[f366,f585]) ).

tff(f585,plain,
    ( spl18_2
  <=> semiring_1(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_2])]) ).

tff(f366,plain,
    semiring_1(int),
    inference(cnf_transformation,[],[f107]) ).

tff(f107,axiom,
    semiring_1(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).

tff(f583,plain,
    ~ spl18_1,
    inference(avatar_split_clause,[],[f365,f580]) ).

tff(f365,plain,
    ~ pp(fFalse),
    inference(cnf_transformation,[],[f126]) ).

tff(f126,axiom,
    ~ pp(fFalse),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SWW541_5 : TPTP v8.2.0. Released v6.0.0.
% 0.04/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n028.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % 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   : Sat May 18 19:37:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (12974)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37  % (12977)WARNING: value z3 for option sas not known
% 0.21/0.38  % (12975)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38  % (12976)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38  % (12977)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)
% 0.21/0.38  % (12978)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38  % (12979)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)
% 0.21/0.38  % (12980)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)
% 0.21/0.38  % (12981)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)
% 0.21/0.38  % (12981)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.38  % Exception at run slice level
% 0.21/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.38  % Exception at run slice level
% 0.21/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.38  % Exception at run slice level
% 0.21/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.40  % (12982)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.40  % (12983)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)
% 0.21/0.40  % (12984)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)
% 0.21/0.40  % (12982)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.40  % (12983)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.40  % Exception at run slice level
% 0.21/0.40  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.42  % (12985)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)
% 36.29/5.52  % (12979)First to succeed.
% 36.52/5.55  % (12979)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-12974"
% 36.52/5.55  % (12979)Refutation found. Thanks to Tanya!
% 36.52/5.55  % SZS status Theorem for theBenchmark
% 36.52/5.55  % SZS output start Proof for theBenchmark
% See solution above
% 36.52/5.57  % (12979)------------------------------
% 36.52/5.57  % (12979)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 36.52/5.57  % (12979)Termination reason: Refutation
% 36.52/5.57  
% 36.52/5.57  % (12979)Memory used [KB]: 22216
% 36.52/5.57  % (12979)Time elapsed: 5.175 s
% 36.52/5.57  % (12979)Instructions burned: 21973 (million)
% 36.52/5.57  % (12974)Success in time 5.103 s
%------------------------------------------------------------------------------