TSTP Solution File: SWW542_5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWW542_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 : n007.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 07:27:20 EDT 2024

% Result   : Theorem 3.88s 0.93s
% Output   : Refutation 4.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :  584
% Syntax   : Number of formulae    : 1752 ( 243 unt;  61 typ;   0 def)
%            Number of atoms       : 5161 (1047 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives : 5743 (2273   ~;2714   |; 136   &)
%                                         ( 443 <=>; 177  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :   10 (   1 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :   64 (  43   >;  21   *;   0   +;   0  <<)
%            Number of predicates  :  420 ( 418 usr; 405 prp; 0-3 aty)
%            Number of functors    :   43 (  43 usr;   6 con; 0-5 aty)
%            Number of variables   : 4032 (3922   !;  69   ?;4032   :)
%                                         (  41  !>;   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: int > nat ).

tff(func_def_23,type,
    sK3: int > nat ).

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

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

tff(func_def_26,type,
    sK6: fun(int,bool) > int ).

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

tff(func_def_28,type,
    sK8: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

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

tff(func_def_30,type,
    sK10: ( nat * fun(nat,bool) ) > nat ).

tff(func_def_31,type,
    sK11: fun(nat,bool) > nat ).

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

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

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

tff(func_def_35,type,
    sK15: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).

tff(func_def_36,type,
    sK16: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).

tff(func_def_37,type,
    sK17: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).

tff(func_def_38,type,
    sK18: fun(nat,nat) > nat ).

tff(func_def_39,type,
    sK19: fun(nat,nat) > nat ).

tff(func_def_40,type,
    sK20: 
      !>[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,
    semiring_1: 
      !>[X0: $tType] : $o ).

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

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

tff(pred_def_6,type,
    semiring_char_0: 
      !>[X0: $tType] : $o ).

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

tff(pred_def_8,type,
    huffma1518433673istent: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > $o ) ).

tff(pred_def_9,type,
    huffma1393970616ptimum: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > $o ) ).

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

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

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

tff(pred_def_13,type,
    pp: bool > $o ).

tff(pred_def_14,type,
    sP0: ( nat * nat * fun(nat,fun(nat,bool)) ) > $o ).

tff(f8460,plain,
    $false,
    inference(avatar_sat_refutation,[],[f579,f584,f589,f594,f599,f604,f609,f614,f619,f624,f629,f634,f639,f644,f649,f654,f659,f664,f669,f673,f677,f681,f690,f695,f699,f703,f708,f712,f716,f720,f724,f728,f736,f740,f744,f748,f752,f756,f765,f769,f774,f778,f782,f788,f792,f800,f804,f808,f812,f816,f820,f824,f828,f852,f856,f860,f864,f869,f873,f877,f881,f897,f901,f905,f909,f913,f917,f921,f925,f929,f933,f937,f942,f1003,f1007,f1011,f1015,f1019,f1023,f1027,f1031,f1036,f1040,f1044,f1048,f1052,f1078,f1105,f1109,f1113,f1117,f1122,f1126,f1145,f1153,f1157,f1161,f1165,f1169,f1173,f1177,f1181,f1215,f1268,f1272,f1276,f1291,f1295,f1299,f1303,f1307,f1311,f1321,f1330,f1334,f1338,f1351,f1355,f1359,f1363,f1391,f1447,f1451,f1505,f1509,f1529,f1534,f1538,f1559,f1563,f1584,f1588,f1601,f1612,f1616,f1620,f1624,f1628,f1657,f1680,f1684,f1688,f1708,f1712,f1729,f1741,f1761,f1774,f1852,f1858,f2146,f2150,f2154,f2158,f2162,f2169,f2173,f2249,f2301,f2305,f2337,f2351,f2355,f2359,f2363,f2367,f2371,f2375,f2379,f2472,f2482,f2486,f2495,f2506,f2510,f2523,f2527,f2531,f2538,f2551,f2555,f2559,f2563,f2567,f2659,f2663,f2682,f2687,f2704,f2715,f2719,f2723,f2727,f2773,f2777,f2790,f2832,f2836,f2840,f2844,f2848,f2928,f2944,f2948,f2952,f2956,f2992,f3023,f3029,f3041,f3042,f3043,f3049,f3059,f3075,f3088,f3128,f3133,f3142,f3152,f3168,f3169,f3171,f3176,f3201,f3205,f3215,f3219,f3231,f3259,f3273,f3304,f3316,f3386,f3390,f3394,f3398,f3403,f3407,f3411,f3415,f3419,f3513,f3523,f3603,f3607,f3611,f3615,f3649,f3658,f3675,f3679,f3688,f3702,f3716,f3720,f3724,f3728,f3732,f3796,f3800,f3804,f3926,f3965,f3969,f3973,f3986,f3999,f4003,f4007,f4015,f4048,f4113,f4117,f4121,f4141,f4145,f4149,f4153,f4157,f4161,f4165,f4169,f4173,f4177,f4181,f4390,f4638,f4642,f4646,f4656,f4660,f4664,f4668,f4672,f4676,f4680,f4772,f4788,f4792,f4796,f4800,f4804,f4808,f4862,f4908,f4912,f4916,f4920,f4924,f4949,f5001,f5065,f5069,f5073,f5133,f5137,f5141,f5145,f5149,f5153,f5157,f5161,f5165,f5169,f5483,f5515,f5519,f5543,f5561,f5565,f5569,f5573,f5577,f5608,f5612,f5642,f5724,f5743,f5747,f5751,f5755,f5759,f5763,f5767,f5771,f5775,f5779,f5783,f5787,f5791,f5795,f5799,f6590,f6594,f6598,f6602,f6653,f6657,f6661,f6665,f6669,f6673,f6678,f6806,f6810,f6814,f6818,f6822,f6826,f6830,f6834,f7008,f7012,f7016,f7020,f7090,f7094,f7098,f7102,f7250,f7254,f7290,f7295,f7299,f7303,f7307,f7311,f7444,f7448,f7496,f7500,f7504,f7508,f7534,f7607,f7611,f7615,f7619,f7643,f7713,f7717,f7721,f7725,f7854,f7858,f7862,f7866,f7870,f7874,f8091,f8095,f8099,f8103,f8201,f8241,f8245,f8371,f8444,f8448,f8452,f8458]) ).

tff(f8458,plain,
    ( spl21_23
    | ~ spl21_398 ),
    inference(avatar_contradiction_clause,[],[f8457]) ).

tff(f8457,plain,
    ( $false
    | spl21_23
    | ~ spl21_398 ),
    inference(trivial_inequality_removal,[],[f8455]) ).

tff(f8455,plain,
    ( ( huffma1401021291ibling(a1,t_1,a) != huffma1401021291ibling(a1,t_1,a) )
    | spl21_23
    | ~ spl21_398 ),
    inference(superposition,[],[f685,f8200]) ).

tff(f8200,plain,
    ( ! [X0: nat,X1: huffma1450048681e_tree(a1)] : ( huffma1401021291ibling(a1,t_1,a) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,X1),a) )
    | ~ spl21_398 ),
    inference(avatar_component_clause,[],[f8199]) ).

tff(f8199,plain,
    ( spl21_398
  <=> ! [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,[spl21_398])]) ).

tff(f685,plain,
    ( ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) != huffma1401021291ibling(a1,t_1,a) )
    | spl21_23 ),
    inference(avatar_component_clause,[],[f683]) ).

tff(f683,plain,
    ( spl21_23
  <=> ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) = huffma1401021291ibling(a1,t_1,a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_23])]) ).

tff(f8452,plain,
    ( spl21_404
    | ~ spl21_126
    | ~ spl21_142 ),
    inference(avatar_split_clause,[],[f1672,f1655,f1449,f8450]) ).

tff(f8450,plain,
    ( spl21_404
  <=> ! [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))] :
        ( ~ ord_less_eq(X1,aa(X0,X1,X4,sK8(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4)),huffma1280178957ee_rec(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,sK8(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4))))
        | ord_less_eq(fun(X0,X1),X4,aa(nat,fun(X0,X1),X2,X3))
        | ~ ord(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_404])]) ).

tff(f1449,plain,
    ( spl21_126
  <=> ! [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,[spl21_126])]) ).

tff(f1655,plain,
    ( spl21_142
  <=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
        ( ord_less_eq(fun(X1,X0),X3,X2)
        | ~ ord_less_eq(X0,aa(X1,X0,X3,sK8(X0,X1,X2,X3)),aa(X1,X0,X2,sK8(X0,X1,X2,X3)))
        | ~ ord(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_142])]) ).

tff(f1672,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)))))] :
        ( ~ ord_less_eq(X1,aa(X0,X1,X4,sK8(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4)),huffma1280178957ee_rec(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,sK8(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4))))
        | ord_less_eq(fun(X0,X1),X4,aa(nat,fun(X0,X1),X2,X3))
        | ~ ord(X1) )
    | ~ spl21_126
    | ~ spl21_142 ),
    inference(superposition,[],[f1656,f1450]) ).

tff(f1450,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)) )
    | ~ spl21_126 ),
    inference(avatar_component_clause,[],[f1449]) ).

tff(f1656,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
        ( ~ ord_less_eq(X0,aa(X1,X0,X3,sK8(X0,X1,X2,X3)),aa(X1,X0,X2,sK8(X0,X1,X2,X3)))
        | ord_less_eq(fun(X1,X0),X3,X2)
        | ~ ord(X0) )
    | ~ spl21_142 ),
    inference(avatar_component_clause,[],[f1655]) ).

tff(f8448,plain,
    ( spl21_403
    | ~ spl21_125
    | ~ spl21_142 ),
    inference(avatar_split_clause,[],[f1668,f1655,f1445,f8446]) ).

tff(f8446,plain,
    ( spl21_403
  <=> ! [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))] :
        ( ~ ord_less_eq(X1,huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,sK8(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3)))),aa(X0,X1,X4,sK8(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3))))
        | ord_less_eq(fun(X0,X1),aa(nat,fun(X0,X1),X2,X3),X4)
        | ~ ord(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_403])]) ).

tff(f1445,plain,
    ( spl21_125
  <=> ! [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,[spl21_125])]) ).

tff(f1668,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)))] :
        ( ~ ord_less_eq(X1,huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,sK8(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3)))),aa(X0,X1,X4,sK8(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3))))
        | ord_less_eq(fun(X0,X1),aa(nat,fun(X0,X1),X2,X3),X4)
        | ~ ord(X1) )
    | ~ spl21_125
    | ~ spl21_142 ),
    inference(superposition,[],[f1656,f1446]) ).

tff(f1446,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) )
    | ~ spl21_125 ),
    inference(avatar_component_clause,[],[f1445]) ).

tff(f8444,plain,
    ( spl21_402
    | ~ spl21_126
    | ~ spl21_142 ),
    inference(avatar_split_clause,[],[f1667,f1655,f1449,f8442]) ).

tff(f8442,plain,
    ( spl21_402
  <=> ! [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))] :
        ( ~ ord_less_eq(X1,huffma1280178957ee_rec(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,sK8(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3)))),aa(X0,X1,X4,sK8(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3))))
        | ord_less_eq(fun(X0,X1),aa(nat,fun(X0,X1),X2,X3),X4)
        | ~ ord(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_402])]) ).

tff(f1667,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)))))] :
        ( ~ ord_less_eq(X1,huffma1280178957ee_rec(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,sK8(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3)))),aa(X0,X1,X4,sK8(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3))))
        | ord_less_eq(fun(X0,X1),aa(nat,fun(X0,X1),X2,X3),X4)
        | ~ ord(X1) )
    | ~ spl21_126
    | ~ spl21_142 ),
    inference(superposition,[],[f1656,f1450]) ).

tff(f8371,plain,
    ( spl21_401
    | ~ spl21_129
    | ~ spl21_132 ),
    inference(avatar_split_clause,[],[f1564,f1557,f1527,f8369]) ).

tff(f8369,plain,
    ( spl21_401
  <=> ! [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,sK11(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,[spl21_401])]) ).

tff(f1527,plain,
    ( spl21_129
  <=> ! [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,[spl21_129])]) ).

tff(f1557,plain,
    ( spl21_132
  <=> ! [X0: nat,X1: fun(nat,bool),X3: nat] :
        ( pp(aa(nat,bool,X1,X0))
        | pp(aa(nat,bool,X1,X3))
        | ~ ord_less(nat,X3,sK11(X1))
        | ~ pp(aa(nat,bool,X1,zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_132])]) ).

tff(f1564,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,sK11(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) )
    | ~ spl21_129
    | ~ spl21_132 ),
    inference(resolution,[],[f1558,f1528]) ).

tff(f1528,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) )
    | ~ spl21_129 ),
    inference(avatar_component_clause,[],[f1527]) ).

tff(f1558,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,sK11(X1))
        | pp(aa(nat,bool,X1,X0)) )
    | ~ spl21_132 ),
    inference(avatar_component_clause,[],[f1557]) ).

tff(f8245,plain,
    ( spl21_400
    | ~ spl21_135
    | ~ spl21_149 ),
    inference(avatar_split_clause,[],[f1742,f1739,f1586,f8243]) ).

tff(f8243,plain,
    ( spl21_400
  <=> ! [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,sK12(X0,X1)),sK13(X0,X1)),sK14(X0,X1)) = huffma107959123e_case(X0,X2,X3,X4,X1) )
        | ( huffma2021818691e_Leaf(X0,sK15(X0,X1),sK16(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_400])]) ).

tff(f1586,plain,
    ( spl21_135
  <=> ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma1146269203erNode(X0,sK12(X0,X1),sK13(X0,X1),sK14(X0,X1)) = X1 )
        | ( huffma2021818691e_Leaf(X0,sK15(X0,X1),sK16(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_135])]) ).

tff(f1739,plain,
    ( spl21_149
  <=> ! [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,[spl21_149])]) ).

tff(f1742,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,sK12(X0,X1)),sK13(X0,X1)),sK14(X0,X1)) = huffma107959123e_case(X0,X2,X3,X4,X1) )
        | ( huffma2021818691e_Leaf(X0,sK15(X0,X1),sK16(X0,X1)) = X1 ) )
    | ~ spl21_135
    | ~ spl21_149 ),
    inference(superposition,[],[f1740,f1587]) ).

tff(f1587,plain,
    ( ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma1146269203erNode(X0,sK12(X0,X1),sK13(X0,X1),sK14(X0,X1)) = X1 )
        | ( huffma2021818691e_Leaf(X0,sK15(X0,X1),sK16(X0,X1)) = X1 ) )
    | ~ spl21_135 ),
    inference(avatar_component_clause,[],[f1586]) ).

tff(f1740,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) )
    | ~ spl21_149 ),
    inference(avatar_component_clause,[],[f1739]) ).

tff(f8241,plain,
    ( spl21_399
    | ~ spl21_129
    | ~ spl21_134 ),
    inference(avatar_split_clause,[],[f1590,f1582,f1527,f8239]) ).

tff(f8239,plain,
    ( spl21_399
  <=> ! [X0: nat,X3: nat,X2: fun(nat,fun(nat,bool)),X1: nat] :
        ( ~ ord_less(nat,X0,sK10(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,[spl21_399])]) ).

tff(f1582,plain,
    ( spl21_134
  <=> ! [X0: nat,X1: fun(nat,bool),X3: nat] :
        ( ~ pp(aa(nat,bool,X1,X3))
        | ~ ord_less(nat,X3,sK10(X0,X1))
        | ~ pp(aa(nat,bool,X1,X0))
        | pp(aa(nat,bool,X1,zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_134])]) ).

tff(f1590,plain,
    ( ! [X2: fun(nat,fun(nat,bool)),X3: nat,X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,sK10(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) )
    | ~ spl21_129
    | ~ spl21_134 ),
    inference(resolution,[],[f1583,f1528]) ).

tff(f1583,plain,
    ( ! [X3: nat,X0: nat,X1: fun(nat,bool)] :
        ( ~ pp(aa(nat,bool,X1,X3))
        | ~ ord_less(nat,X3,sK10(X0,X1))
        | ~ pp(aa(nat,bool,X1,X0))
        | pp(aa(nat,bool,X1,zero_zero(nat))) )
    | ~ spl21_134 ),
    inference(avatar_component_clause,[],[f1582]) ).

tff(f8201,plain,
    ( spl21_398
    | ~ spl21_24
    | ~ spl21_222 ),
    inference(avatar_split_clause,[],[f4425,f3271,f687,f8199]) ).

tff(f687,plain,
    ( spl21_24
  <=> member(a1,a,huffma675207370phabet(a1,t_1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_24])]) ).

tff(f3271,plain,
    ( spl21_222
  <=> ! [X2: huffma1450048681e_tree(a1),X0: a1,X1: nat] :
        ( ~ member(a1,X0,huffma675207370phabet(a1,t_1))
        | ( huffma1401021291ibling(a1,t_1,X0) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X1,t_1,X2),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_222])]) ).

tff(f4425,plain,
    ( ! [X0: nat,X1: huffma1450048681e_tree(a1)] : ( huffma1401021291ibling(a1,t_1,a) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,X1),a) )
    | ~ spl21_24
    | ~ spl21_222 ),
    inference(resolution,[],[f688,f3272]) ).

tff(f3272,plain,
    ( ! [X2: huffma1450048681e_tree(a1),X0: a1,X1: nat] :
        ( ~ member(a1,X0,huffma675207370phabet(a1,t_1))
        | ( huffma1401021291ibling(a1,t_1,X0) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X1,t_1,X2),X0) ) )
    | ~ spl21_222 ),
    inference(avatar_component_clause,[],[f3271]) ).

tff(f688,plain,
    ( member(a1,a,huffma675207370phabet(a1,t_1))
    | ~ spl21_24 ),
    inference(avatar_component_clause,[],[f687]) ).

tff(f8103,plain,
    ( spl21_397
    | ~ spl21_144
    | ~ spl21_150 ),
    inference(avatar_split_clause,[],[f1763,f1759,f1682,f8101]) ).

tff(f8101,plain,
    ( spl21_397
  <=> ! [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,[spl21_397])]) ).

tff(f1682,plain,
    ( spl21_144
  <=> ! [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,[spl21_144])]) ).

tff(f1759,plain,
    ( spl21_150
  <=> ! [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,[spl21_150])]) ).

tff(f1763,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 ) )
    | ~ spl21_144
    | ~ spl21_150 ),
    inference(resolution,[],[f1760,f1683]) ).

tff(f1683,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 ) )
    | ~ spl21_144 ),
    inference(avatar_component_clause,[],[f1682]) ).

tff(f1760,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)) )
    | ~ spl21_150 ),
    inference(avatar_component_clause,[],[f1759]) ).

tff(f8099,plain,
    ( spl21_396
    | ~ spl21_145
    | ~ spl21_150 ),
    inference(avatar_split_clause,[],[f1762,f1759,f1686,f8097]) ).

tff(f8097,plain,
    ( spl21_396
  <=> ! [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,[spl21_396])]) ).

tff(f1686,plain,
    ( spl21_145
  <=> ! [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,[spl21_145])]) ).

tff(f1762,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 ) )
    | ~ spl21_145
    | ~ spl21_150 ),
    inference(resolution,[],[f1760,f1687]) ).

tff(f1687,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 ) )
    | ~ spl21_145 ),
    inference(avatar_component_clause,[],[f1686]) ).

tff(f8095,plain,
    ( spl21_395
    | ~ spl21_125
    | ~ spl21_134 ),
    inference(avatar_split_clause,[],[f1596,f1582,f1445,f8093]) ).

tff(f8093,plain,
    ( spl21_395
  <=> ! [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,sK10(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,[spl21_395])]) ).

tff(f1596,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,sK10(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))) )
    | ~ spl21_125
    | ~ spl21_134 ),
    inference(superposition,[],[f1583,f1446]) ).

tff(f8091,plain,
    ( spl21_394
    | ~ spl21_126
    | ~ spl21_134 ),
    inference(avatar_split_clause,[],[f1595,f1582,f1449,f8089]) ).

tff(f8089,plain,
    ( spl21_394
  <=> ! [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,sK10(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,[spl21_394])]) ).

tff(f1595,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,sK10(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))) )
    | ~ spl21_126
    | ~ spl21_134 ),
    inference(superposition,[],[f1583,f1450]) ).

tff(f7874,plain,
    ( spl21_393
    | ~ spl21_125
    | ~ spl21_133 ),
    inference(avatar_split_clause,[],[f1577,f1561,f1445,f7872]) ).

tff(f7872,plain,
    ( spl21_393
  <=> ! [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,sK20(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4)) != huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,sK20(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4))) )
        | ( aa(nat,fun(X0,X1),X2,X3) = X4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_393])]) ).

tff(f1561,plain,
    ( spl21_133
  <=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
        ( ( X2 = X3 )
        | ( aa(X1,X0,X3,sK20(X0,X1,X2,X3)) != aa(X1,X0,X2,sK20(X0,X1,X2,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_133])]) ).

tff(f1577,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,sK20(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4)) != huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,sK20(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4))) )
        | ( aa(nat,fun(X0,X1),X2,X3) = X4 ) )
    | ~ spl21_125
    | ~ spl21_133 ),
    inference(superposition,[],[f1562,f1446]) ).

tff(f1562,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
        ( ( aa(X1,X0,X3,sK20(X0,X1,X2,X3)) != aa(X1,X0,X2,sK20(X0,X1,X2,X3)) )
        | ( X2 = X3 ) )
    | ~ spl21_133 ),
    inference(avatar_component_clause,[],[f1561]) ).

tff(f7870,plain,
    ( spl21_392
    | ~ spl21_126
    | ~ spl21_133 ),
    inference(avatar_split_clause,[],[f1576,f1561,f1449,f7868]) ).

tff(f7868,plain,
    ( spl21_392
  <=> ! [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,sK20(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4))) != aa(X0,X1,X4,sK20(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4)) )
        | ( aa(nat,fun(X0,X1),X2,X3) = X4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_392])]) ).

tff(f1576,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,sK20(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4))) != aa(X0,X1,X4,sK20(X1,X0,aa(nat,fun(X0,X1),X2,X3),X4)) )
        | ( aa(nat,fun(X0,X1),X2,X3) = X4 ) )
    | ~ spl21_126
    | ~ spl21_133 ),
    inference(superposition,[],[f1562,f1450]) ).

tff(f7866,plain,
    ( spl21_391
    | ~ spl21_125
    | ~ spl21_133 ),
    inference(avatar_split_clause,[],[f1572,f1561,f1445,f7864]) ).

tff(f7864,plain,
    ( spl21_391
  <=> ! [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,sK20(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3))) != huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,sK20(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3)))) )
        | ( aa(nat,fun(X0,X1),X2,X3) = X4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_391])]) ).

tff(f1572,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,sK20(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3))) != huffma107959123e_case(X0,X1,X2,X5,huffma2021818691e_Leaf(X0,X3,sK20(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3)))) )
        | ( aa(nat,fun(X0,X1),X2,X3) = X4 ) )
    | ~ spl21_125
    | ~ spl21_133 ),
    inference(superposition,[],[f1562,f1446]) ).

tff(f7862,plain,
    ( spl21_390
    | ~ spl21_126
    | ~ spl21_133 ),
    inference(avatar_split_clause,[],[f1571,f1561,f1449,f7860]) ).

tff(f7860,plain,
    ( spl21_390
  <=> ! [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,sK20(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3)))) != aa(X0,X1,X4,sK20(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3))) )
        | ( aa(nat,fun(X0,X1),X2,X3) = X4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_390])]) ).

tff(f1571,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,sK20(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3)))) != aa(X0,X1,X4,sK20(X1,X0,X4,aa(nat,fun(X0,X1),X2,X3))) )
        | ( aa(nat,fun(X0,X1),X2,X3) = X4 ) )
    | ~ spl21_126
    | ~ spl21_133 ),
    inference(superposition,[],[f1562,f1450]) ).

tff(f7858,plain,
    ( spl21_389
    | ~ spl21_125
    | ~ spl21_132 ),
    inference(avatar_split_clause,[],[f1570,f1557,f1445,f7856]) ).

tff(f7856,plain,
    ( spl21_389
  <=> ! [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,sK11(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,[spl21_389])]) ).

tff(f1570,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,sK11(aa(nat,fun(nat,bool),X0,X1)))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X4)) )
    | ~ spl21_125
    | ~ spl21_132 ),
    inference(superposition,[],[f1558,f1446]) ).

tff(f7854,plain,
    ( spl21_388
    | ~ spl21_126
    | ~ spl21_132 ),
    inference(avatar_split_clause,[],[f1569,f1557,f1449,f7852]) ).

tff(f7852,plain,
    ( spl21_388
  <=> ! [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,sK11(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,[spl21_388])]) ).

tff(f1569,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,sK11(aa(nat,fun(nat,bool),X0,X1)))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X4)) )
    | ~ spl21_126
    | ~ spl21_132 ),
    inference(superposition,[],[f1558,f1450]) ).

tff(f7725,plain,
    ( spl21_387
    | ~ spl21_149
    | ~ spl21_151 ),
    inference(avatar_split_clause,[],[f1779,f1772,f1739,f7723]) ).

tff(f7723,plain,
    ( spl21_387
  <=> ! [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,[spl21_387])]) ).

tff(f1772,plain,
    ( spl21_151
  <=> ! [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,[spl21_151])]) ).

tff(f1779,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)) )
    | ~ spl21_149
    | ~ spl21_151 ),
    inference(superposition,[],[f1773,f1740]) ).

tff(f1773,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)) )
    | ~ spl21_151 ),
    inference(avatar_component_clause,[],[f1772]) ).

tff(f7721,plain,
    ( spl21_386
    | ~ spl21_43
    | ~ spl21_150 ),
    inference(avatar_split_clause,[],[f1764,f1759,f776,f7719]) ).

tff(f7719,plain,
    ( spl21_386
  <=> ! [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)),sK17(X0,huffma1146269203erNode(X0,X3,X4,X5))) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X4,X5),sK17(X0,huffma1146269203erNode(X0,X3,X4,X5))) )
        | member(X0,sK17(X0,huffma1146269203erNode(X0,X3,X4,X5)),huffma675207370phabet(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_386])]) ).

tff(f776,plain,
    ( spl21_43
  <=> ! [X0: $tType,X1: huffma1450048681e_tree(X0)] : member(X0,sK17(X0,X1),huffma675207370phabet(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_43])]) ).

tff(f1764,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)),sK17(X0,huffma1146269203erNode(X0,X3,X4,X5))) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X4,X5),sK17(X0,huffma1146269203erNode(X0,X3,X4,X5))) )
        | member(X0,sK17(X0,huffma1146269203erNode(X0,X3,X4,X5)),huffma675207370phabet(X0,X2)) )
    | ~ spl21_43
    | ~ spl21_150 ),
    inference(resolution,[],[f1760,f777]) ).

tff(f777,plain,
    ( ! [X0: $tType,X1: huffma1450048681e_tree(X0)] : member(X0,sK17(X0,X1),huffma675207370phabet(X0,X1))
    | ~ spl21_43 ),
    inference(avatar_component_clause,[],[f776]) ).

tff(f7717,plain,
    ( spl21_385
    | ~ spl21_122
    | ~ spl21_149 ),
    inference(avatar_split_clause,[],[f1751,f1739,f1357,f7715]) ).

tff(f7715,plain,
    ( spl21_385
  <=> ! [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,[spl21_385])]) ).

tff(f1357,plain,
    ( spl21_122
  <=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X5: X1,X2: fun(X1,X0)] :
        ( ord_less_eq(X0,aa(X1,X0,X3,X5),aa(X1,X0,X2,X5))
        | ~ ord_less_eq(fun(X1,X0),X3,X2)
        | ~ ord(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_122])]) ).

tff(f1751,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) )
    | ~ spl21_122
    | ~ spl21_149 ),
    inference(superposition,[],[f1358,f1740]) ).

tff(f1358,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X5: X1] :
        ( ord_less_eq(X0,aa(X1,X0,X3,X5),aa(X1,X0,X2,X5))
        | ~ ord_less_eq(fun(X1,X0),X3,X2)
        | ~ ord(X0) )
    | ~ spl21_122 ),
    inference(avatar_component_clause,[],[f1357]) ).

tff(f7713,plain,
    ( spl21_384
    | ~ spl21_122
    | ~ spl21_149 ),
    inference(avatar_split_clause,[],[f1750,f1739,f1357,f7711]) ).

tff(f7711,plain,
    ( spl21_384
  <=> ! [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,[spl21_384])]) ).

tff(f1750,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) )
    | ~ spl21_122
    | ~ spl21_149 ),
    inference(superposition,[],[f1358,f1740]) ).

tff(f7643,plain,
    ( spl21_383
    | ~ spl21_95
    | ~ spl21_191 ),
    inference(avatar_split_clause,[],[f3105,f2684,f1124,f7641]) ).

tff(f7641,plain,
    ( spl21_383
  <=> ! [X0: nat,X1: a1] :
        ( ( t_2 != huffma2021818691e_Leaf(a1,X0,X1) )
        | ( sK16(a1,t_2) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_383])]) ).

tff(f1124,plain,
    ( spl21_95
  <=> ! [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,[spl21_95])]) ).

tff(f2684,plain,
    ( spl21_191
  <=> ( t_2 = huffma2021818691e_Leaf(a1,sK15(a1,t_2),sK16(a1,t_2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_191])]) ).

tff(f3105,plain,
    ( ! [X0: nat,X1: a1] :
        ( ( t_2 != huffma2021818691e_Leaf(a1,X0,X1) )
        | ( sK16(a1,t_2) = X1 ) )
    | ~ spl21_95
    | ~ spl21_191 ),
    inference(superposition,[],[f1125,f2686]) ).

tff(f2686,plain,
    ( ( t_2 = huffma2021818691e_Leaf(a1,sK15(a1,t_2),sK16(a1,t_2)) )
    | ~ spl21_191 ),
    inference(avatar_component_clause,[],[f2684]) ).

tff(f1125,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: X0,X4: nat] :
        ( ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) )
        | ( X1 = X3 ) )
    | ~ spl21_95 ),
    inference(avatar_component_clause,[],[f1124]) ).

tff(f7619,plain,
    ( spl21_382
    | ~ spl21_125
    | ~ spl21_127 ),
    inference(avatar_split_clause,[],[f1520,f1503,f1445,f7617]) ).

tff(f7617,plain,
    ( spl21_382
  <=> ! [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,sK18(aa(nat,fun(nat,nat),X0,X1)),sK19(aa(nat,fun(nat,nat),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_382])]) ).

tff(f1503,plain,
    ( spl21_127
  <=> ! [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,sK18(X2),sK19(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_127])]) ).

tff(f1520,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,sK18(aa(nat,fun(nat,nat),X0,X1)),sK19(aa(nat,fun(nat,nat),X0,X1))) )
    | ~ spl21_125
    | ~ spl21_127 ),
    inference(superposition,[],[f1504,f1446]) ).

tff(f1504,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,sK18(X2),sK19(X2)) )
    | ~ spl21_127 ),
    inference(avatar_component_clause,[],[f1503]) ).

tff(f7615,plain,
    ( spl21_381
    | ~ spl21_126
    | ~ spl21_127 ),
    inference(avatar_split_clause,[],[f1519,f1503,f1449,f7613]) ).

tff(f7613,plain,
    ( spl21_381
  <=> ! [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,sK18(aa(nat,fun(nat,nat),X0,X1)),sK19(aa(nat,fun(nat,nat),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_381])]) ).

tff(f1519,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,sK18(aa(nat,fun(nat,nat),X0,X1)),sK19(aa(nat,fun(nat,nat),X0,X1))) )
    | ~ spl21_126
    | ~ spl21_127 ),
    inference(superposition,[],[f1504,f1450]) ).

tff(f7611,plain,
    ( spl21_380
    | ~ spl21_125
    | ~ spl21_127 ),
    inference(avatar_split_clause,[],[f1516,f1503,f1445,f7609]) ).

tff(f7609,plain,
    ( spl21_380
  <=> ! [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,sK18(aa(nat,fun(nat,nat),X0,X1)),sK19(aa(nat,fun(nat,nat),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_380])]) ).

tff(f1516,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,sK18(aa(nat,fun(nat,nat),X0,X1)),sK19(aa(nat,fun(nat,nat),X0,X1))) )
    | ~ spl21_125
    | ~ spl21_127 ),
    inference(superposition,[],[f1504,f1446]) ).

tff(f7607,plain,
    ( spl21_379
    | ~ spl21_126
    | ~ spl21_127 ),
    inference(avatar_split_clause,[],[f1515,f1503,f1449,f7605]) ).

tff(f7605,plain,
    ( spl21_379
  <=> ! [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,sK18(aa(nat,fun(nat,nat),X0,X1)),sK19(aa(nat,fun(nat,nat),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_379])]) ).

tff(f1515,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,sK18(aa(nat,fun(nat,nat),X0,X1)),sK19(aa(nat,fun(nat,nat),X0,X1))) )
    | ~ spl21_126
    | ~ spl21_127 ),
    inference(superposition,[],[f1504,f1450]) ).

tff(f7534,plain,
    ( ~ spl21_18
    | spl21_378
    | ~ spl21_112
    | ~ spl21_142 ),
    inference(avatar_split_clause,[],[f1675,f1655,f1297,f7532,f661]) ).

tff(f661,plain,
    ( spl21_18
  <=> ord(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_18])]) ).

tff(f7532,plain,
    ( spl21_378
  <=> ! [X0: $tType,X3: fun(X0,nat),X2: X0,X1: nat] :
        ( ~ ord_less_eq(nat,aa(X0,nat,X3,sK8(nat,X0,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3)),zero_zero(nat))
        | ( sK8(nat,X0,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3) = X2 )
        | ord_less_eq(fun(X0,nat),X3,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_378])]) ).

tff(f1297,plain,
    ( spl21_112
  <=> ! [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,[spl21_112])]) ).

tff(f1675,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,nat),X1: nat] :
        ( ~ ord_less_eq(nat,aa(X0,nat,X3,sK8(nat,X0,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3)),zero_zero(nat))
        | ord_less_eq(fun(X0,nat),X3,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)))
        | ~ ord(nat)
        | ( sK8(nat,X0,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3) = X2 ) )
    | ~ spl21_112
    | ~ spl21_142 ),
    inference(superposition,[],[f1656,f1298]) ).

tff(f1298,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 ) )
    | ~ spl21_112 ),
    inference(avatar_component_clause,[],[f1297]) ).

tff(f7508,plain,
    ( spl21_377
    | ~ spl21_93
    | ~ spl21_191 ),
    inference(avatar_split_clause,[],[f3103,f2684,f1115,f7506]) ).

tff(f7506,plain,
    ( spl21_377
  <=> ! [X0: nat,X1: a1] :
        ( ( t_2 != huffma2021818691e_Leaf(a1,X0,X1) )
        | ( sK15(a1,t_2) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_377])]) ).

tff(f1115,plain,
    ( spl21_93
  <=> ! [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,[spl21_93])]) ).

tff(f3103,plain,
    ( ! [X0: nat,X1: a1] :
        ( ( t_2 != huffma2021818691e_Leaf(a1,X0,X1) )
        | ( sK15(a1,t_2) = X0 ) )
    | ~ spl21_93
    | ~ spl21_191 ),
    inference(superposition,[],[f1116,f2686]) ).

tff(f1116,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: X0,X4: nat] :
        ( ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) )
        | ( X2 = X4 ) )
    | ~ spl21_93 ),
    inference(avatar_component_clause,[],[f1115]) ).

tff(f7504,plain,
    ( ~ spl21_18
    | spl21_376
    | ~ spl21_112
    | ~ spl21_142 ),
    inference(avatar_split_clause,[],[f1670,f1655,f1297,f7502,f661]) ).

tff(f7502,plain,
    ( spl21_376
  <=> ! [X0: $tType,X3: fun(X0,nat),X2: X0,X1: nat] :
        ( ~ ord_less_eq(nat,zero_zero(nat),aa(X0,nat,X3,sK8(nat,X0,X3,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)))))
        | ( sK8(nat,X0,X3,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2))) = X2 )
        | ord_less_eq(fun(X0,nat),huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_376])]) ).

tff(f1670,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,nat),X1: nat] :
        ( ~ ord_less_eq(nat,zero_zero(nat),aa(X0,nat,X3,sK8(nat,X0,X3,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)))))
        | ord_less_eq(fun(X0,nat),huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3)
        | ~ ord(nat)
        | ( sK8(nat,X0,X3,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2))) = X2 ) )
    | ~ spl21_112
    | ~ spl21_142 ),
    inference(superposition,[],[f1656,f1298]) ).

tff(f7500,plain,
    ( spl21_375
    | ~ spl21_124
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1498,f1449,f1389,f7498]) ).

tff(f7498,plain,
    ( spl21_375
  <=> ! [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,sK10(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,[spl21_375])]) ).

tff(f1389,plain,
    ( spl21_124
  <=> ! [X0: nat,X1: fun(nat,bool)] :
        ( pp(aa(nat,bool,X1,sK10(X0,X1)))
        | ~ pp(aa(nat,bool,X1,X0))
        | pp(aa(nat,bool,X1,zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_124])]) ).

tff(f1498,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,sK10(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))) )
    | ~ spl21_124
    | ~ spl21_126 ),
    inference(superposition,[],[f1390,f1450]) ).

tff(f1390,plain,
    ( ! [X0: nat,X1: fun(nat,bool)] :
        ( pp(aa(nat,bool,X1,sK10(X0,X1)))
        | ~ pp(aa(nat,bool,X1,X0))
        | pp(aa(nat,bool,X1,zero_zero(nat))) )
    | ~ spl21_124 ),
    inference(avatar_component_clause,[],[f1389]) ).

tff(f7496,plain,
    ( spl21_374
    | ~ spl21_124
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1475,f1445,f1389,f7494]) ).

tff(f7494,plain,
    ( spl21_374
  <=> ! [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,sK10(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,[spl21_374])]) ).

tff(f1475,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,sK10(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))) )
    | ~ spl21_124
    | ~ spl21_125 ),
    inference(superposition,[],[f1390,f1446]) ).

tff(f7448,plain,
    ( spl21_373
    | ~ spl21_123
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1499,f1449,f1361,f7446]) ).

tff(f7446,plain,
    ( spl21_373
  <=> ! [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,sK11(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,[spl21_373])]) ).

tff(f1361,plain,
    ( spl21_123
  <=> ! [X0: nat,X1: fun(nat,bool)] :
        ( pp(aa(nat,bool,X1,X0))
        | ~ pp(aa(nat,bool,X1,sK11(X1)))
        | ~ pp(aa(nat,bool,X1,zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_123])]) ).

tff(f1499,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,sK11(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))) )
    | ~ spl21_123
    | ~ spl21_126 ),
    inference(superposition,[],[f1362,f1450]) ).

tff(f1362,plain,
    ( ! [X0: nat,X1: fun(nat,bool)] :
        ( ~ pp(aa(nat,bool,X1,sK11(X1)))
        | pp(aa(nat,bool,X1,X0))
        | ~ pp(aa(nat,bool,X1,zero_zero(nat))) )
    | ~ spl21_123 ),
    inference(avatar_component_clause,[],[f1361]) ).

tff(f7444,plain,
    ( spl21_372
    | ~ spl21_123
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1476,f1445,f1361,f7442]) ).

tff(f7442,plain,
    ( spl21_372
  <=> ! [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,sK11(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,[spl21_372])]) ).

tff(f1476,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,sK11(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))) )
    | ~ spl21_123
    | ~ spl21_125 ),
    inference(superposition,[],[f1362,f1446]) ).

tff(f7311,plain,
    ( spl21_371
    | ~ spl21_110
    | ~ spl21_150 ),
    inference(avatar_split_clause,[],[f1768,f1759,f1289,f7309]) ).

tff(f7309,plain,
    ( spl21_371
  <=> ! [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,[spl21_371])]) ).

tff(f1289,plain,
    ( spl21_110
  <=> ! [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,[spl21_110])]) ).

tff(f1768,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) ) )
    | ~ spl21_110
    | ~ spl21_150 ),
    inference(resolution,[],[f1760,f1290]) ).

tff(f1290,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) ) )
    | ~ spl21_110 ),
    inference(avatar_component_clause,[],[f1289]) ).

tff(f7307,plain,
    ( spl21_370
    | ~ spl21_144
    | ~ spl21_146 ),
    inference(avatar_split_clause,[],[f1718,f1706,f1682,f7305]) ).

tff(f7305,plain,
    ( spl21_370
  <=> ! [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,[spl21_370])]) ).

tff(f1706,plain,
    ( spl21_146
  <=> ! [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,[spl21_146])]) ).

tff(f1718,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 ) )
    | ~ spl21_144
    | ~ spl21_146 ),
    inference(resolution,[],[f1707,f1683]) ).

tff(f1707,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) ) )
    | ~ spl21_146 ),
    inference(avatar_component_clause,[],[f1706]) ).

tff(f7303,plain,
    ( spl21_369
    | ~ spl21_145
    | ~ spl21_146 ),
    inference(avatar_split_clause,[],[f1717,f1706,f1686,f7301]) ).

tff(f7301,plain,
    ( spl21_369
  <=> ! [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,[spl21_369])]) ).

tff(f1717,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 ) )
    | ~ spl21_145
    | ~ spl21_146 ),
    inference(resolution,[],[f1707,f1687]) ).

tff(f7299,plain,
    ( spl21_368
    | ~ spl21_131
    | ~ spl21_145 ),
    inference(avatar_split_clause,[],[f1702,f1686,f1536,f7297]) ).

tff(f7297,plain,
    ( spl21_368
  <=> ! [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,[spl21_368])]) ).

tff(f1536,plain,
    ( spl21_131
  <=> ! [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,[spl21_131])]) ).

tff(f1702,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) ) )
    | ~ spl21_131
    | ~ spl21_145 ),
    inference(resolution,[],[f1687,f1537]) ).

tff(f1537,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) ) )
    | ~ spl21_131 ),
    inference(avatar_component_clause,[],[f1536]) ).

tff(f7295,plain,
    ( spl21_367
    | ~ spl21_131
    | ~ spl21_144 ),
    inference(avatar_split_clause,[],[f1698,f1682,f1536,f7293]) ).

tff(f7293,plain,
    ( spl21_367
  <=> ! [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,[spl21_367])]) ).

tff(f1698,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) ) )
    | ~ spl21_131
    | ~ spl21_144 ),
    inference(resolution,[],[f1683,f1537]) ).

tff(f7290,plain,
    ( spl21_366
    | ~ spl21_71
    | ~ spl21_146 ),
    inference(avatar_split_clause,[],[f1720,f1706,f923,f7288]) ).

tff(f7288,plain,
    ( spl21_366
  <=> ! [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),sK9(X0,huffma1146269203erNode(X0,X2,X3,X4))) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X3,X4),sK9(X0,huffma1146269203erNode(X0,X2,X3,X4))) )
        | ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X2,X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_366])]) ).

tff(f923,plain,
    ( spl21_71
  <=> ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
        ( member(X0,sK9(X0,X1),huffma675207370phabet(X0,X1))
        | ~ huffma1518433673istent(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_71])]) ).

tff(f1720,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),sK9(X0,huffma1146269203erNode(X0,X2,X3,X4))) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X3,X4),sK9(X0,huffma1146269203erNode(X0,X2,X3,X4))) )
        | ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X2,X3,X4)) )
    | ~ spl21_71
    | ~ spl21_146 ),
    inference(resolution,[],[f1707,f924]) ).

tff(f924,plain,
    ( ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
        ( member(X0,sK9(X0,X1),huffma675207370phabet(X0,X1))
        | ~ huffma1518433673istent(X0,X1) )
    | ~ spl21_71 ),
    inference(avatar_component_clause,[],[f923]) ).

tff(f7254,plain,
    ( spl21_365
    | ~ spl21_112
    | ~ spl21_133 ),
    inference(avatar_split_clause,[],[f1579,f1561,f1297,f7252]) ).

tff(f7252,plain,
    ( spl21_365
  <=> ! [X0: $tType,X3: fun(X0,nat),X2: X0,X1: nat] :
        ( ( zero_zero(nat) != aa(X0,nat,X3,sK20(nat,X0,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3)) )
        | ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)) = X3 )
        | ( sK20(nat,X0,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3) = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_365])]) ).

tff(f1579,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,nat),X1: nat] :
        ( ( zero_zero(nat) != aa(X0,nat,X3,sK20(nat,X0,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3)) )
        | ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)) = X3 )
        | ( sK20(nat,X0,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)),X3) = X2 ) )
    | ~ spl21_112
    | ~ spl21_133 ),
    inference(superposition,[],[f1562,f1298]) ).

tff(f7250,plain,
    ( spl21_364
    | ~ spl21_112
    | ~ spl21_133 ),
    inference(avatar_split_clause,[],[f1574,f1561,f1297,f7248]) ).

tff(f7248,plain,
    ( spl21_364
  <=> ! [X0: $tType,X3: fun(X0,nat),X2: X0,X1: nat] :
        ( ( zero_zero(nat) != aa(X0,nat,X3,sK20(nat,X0,X3,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)))) )
        | ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)) = X3 )
        | ( sK20(nat,X0,X3,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2))) = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_364])]) ).

tff(f1574,plain,
    ( ! [X0: $tType,X2: X0,X3: fun(X0,nat),X1: nat] :
        ( ( zero_zero(nat) != aa(X0,nat,X3,sK20(nat,X0,X3,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)))) )
        | ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2)) = X3 )
        | ( sK20(nat,X0,X3,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2))) = X2 ) )
    | ~ spl21_112
    | ~ spl21_133 ),
    inference(superposition,[],[f1562,f1298]) ).

tff(f7102,plain,
    ( spl21_363
    | ~ spl21_29
    | ~ spl21_149 ),
    inference(avatar_split_clause,[],[f1749,f1739,f710,f7100]) ).

tff(f7100,plain,
    ( spl21_363
  <=> ! [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,[spl21_363])]) ).

tff(f710,plain,
    ( spl21_29
  <=> ! [X0: bool] :
        ( ( fFalse = X0 )
        | ( fTrue = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_29])]) ).

tff(f1749,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) ) )
    | ~ spl21_29
    | ~ spl21_149 ),
    inference(superposition,[],[f1740,f711]) ).

tff(f711,plain,
    ( ! [X0: bool] :
        ( ( fTrue = X0 )
        | ( fFalse = X0 ) )
    | ~ spl21_29 ),
    inference(avatar_component_clause,[],[f710]) ).

tff(f7098,plain,
    ( spl21_362
    | ~ spl21_29
    | ~ spl21_149 ),
    inference(avatar_split_clause,[],[f1743,f1739,f710,f7096]) ).

tff(f7096,plain,
    ( spl21_362
  <=> ! [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,[spl21_362])]) ).

tff(f1743,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)) ) )
    | ~ spl21_29
    | ~ spl21_149 ),
    inference(superposition,[],[f1740,f711]) ).

tff(f7094,plain,
    ( spl21_361
    | ~ spl21_118
    | ~ spl21_129 ),
    inference(avatar_split_clause,[],[f1541,f1527,f1332,f7092]) ).

tff(f7092,plain,
    ( spl21_361
  <=> ! [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),sK11(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,[spl21_361])]) ).

tff(f1332,plain,
    ( spl21_118
  <=> ! [X0: nat,X1: fun(nat,bool)] :
        ( pp(aa(nat,bool,X1,X0))
        | ord_less(nat,zero_zero(nat),sK11(X1))
        | ~ pp(aa(nat,bool,X1,zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_118])]) ).

tff(f1541,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),sK11(aa(nat,fun(nat,bool),X1,X0)))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X1,X0),X2)) )
    | ~ spl21_118
    | ~ spl21_129 ),
    inference(resolution,[],[f1528,f1333]) ).

tff(f1333,plain,
    ( ! [X0: nat,X1: fun(nat,bool)] :
        ( ~ pp(aa(nat,bool,X1,zero_zero(nat)))
        | ord_less(nat,zero_zero(nat),sK11(X1))
        | pp(aa(nat,bool,X1,X0)) )
    | ~ spl21_118 ),
    inference(avatar_component_clause,[],[f1332]) ).

tff(f7090,plain,
    ( ~ spl21_228
    | spl21_25
    | ~ spl21_351 ),
    inference(avatar_split_clause,[],[f6954,f6812,f692,f3400]) ).

tff(f3400,plain,
    ( spl21_228
  <=> ( a = huffma1401021291ibling(a1,t_2,a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_228])]) ).

tff(f692,plain,
    ( spl21_25
  <=> ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) = huffma1401021291ibling(a1,t_2,a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_25])]) ).

tff(f6812,plain,
    ( spl21_351
  <=> ! [X0: nat,X1: huffma1450048681e_tree(a1)] : ( a = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,X1),a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_351])]) ).

tff(f6954,plain,
    ( ( a != huffma1401021291ibling(a1,t_2,a) )
    | spl21_25
    | ~ spl21_351 ),
    inference(superposition,[],[f694,f6813]) ).

tff(f6813,plain,
    ( ! [X0: nat,X1: huffma1450048681e_tree(a1)] : ( a = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,X1),a) )
    | ~ spl21_351 ),
    inference(avatar_component_clause,[],[f6812]) ).

tff(f694,plain,
    ( ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) != huffma1401021291ibling(a1,t_2,a) )
    | spl21_25 ),
    inference(avatar_component_clause,[],[f692]) ).

tff(f7020,plain,
    ( spl21_360
    | ~ spl21_86
    | ~ spl21_150 ),
    inference(avatar_split_clause,[],[f1769,f1759,f1042,f7018]) ).

tff(f7018,plain,
    ( spl21_360
  <=> ! [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,[spl21_360])]) ).

tff(f1042,plain,
    ( spl21_86
  <=> ! [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,[spl21_86])]) ).

tff(f1769,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 ) )
    | ~ spl21_86
    | ~ spl21_150 ),
    inference(resolution,[],[f1760,f1043]) ).

tff(f1043,plain,
    ( ! [X0: $tType,X2: X0,X1: huffma1450048681e_tree(X0)] :
        ( member(X0,X2,huffma675207370phabet(X0,X1))
        | ( huffma1401021291ibling(X0,X1,X2) = X2 ) )
    | ~ spl21_86 ),
    inference(avatar_component_clause,[],[f1042]) ).

tff(f7016,plain,
    ( spl21_359
    | ~ spl21_110
    | ~ spl21_148 ),
    inference(avatar_split_clause,[],[f1734,f1727,f1289,f7014]) ).

tff(f7014,plain,
    ( spl21_359
  <=> ! [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,[spl21_359])]) ).

tff(f1727,plain,
    ( spl21_148
  <=> ! [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,[spl21_148])]) ).

tff(f1734,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) ) )
    | ~ spl21_110
    | ~ spl21_148 ),
    inference(resolution,[],[f1728,f1290]) ).

tff(f1728,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))) )
    | ~ spl21_148 ),
    inference(avatar_component_clause,[],[f1727]) ).

tff(f7012,plain,
    ( spl21_358
    | ~ spl21_112
    | ~ spl21_127 ),
    inference(avatar_split_clause,[],[f1518,f1503,f1297,f7010]) ).

tff(f7010,plain,
    ( spl21_358
  <=> ! [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,sK18(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1))),sK19(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1))))
        | ( X1 = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_358])]) ).

tff(f1518,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,sK18(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1))),sK19(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1))))
        | ( X1 = X2 ) )
    | ~ spl21_112
    | ~ spl21_127 ),
    inference(superposition,[],[f1504,f1298]) ).

tff(f7008,plain,
    ( spl21_357
    | ~ spl21_111
    | ~ spl21_124 ),
    inference(avatar_split_clause,[],[f1452,f1389,f1293,f7006]) ).

tff(f7006,plain,
    ( spl21_357
  <=> ! [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(sK10(X2,aa(nat,fun(nat,bool),X0,X1)),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_357])]) ).

tff(f1293,plain,
    ( spl21_111
  <=> ! [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,[spl21_111])]) ).

tff(f1452,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(sK10(X2,aa(nat,fun(nat,bool),X0,X1)),X1,X0) )
    | ~ spl21_111
    | ~ spl21_124 ),
    inference(resolution,[],[f1390,f1294]) ).

tff(f1294,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) )
    | ~ spl21_111 ),
    inference(avatar_component_clause,[],[f1293]) ).

tff(f6834,plain,
    ( spl21_356
    | ~ spl21_135
    | ~ spl21_150 ),
    inference(avatar_split_clause,[],[f1770,f1759,f1586,f6832]) ).

tff(f6832,plain,
    ( spl21_356
  <=> ! [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,sK15(X0,X1),sK16(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_356])]) ).

tff(f1770,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,sK15(X0,X1),sK16(X0,X1)) = X1 ) )
    | ~ spl21_135
    | ~ spl21_150 ),
    inference(superposition,[],[f1760,f1587]) ).

tff(f6830,plain,
    ( spl21_355
    | ~ spl21_71
    | ~ spl21_148 ),
    inference(avatar_split_clause,[],[f1731,f1727,f923,f6828]) ).

tff(f6828,plain,
    ( spl21_355
  <=> ! [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),sK9(X0,X5)) = huffma1401021291ibling(X0,X5,sK9(X0,X5)) )
        | member(X0,sK9(X0,X5),huffma675207370phabet(X0,huffma1146269203erNode(X0,X2,X3,X4)))
        | ~ huffma1518433673istent(X0,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_355])]) ).

tff(f1731,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),sK9(X0,X5)) = huffma1401021291ibling(X0,X5,sK9(X0,X5)) )
        | member(X0,sK9(X0,X5),huffma675207370phabet(X0,huffma1146269203erNode(X0,X2,X3,X4)))
        | ~ huffma1518433673istent(X0,X5) )
    | ~ spl21_71
    | ~ spl21_148 ),
    inference(resolution,[],[f1728,f924]) ).

tff(f6826,plain,
    ( spl21_354
    | ~ spl21_117
    | ~ spl21_129 ),
    inference(avatar_split_clause,[],[f1540,f1527,f1328,f6824]) ).

tff(f6824,plain,
    ( spl21_354
  <=> ! [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,sK10(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,[spl21_354])]) ).

tff(f1328,plain,
    ( spl21_117
  <=> ! [X0: nat,X1: fun(nat,bool)] :
        ( ord_less_eq(nat,sK10(X0,X1),X0)
        | ~ pp(aa(nat,bool,X1,X0))
        | pp(aa(nat,bool,X1,zero_zero(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_117])]) ).

tff(f1540,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,sK10(X1,aa(nat,fun(nat,bool),X2,X0)),X1)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X0),zero_zero(nat))) )
    | ~ spl21_117
    | ~ spl21_129 ),
    inference(resolution,[],[f1528,f1329]) ).

tff(f1329,plain,
    ( ! [X0: nat,X1: fun(nat,bool)] :
        ( ~ pp(aa(nat,bool,X1,X0))
        | ord_less_eq(nat,sK10(X0,X1),X0)
        | pp(aa(nat,bool,X1,zero_zero(nat))) )
    | ~ spl21_117 ),
    inference(avatar_component_clause,[],[f1328]) ).

tff(f6822,plain,
    ( spl21_353
    | ~ spl21_121
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1494,f1449,f1353,f6820]) ).

tff(f6820,plain,
    ( spl21_353
  <=> ! [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,sK7(aa(nat,fun(int,bool),X0,X1)))))
        | ~ ord_less_eq(int,zero_zero(int),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_353])]) ).

tff(f1353,plain,
    ( spl21_121
  <=> ! [X4: int,X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK7(X0))))
        | ~ pp(aa(int,bool,X0,X4))
        | ~ ord_less_eq(int,zero_zero(int),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_121])]) ).

tff(f1494,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,sK7(aa(nat,fun(int,bool),X0,X1)))))
        | ~ ord_less_eq(int,zero_zero(int),X2) )
    | ~ spl21_121
    | ~ spl21_126 ),
    inference(superposition,[],[f1354,f1450]) ).

tff(f1354,plain,
    ( ! [X0: fun(int,bool),X4: int] :
        ( ~ pp(aa(int,bool,X0,X4))
        | pp(aa(int,bool,X0,semiring_1_of_nat(int,sK7(X0))))
        | ~ ord_less_eq(int,zero_zero(int),X4) )
    | ~ spl21_121 ),
    inference(avatar_component_clause,[],[f1353]) ).

tff(f6818,plain,
    ( spl21_352
    | ~ spl21_120
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1492,f1449,f1349,f6816]) ).

tff(f6816,plain,
    ( spl21_352
  <=> ! [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,sK4(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,[spl21_352])]) ).

tff(f1349,plain,
    ( spl21_120
  <=> ! [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,sK4(X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_120])]) ).

tff(f1492,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,sK4(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)) )
    | ~ spl21_120
    | ~ spl21_126 ),
    inference(superposition,[],[f1350,f1450]) ).

tff(f1350,plain,
    ( ! [X0: fun(int,bool),X1: int] :
        ( ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,sK4(X0))))
        | ~ ord_less_eq(int,zero_zero(int),X1)
        | pp(aa(int,bool,X0,X1)) )
    | ~ spl21_120 ),
    inference(avatar_component_clause,[],[f1349]) ).

tff(f6814,plain,
    ( spl21_351
    | ~ spl21_24
    | ~ spl21_136
    | ~ spl21_222
    | ~ spl21_258 ),
    inference(avatar_split_clause,[],[f4431,f4001,f3271,f1599,f687,f6812]) ).

tff(f1599,plain,
    ( spl21_136
  <=> ! [X2: huffma1450048681e_tree(a1),X0: nat,X1: nat,X3: huffma1450048681e_tree(a1)] : ( a = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,huffma1146269203erNode(a1,X1,X2,X3)),a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_136])]) ).

tff(f4001,plain,
    ( spl21_258
  <=> ! [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,[spl21_258])]) ).

tff(f4431,plain,
    ( ! [X0: nat,X1: huffma1450048681e_tree(a1)] : ( a = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,X1),a) )
    | ~ spl21_24
    | ~ spl21_136
    | ~ spl21_222
    | ~ spl21_258 ),
    inference(forward_demodulation,[],[f4425,f4069]) ).

tff(f4069,plain,
    ( ( a = huffma1401021291ibling(a1,t_1,a) )
    | ~ spl21_136
    | ~ spl21_258 ),
    inference(duplicate_literal_removal,[],[f4068]) ).

tff(f4068,plain,
    ( ( a = huffma1401021291ibling(a1,t_1,a) )
    | ( a = huffma1401021291ibling(a1,t_1,a) )
    | ~ spl21_136
    | ~ spl21_258 ),
    inference(superposition,[],[f1600,f4002]) ).

tff(f4002,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 ) )
    | ~ spl21_258 ),
    inference(avatar_component_clause,[],[f4001]) ).

tff(f1600,plain,
    ( ! [X2: huffma1450048681e_tree(a1),X3: huffma1450048681e_tree(a1),X0: nat,X1: nat] : ( a = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,huffma1146269203erNode(a1,X1,X2,X3)),a) )
    | ~ spl21_136 ),
    inference(avatar_component_clause,[],[f1599]) ).

tff(f6810,plain,
    ( spl21_350
    | ~ spl21_121
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1471,f1445,f1353,f6808]) ).

tff(f6808,plain,
    ( spl21_350
  <=> ! [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,sK7(aa(nat,fun(int,bool),X0,X1)))))
        | ~ ord_less_eq(int,zero_zero(int),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_350])]) ).

tff(f1471,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,sK7(aa(nat,fun(int,bool),X0,X1)))))
        | ~ ord_less_eq(int,zero_zero(int),X2) )
    | ~ spl21_121
    | ~ spl21_125 ),
    inference(superposition,[],[f1354,f1446]) ).

tff(f6806,plain,
    ( spl21_349
    | ~ spl21_120
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1469,f1445,f1349,f6804]) ).

tff(f6804,plain,
    ( spl21_349
  <=> ! [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,sK4(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,[spl21_349])]) ).

tff(f1469,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,sK4(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)) )
    | ~ spl21_120
    | ~ spl21_125 ),
    inference(superposition,[],[f1350,f1446]) ).

tff(f6678,plain,
    ( spl21_348
    | ~ spl21_110
    | ~ spl21_146 ),
    inference(avatar_split_clause,[],[f1723,f1706,f1289,f6676]) ).

tff(f6676,plain,
    ( spl21_348
  <=> ! [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,[spl21_348])]) ).

tff(f1723,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) ) )
    | ~ spl21_110
    | ~ spl21_146 ),
    inference(resolution,[],[f1707,f1290]) ).

tff(f6673,plain,
    ( spl21_347
    | ~ spl21_125
    | ~ spl21_129 ),
    inference(avatar_split_clause,[],[f1546,f1527,f1445,f6671]) ).

tff(f6671,plain,
    ( spl21_347
  <=> ! [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,[spl21_347])]) ).

tff(f1546,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)) )
    | ~ spl21_125
    | ~ spl21_129 ),
    inference(superposition,[],[f1528,f1446]) ).

tff(f6669,plain,
    ( spl21_346
    | ~ spl21_126
    | ~ spl21_129 ),
    inference(avatar_split_clause,[],[f1545,f1527,f1449,f6667]) ).

tff(f6667,plain,
    ( spl21_346
  <=> ! [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,[spl21_346])]) ).

tff(f1545,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)) )
    | ~ spl21_126
    | ~ spl21_129 ),
    inference(superposition,[],[f1528,f1450]) ).

tff(f6665,plain,
    ( spl21_345
    | ~ spl21_118
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1497,f1449,f1332,f6663]) ).

tff(f6663,plain,
    ( spl21_345
  <=> ! [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),sK11(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,[spl21_345])]) ).

tff(f1497,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),sK11(aa(nat,fun(nat,bool),X0,X1)))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X3)) )
    | ~ spl21_118
    | ~ spl21_126 ),
    inference(superposition,[],[f1333,f1450]) ).

tff(f6661,plain,
    ( spl21_344
    | ~ spl21_117
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1496,f1449,f1328,f6659]) ).

tff(f6659,plain,
    ( spl21_344
  <=> ! [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,sK10(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,[spl21_344])]) ).

tff(f1496,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,sK10(X2,aa(nat,fun(nat,bool),X0,X1)),X2)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat))) )
    | ~ spl21_117
    | ~ spl21_126 ),
    inference(superposition,[],[f1329,f1450]) ).

tff(f6657,plain,
    ( spl21_343
    | ~ spl21_118
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1474,f1445,f1332,f6655]) ).

tff(f6655,plain,
    ( spl21_343
  <=> ! [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),sK11(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,[spl21_343])]) ).

tff(f1474,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),sK11(aa(nat,fun(nat,bool),X0,X1)))
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X3)) )
    | ~ spl21_118
    | ~ spl21_125 ),
    inference(superposition,[],[f1333,f1446]) ).

tff(f6653,plain,
    ( spl21_342
    | ~ spl21_117
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1473,f1445,f1328,f6651]) ).

tff(f6651,plain,
    ( spl21_342
  <=> ! [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,sK10(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,[spl21_342])]) ).

tff(f1473,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,sK10(X2,aa(nat,fun(nat,bool),X0,X1)),X2)
        | pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),zero_zero(nat))) )
    | ~ spl21_117
    | ~ spl21_125 ),
    inference(superposition,[],[f1329,f1446]) ).

tff(f6602,plain,
    ( spl21_341
    | ~ spl21_61
    | ~ spl21_149 ),
    inference(avatar_split_clause,[],[f1757,f1739,f871,f6600]) ).

tff(f6600,plain,
    ( spl21_341
  <=> ! [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,[spl21_341])]) ).

tff(f871,plain,
    ( spl21_61
  <=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( pp(aa(X0,bool,X1,X2))
        | ~ member(X0,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_61])]) ).

tff(f1757,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)) )
    | ~ spl21_61
    | ~ spl21_149 ),
    inference(superposition,[],[f872,f1740]) ).

tff(f872,plain,
    ( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( pp(aa(X0,bool,X1,X2))
        | ~ member(X0,X2,X1) )
    | ~ spl21_61 ),
    inference(avatar_component_clause,[],[f871]) ).

tff(f6598,plain,
    ( spl21_340
    | ~ spl21_75
    | ~ spl21_191 ),
    inference(avatar_split_clause,[],[f3101,f2684,f940,f6596]) ).

tff(f6596,plain,
    ( spl21_340
  <=> ! [X2: huffma1450048681e_tree(a1),X0: nat,X1: huffma1450048681e_tree(a1)] : ( t_2 != huffma1146269203erNode(a1,X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_340])]) ).

tff(f940,plain,
    ( spl21_75
  <=> ! [X0: $tType,X2: nat,X4: huffma1450048681e_tree(X0),X5: nat,X3: huffma1450048681e_tree(X0),X1: X0] : ( huffma2021818691e_Leaf(X0,X2,X1) != huffma1146269203erNode(X0,X5,X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_75])]) ).

tff(f3101,plain,
    ( ! [X2: huffma1450048681e_tree(a1),X0: nat,X1: huffma1450048681e_tree(a1)] : ( t_2 != huffma1146269203erNode(a1,X0,X1,X2) )
    | ~ spl21_75
    | ~ spl21_191 ),
    inference(superposition,[],[f941,f2686]) ).

tff(f941,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: X0,X4: huffma1450048681e_tree(X0),X5: nat] : ( huffma2021818691e_Leaf(X0,X2,X1) != huffma1146269203erNode(X0,X5,X4,X3) )
    | ~ spl21_75 ),
    inference(avatar_component_clause,[],[f940]) ).

tff(f6594,plain,
    ( spl21_339
    | ~ spl21_62
    | ~ spl21_149 ),
    inference(avatar_split_clause,[],[f1756,f1739,f875,f6592]) ).

tff(f6592,plain,
    ( spl21_339
  <=> ! [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,[spl21_339])]) ).

tff(f875,plain,
    ( spl21_62
  <=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( member(X0,X2,X1)
        | ~ pp(aa(X0,bool,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_62])]) ).

tff(f1756,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)) )
    | ~ spl21_62
    | ~ spl21_149 ),
    inference(superposition,[],[f876,f1740]) ).

tff(f876,plain,
    ( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
        ( ~ pp(aa(X0,bool,X1,X2))
        | member(X0,X2,X1) )
    | ~ spl21_62 ),
    inference(avatar_component_clause,[],[f875]) ).

tff(f6590,plain,
    ( spl21_338
    | ~ spl21_92
    | ~ spl21_134 ),
    inference(avatar_split_clause,[],[f1592,f1582,f1111,f6588]) ).

tff(f6588,plain,
    ( spl21_338
  <=> ! [X4: nat,X0: nat,X3: nat,X2: fun(nat,bool),X1: nat] :
        ( ~ ord_less(nat,X0,sK10(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,[spl21_338])]) ).

tff(f1111,plain,
    ( spl21_92
  <=> ! [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,[spl21_92])]) ).

tff(f1592,plain,
    ( ! [X2: fun(nat,bool),X3: nat,X0: nat,X1: nat,X4: nat] :
        ( ~ ord_less(nat,X0,sK10(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)) ) )
    | ~ spl21_92
    | ~ spl21_134 ),
    inference(resolution,[],[f1583,f1112]) ).

tff(f1112,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)) ) )
    | ~ spl21_92 ),
    inference(avatar_component_clause,[],[f1111]) ).

tff(f5799,plain,
    ( spl21_337
    | ~ spl21_86
    | ~ spl21_148 ),
    inference(avatar_split_clause,[],[f1735,f1727,f1042,f5797]) ).

tff(f5797,plain,
    ( spl21_337
  <=> ! [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,[spl21_337])]) ).

tff(f1735,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 ) )
    | ~ spl21_86
    | ~ spl21_148 ),
    inference(resolution,[],[f1728,f1043]) ).

tff(f5795,plain,
    ( spl21_336
    | ~ spl21_43
    | ~ spl21_148 ),
    inference(avatar_split_clause,[],[f1730,f1727,f776,f5793]) ).

tff(f5793,plain,
    ( spl21_336
  <=> ! [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),sK17(X0,X5)) = huffma1401021291ibling(X0,X5,sK17(X0,X5)) )
        | member(X0,sK17(X0,X5),huffma675207370phabet(X0,huffma1146269203erNode(X0,X2,X3,X4))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_336])]) ).

tff(f1730,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),sK17(X0,X5)) = huffma1401021291ibling(X0,X5,sK17(X0,X5)) )
        | member(X0,sK17(X0,X5),huffma675207370phabet(X0,huffma1146269203erNode(X0,X2,X3,X4))) )
    | ~ spl21_43
    | ~ spl21_148 ),
    inference(resolution,[],[f1728,f777]) ).

tff(f5791,plain,
    ( spl21_335
    | ~ spl21_43
    | ~ spl21_146 ),
    inference(avatar_split_clause,[],[f1719,f1706,f776,f5789]) ).

tff(f5789,plain,
    ( spl21_335
  <=> ! [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),sK17(X0,huffma1146269203erNode(X0,X2,X3,X4))) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X3,X4),sK17(X0,huffma1146269203erNode(X0,X2,X3,X4))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_335])]) ).

tff(f1719,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),sK17(X0,huffma1146269203erNode(X0,X2,X3,X4))) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X3,X4),sK17(X0,huffma1146269203erNode(X0,X2,X3,X4))) )
    | ~ spl21_43
    | ~ spl21_146 ),
    inference(resolution,[],[f1707,f777]) ).

tff(f5787,plain,
    ( spl21_334
    | ~ spl21_135
    | ~ spl21_145 ),
    inference(avatar_split_clause,[],[f1704,f1686,f1586,f5785]) ).

tff(f5785,plain,
    ( spl21_334
  <=> ! [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,sK15(X0,X1),sK16(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_334])]) ).

tff(f1704,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,sK15(X0,X1),sK16(X0,X1)) = X1 ) )
    | ~ spl21_135
    | ~ spl21_145 ),
    inference(superposition,[],[f1687,f1587]) ).

tff(f5783,plain,
    ( spl21_333
    | ~ spl21_135
    | ~ spl21_144 ),
    inference(avatar_split_clause,[],[f1700,f1682,f1586,f5781]) ).

tff(f5781,plain,
    ( spl21_333
  <=> ! [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,sK15(X0,X1),sK16(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_333])]) ).

tff(f1700,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,sK15(X0,X1),sK16(X0,X1)) = X1 ) )
    | ~ spl21_135
    | ~ spl21_144 ),
    inference(superposition,[],[f1683,f1587]) ).

tff(f5779,plain,
    ( spl21_332
    | ~ spl21_92
    | ~ spl21_132 ),
    inference(avatar_split_clause,[],[f1566,f1557,f1111,f5777]) ).

tff(f5777,plain,
    ( spl21_332
  <=> ! [X4: nat,X0: fun(nat,bool),X3: nat,X2: nat,X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ ord_less(nat,X1,sK11(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,[spl21_332])]) ).

tff(f1566,plain,
    ( ! [X2: nat,X3: nat,X0: fun(nat,bool),X1: nat,X4: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ ord_less(nat,X1,sK11(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)) ) )
    | ~ spl21_92
    | ~ spl21_132 ),
    inference(resolution,[],[f1558,f1112]) ).

tff(f5775,plain,
    ( spl21_331
    | ~ spl21_88
    | ~ spl21_127 ),
    inference(avatar_split_clause,[],[f1517,f1503,f1050,f5773]) ).

tff(f5773,plain,
    ( spl21_331
  <=> ! [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,sK18(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1))),sK19(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_331])]) ).

tff(f1050,plain,
    ( spl21_88
  <=> ! [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,[spl21_88])]) ).

tff(f1517,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,sK18(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1))),sK19(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)))) )
    | ~ spl21_88
    | ~ spl21_127 ),
    inference(superposition,[],[f1504,f1051]) ).

tff(f1051,plain,
    ( ! [X0: $tType,X3: X0,X1: nat] : ( aa(X0,nat,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X3)),X3) = X1 )
    | ~ spl21_88 ),
    inference(avatar_component_clause,[],[f1050]) ).

tff(f5771,plain,
    ( spl21_330
    | ~ spl21_88
    | ~ spl21_127 ),
    inference(avatar_split_clause,[],[f1513,f1503,f1050,f5769]) ).

tff(f5769,plain,
    ( spl21_330
  <=> ! [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,sK18(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1))),sK19(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_330])]) ).

tff(f1513,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,sK18(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1))),sK19(huffma1352802255e_freq(nat,huffma2021818691e_Leaf(nat,X0,X1)))) )
    | ~ spl21_88
    | ~ spl21_127 ),
    inference(superposition,[],[f1504,f1051]) ).

tff(f5767,plain,
    ( spl21_329
    | ~ spl21_72
    | ~ spl21_127 ),
    inference(avatar_split_clause,[],[f1512,f1503,f927,f5765]) ).

tff(f5765,plain,
    ( spl21_329
  <=> ! [X2: fun(nat,nat),X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less(nat,sK18(X2),sK19(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,[spl21_329])]) ).

tff(f927,plain,
    ( spl21_72
  <=> ! [X0: nat,X1: nat] :
        ( ord_less(nat,X1,X0)
        | ( X0 = X1 )
        | ~ ord_less_eq(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_72])]) ).

tff(f1512,plain,
    ( ! [X2: fun(nat,nat),X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less(nat,sK18(X2),sK19(X2))
        | ( aa(nat,nat,X2,X1) = aa(nat,nat,X2,X0) )
        | ord_less(nat,aa(nat,nat,X2,X0),aa(nat,nat,X2,X1)) )
    | ~ spl21_72
    | ~ spl21_127 ),
    inference(resolution,[],[f1504,f928]) ).

tff(f928,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X1,X0)
        | ( X0 = X1 )
        | ord_less(nat,X1,X0) )
    | ~ spl21_72 ),
    inference(avatar_component_clause,[],[f927]) ).

tff(f5763,plain,
    ( spl21_328
    | ~ spl21_73
    | ~ spl21_127 ),
    inference(avatar_split_clause,[],[f1511,f1503,f931,f5761]) ).

tff(f5761,plain,
    ( spl21_328
  <=> ! [X2: fun(nat,nat),X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less(nat,sK18(X2),sK19(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,[spl21_328])]) ).

tff(f931,plain,
    ( spl21_73
  <=> ! [X0: nat,X1: nat] :
        ( ( X0 = X1 )
        | ~ ord_less_eq(nat,X0,X1)
        | ~ ord_less_eq(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_73])]) ).

tff(f1511,plain,
    ( ! [X2: fun(nat,nat),X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less(nat,sK18(X2),sK19(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) ) )
    | ~ spl21_73
    | ~ spl21_127 ),
    inference(resolution,[],[f1504,f932]) ).

tff(f932,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X1,X0)
        | ~ ord_less_eq(nat,X0,X1)
        | ( X0 = X1 ) )
    | ~ spl21_73 ),
    inference(avatar_component_clause,[],[f931]) ).

tff(f5759,plain,
    ( spl21_327
    | ~ spl21_125
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1501,f1449,f1445,f5757]) ).

tff(f5757,plain,
    ( spl21_327
  <=> ! [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,[spl21_327])]) ).

tff(f1501,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) )
    | ~ spl21_125
    | ~ spl21_126 ),
    inference(superposition,[],[f1446,f1450]) ).

tff(f5755,plain,
    ( spl21_326
    | ~ spl21_125
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1479,f1449,f1445,f5753]) ).

tff(f5753,plain,
    ( spl21_326
  <=> ! [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,[spl21_326])]) ).

tff(f1479,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) )
    | ~ spl21_125
    | ~ spl21_126 ),
    inference(superposition,[],[f1450,f1446]) ).

tff(f5751,plain,
    ( spl21_325
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1478,f1449,f5749]) ).

tff(f5749,plain,
    ( spl21_325
  <=> ! [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,[spl21_325])]) ).

tff(f1478,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) )
    | ~ spl21_126 ),
    inference(superposition,[],[f1450,f1450]) ).

tff(f5747,plain,
    ( spl21_324
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1459,f1445,f5745]) ).

tff(f5745,plain,
    ( spl21_324
  <=> ! [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,[spl21_324])]) ).

tff(f1459,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) )
    | ~ spl21_125 ),
    inference(superposition,[],[f1446,f1446]) ).

tff(f5743,plain,
    ( spl21_323
    | ~ spl21_63
    | ~ spl21_191 ),
    inference(avatar_split_clause,[],[f3100,f2684,f879,f5741]) ).

tff(f5741,plain,
    ( spl21_323
  <=> ! [X0: a1] : ( zero_zero(nat) = huffma410068972_depth(a1,t_2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_323])]) ).

tff(f879,plain,
    ( spl21_63
  <=> ! [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,[spl21_63])]) ).

tff(f3100,plain,
    ( ! [X0: a1] : ( zero_zero(nat) = huffma410068972_depth(a1,t_2,X0) )
    | ~ spl21_63
    | ~ spl21_191 ),
    inference(superposition,[],[f880,f2686]) ).

tff(f880,plain,
    ( ! [X0: $tType,X2: X0,X3: nat,X1: X0] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) )
    | ~ spl21_63 ),
    inference(avatar_component_clause,[],[f879]) ).

tff(f5724,plain,
    ( spl21_322
    | ~ spl21_91
    | ~ spl21_129 ),
    inference(avatar_split_clause,[],[f1544,f1527,f1107,f5722]) ).

tff(f5722,plain,
    ( spl21_322
  <=> ! [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,[spl21_322])]) ).

tff(f1107,plain,
    ( spl21_91
  <=> ! [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,[spl21_91])]) ).

tff(f1544,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)) ) )
    | ~ spl21_91
    | ~ spl21_129 ),
    inference(resolution,[],[f1528,f1108]) ).

tff(f1108,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)) ) )
    | ~ spl21_91 ),
    inference(avatar_component_clause,[],[f1107]) ).

tff(f5642,plain,
    ( spl21_321
    | ~ spl21_86
    | ~ spl21_146 ),
    inference(avatar_split_clause,[],[f1724,f1706,f1042,f5640]) ).

tff(f5640,plain,
    ( spl21_321
  <=> ! [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,[spl21_321])]) ).

tff(f1724,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 ) )
    | ~ spl21_86
    | ~ spl21_146 ),
    inference(resolution,[],[f1707,f1043]) ).

tff(f5612,plain,
    ( ~ spl21_14
    | spl21_320
    | ~ spl21_29
    | ~ spl21_142 ),
    inference(avatar_split_clause,[],[f1674,f1655,f710,f5610,f641]) ).

tff(f641,plain,
    ( spl21_14
  <=> ord(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_14])]) ).

tff(f5610,plain,
    ( spl21_320
  <=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
        ( ~ ord_less_eq(bool,aa(X0,bool,X2,sK8(bool,X0,X1,X2)),fTrue)
        | ( fFalse = aa(X0,bool,X1,sK8(bool,X0,X1,X2)) )
        | ord_less_eq(fun(X0,bool),X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_320])]) ).

tff(f1674,plain,
    ( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
        ( ~ ord_less_eq(bool,aa(X0,bool,X2,sK8(bool,X0,X1,X2)),fTrue)
        | ord_less_eq(fun(X0,bool),X2,X1)
        | ~ ord(bool)
        | ( fFalse = aa(X0,bool,X1,sK8(bool,X0,X1,X2)) ) )
    | ~ spl21_29
    | ~ spl21_142 ),
    inference(superposition,[],[f1656,f711]) ).

tff(f5608,plain,
    ( spl21_319
    | ~ spl21_59
    | ~ spl21_191 ),
    inference(avatar_split_clause,[],[f3099,f2684,f862,f5605]) ).

tff(f5605,plain,
    ( spl21_319
  <=> ( zero_zero(nat) = size_size(huffma1450048681e_tree(a1),t_2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_319])]) ).

tff(f862,plain,
    ( spl21_59
  <=> ! [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,[spl21_59])]) ).

tff(f3099,plain,
    ( ( zero_zero(nat) = size_size(huffma1450048681e_tree(a1),t_2) )
    | ~ spl21_59
    | ~ spl21_191 ),
    inference(superposition,[],[f863,f2686]) ).

tff(f863,plain,
    ( ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X2,X1)) )
    | ~ spl21_59 ),
    inference(avatar_component_clause,[],[f862]) ).

tff(f5577,plain,
    ( ~ spl21_14
    | spl21_318
    | ~ spl21_29
    | ~ spl21_142 ),
    inference(avatar_split_clause,[],[f1669,f1655,f710,f5575,f641]) ).

tff(f5575,plain,
    ( spl21_318
  <=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
        ( ~ ord_less_eq(bool,fTrue,aa(X0,bool,X2,sK8(bool,X0,X2,X1)))
        | ( fFalse = aa(X0,bool,X1,sK8(bool,X0,X2,X1)) )
        | ord_less_eq(fun(X0,bool),X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_318])]) ).

tff(f1669,plain,
    ( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
        ( ~ ord_less_eq(bool,fTrue,aa(X0,bool,X2,sK8(bool,X0,X2,X1)))
        | ord_less_eq(fun(X0,bool),X1,X2)
        | ~ ord(bool)
        | ( fFalse = aa(X0,bool,X1,sK8(bool,X0,X2,X1)) ) )
    | ~ spl21_29
    | ~ spl21_142 ),
    inference(superposition,[],[f1656,f711]) ).

tff(f5573,plain,
    ( spl21_317
    | ~ spl21_107
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1493,f1449,f1266,f5571]) ).

tff(f5571,plain,
    ( spl21_317
  <=> ! [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,sK5(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,[spl21_317])]) ).

tff(f1266,plain,
    ( spl21_107
  <=> ! [X0: fun(int,bool),X3: nat] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,X3)))
        | ~ pp(aa(int,bool,X0,sK5(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_107])]) ).

tff(f1493,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,sK5(aa(nat,fun(int,bool),X0,X1)))))
        | pp(aa(int,bool,aa(nat,fun(int,bool),X0,X1),semiring_1_of_nat(int,X3))) )
    | ~ spl21_107
    | ~ spl21_126 ),
    inference(superposition,[],[f1267,f1450]) ).

tff(f1267,plain,
    ( ! [X3: nat,X0: fun(int,bool)] :
        ( ~ pp(aa(int,bool,X0,sK5(X0)))
        | pp(aa(int,bool,X0,semiring_1_of_nat(int,X3))) )
    | ~ spl21_107 ),
    inference(avatar_component_clause,[],[f1266]) ).

tff(f5569,plain,
    ( spl21_316
    | ~ spl21_108
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1489,f1449,f1270,f5567]) ).

tff(f5567,plain,
    ( spl21_316
  <=> ! [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),sK6(aa(nat,fun(int,bool),X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_316])]) ).

tff(f1270,plain,
    ( spl21_108
  <=> ! [X2: nat,X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,sK6(X0)))
        | ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_108])]) ).

tff(f1489,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),sK6(aa(nat,fun(int,bool),X0,X1)))) )
    | ~ spl21_108
    | ~ spl21_126 ),
    inference(superposition,[],[f1271,f1450]) ).

tff(f1271,plain,
    ( ! [X2: nat,X0: fun(int,bool)] :
        ( ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,X2)))
        | pp(aa(int,bool,X0,sK6(X0))) )
    | ~ spl21_108 ),
    inference(avatar_component_clause,[],[f1270]) ).

tff(f5565,plain,
    ( spl21_315
    | ~ spl21_107
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1470,f1445,f1266,f5563]) ).

tff(f5563,plain,
    ( spl21_315
  <=> ! [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,sK5(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,[spl21_315])]) ).

tff(f1470,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,sK5(aa(nat,fun(int,bool),X0,X1)))))
        | pp(aa(int,bool,aa(nat,fun(int,bool),X0,X1),semiring_1_of_nat(int,X3))) )
    | ~ spl21_107
    | ~ spl21_125 ),
    inference(superposition,[],[f1267,f1446]) ).

tff(f5561,plain,
    ( spl21_314
    | ~ spl21_108
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1466,f1445,f1270,f5559]) ).

tff(f5559,plain,
    ( spl21_314
  <=> ! [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),sK6(aa(nat,fun(int,bool),X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_314])]) ).

tff(f1466,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),sK6(aa(nat,fun(int,bool),X0,X1)))) )
    | ~ spl21_108
    | ~ spl21_125 ),
    inference(superposition,[],[f1271,f1446]) ).

tff(f5543,plain,
    ( ~ spl21_15
    | spl21_313
    | ~ spl21_74
    | ~ spl21_122 ),
    inference(avatar_split_clause,[],[f1377,f1357,f935,f5541,f646]) ).

tff(f646,plain,
    ( spl21_15
  <=> ord(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_15])]) ).

tff(f5541,plain,
    ( spl21_313
  <=> ! [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,[spl21_313])]) ).

tff(f935,plain,
    ( spl21_74
  <=> ! [X0: int,X1: int] :
        ( ord_less(int,X1,X0)
        | ( X0 = X1 )
        | ~ ord_less_eq(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_74])]) ).

tff(f1377,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)) )
    | ~ spl21_74
    | ~ spl21_122 ),
    inference(resolution,[],[f1358,f936]) ).

tff(f936,plain,
    ( ! [X0: int,X1: int] :
        ( ~ ord_less_eq(int,X1,X0)
        | ( X0 = X1 )
        | ord_less(int,X1,X0) )
    | ~ spl21_74 ),
    inference(avatar_component_clause,[],[f935]) ).

tff(f5519,plain,
    ( ~ spl21_18
    | spl21_312
    | ~ spl21_72
    | ~ spl21_122 ),
    inference(avatar_split_clause,[],[f1376,f1357,f927,f5517,f661]) ).

tff(f5517,plain,
    ( spl21_312
  <=> ! [X0: $tType,X3: X0,X2: fun(X0,nat),X1: fun(X0,nat)] :
        ( ~ ord_less_eq(fun(X0,nat),X1,X2)
        | ord_less(nat,aa(X0,nat,X1,X3),aa(X0,nat,X2,X3))
        | ( aa(X0,nat,X2,X3) = aa(X0,nat,X1,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_312])]) ).

tff(f1376,plain,
    ( ! [X0: $tType,X2: fun(X0,nat),X3: X0,X1: fun(X0,nat)] :
        ( ~ ord_less_eq(fun(X0,nat),X1,X2)
        | ~ ord(nat)
        | ( aa(X0,nat,X2,X3) = aa(X0,nat,X1,X3) )
        | ord_less(nat,aa(X0,nat,X1,X3),aa(X0,nat,X2,X3)) )
    | ~ spl21_72
    | ~ spl21_122 ),
    inference(resolution,[],[f1358,f928]) ).

tff(f5515,plain,
    ( spl21_228
    | ~ spl21_301 ),
    inference(avatar_contradiction_clause,[],[f5514]) ).

tff(f5514,plain,
    ( $false
    | spl21_228
    | ~ spl21_301 ),
    inference(trivial_inequality_removal,[],[f5513]) ).

tff(f5513,plain,
    ( ( a != a )
    | spl21_228
    | ~ spl21_301 ),
    inference(superposition,[],[f3402,f5132]) ).

tff(f5132,plain,
    ( ! [X0: a1] : ( huffma1401021291ibling(a1,t_2,X0) = X0 )
    | ~ spl21_301 ),
    inference(avatar_component_clause,[],[f5131]) ).

tff(f5131,plain,
    ( spl21_301
  <=> ! [X0: a1] : ( huffma1401021291ibling(a1,t_2,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_301])]) ).

tff(f3402,plain,
    ( ( a != huffma1401021291ibling(a1,t_2,a) )
    | spl21_228 ),
    inference(avatar_component_clause,[],[f3400]) ).

tff(f5483,plain,
    ( ~ spl21_18
    | spl21_311
    | ~ spl21_73
    | ~ spl21_122 ),
    inference(avatar_split_clause,[],[f1375,f1357,f931,f5481,f661]) ).

tff(f5481,plain,
    ( spl21_311
  <=> ! [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,[spl21_311])]) ).

tff(f1375,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) ) )
    | ~ spl21_73
    | ~ spl21_122 ),
    inference(resolution,[],[f1358,f932]) ).

tff(f5169,plain,
    ( spl21_310
    | ~ spl21_125
    | ~ spl21_149 ),
    inference(avatar_split_clause,[],[f1747,f1739,f1445,f5167]) ).

tff(f5167,plain,
    ( spl21_310
  <=> ! [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,[spl21_310])]) ).

tff(f1747,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) )
    | ~ spl21_125
    | ~ spl21_149 ),
    inference(superposition,[],[f1740,f1446]) ).

tff(f5165,plain,
    ( spl21_309
    | ~ spl21_126
    | ~ spl21_149 ),
    inference(avatar_split_clause,[],[f1746,f1739,f1449,f5163]) ).

tff(f5163,plain,
    ( spl21_309
  <=> ! [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,[spl21_309])]) ).

tff(f1746,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) )
    | ~ spl21_126
    | ~ spl21_149 ),
    inference(superposition,[],[f1740,f1450]) ).

tff(f5161,plain,
    ( spl21_308
    | ~ spl21_135
    | ~ spl21_146 ),
    inference(avatar_split_clause,[],[f1725,f1706,f1586,f5159]) ).

tff(f5159,plain,
    ( spl21_308
  <=> ! [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,sK15(X0,X1),sK16(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_308])]) ).

tff(f1725,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,sK15(X0,X1),sK16(X0,X1)) = X1 ) )
    | ~ spl21_135
    | ~ spl21_146 ),
    inference(superposition,[],[f1707,f1587]) ).

tff(f5157,plain,
    ( spl21_307
    | ~ spl21_56
    | ~ spl21_142 ),
    inference(avatar_split_clause,[],[f1665,f1655,f850,f5155]) ).

tff(f5155,plain,
    ( spl21_307
  <=> ! [X1: $tType,X0: $tType,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,sK8(X1,X0,X3,X2)),aa(X0,X1,X2,sK8(X1,X0,X3,X2)))
        | ~ linorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_307])]) ).

tff(f850,plain,
    ( spl21_56
  <=> ! [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,[spl21_56])]) ).

tff(f1665,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(X0,X1),X3: fun(X0,X1)] :
        ( ord_less_eq(fun(X0,X1),X2,X3)
        | ~ ord(X1)
        | ord_less_eq(X1,aa(X0,X1,X3,sK8(X1,X0,X3,X2)),aa(X0,X1,X2,sK8(X1,X0,X3,X2)))
        | ~ linorder(X1) )
    | ~ spl21_56
    | ~ spl21_142 ),
    inference(resolution,[],[f1656,f851]) ).

tff(f851,plain,
    ( ! [X0: $tType,X2: X0,X1: X0] :
        ( ord_less_eq(X0,X2,X1)
        | ord_less_eq(X0,X1,X2)
        | ~ linorder(X0) )
    | ~ spl21_56 ),
    inference(avatar_component_clause,[],[f850]) ).

tff(f5153,plain,
    ( spl21_306
    | ~ spl21_122
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1486,f1449,f1357,f5151]) ).

tff(f5151,plain,
    ( spl21_306
  <=> ! [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,[spl21_306])]) ).

tff(f1486,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) )
    | ~ spl21_122
    | ~ spl21_126 ),
    inference(superposition,[],[f1358,f1450]) ).

tff(f5149,plain,
    ( spl21_305
    | ~ spl21_122
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1485,f1449,f1357,f5147]) ).

tff(f5147,plain,
    ( spl21_305
  <=> ! [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,[spl21_305])]) ).

tff(f1485,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) )
    | ~ spl21_122
    | ~ spl21_126 ),
    inference(superposition,[],[f1358,f1450]) ).

tff(f5145,plain,
    ( spl21_304
    | ~ spl21_122
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1463,f1445,f1357,f5143]) ).

tff(f5143,plain,
    ( spl21_304
  <=> ! [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,[spl21_304])]) ).

tff(f1463,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) )
    | ~ spl21_122
    | ~ spl21_125 ),
    inference(superposition,[],[f1358,f1446]) ).

tff(f5141,plain,
    ( spl21_303
    | ~ spl21_122
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1462,f1445,f1357,f5139]) ).

tff(f5139,plain,
    ( spl21_303
  <=> ! [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,[spl21_303])]) ).

tff(f1462,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) )
    | ~ spl21_122
    | ~ spl21_125 ),
    inference(superposition,[],[f1358,f1446]) ).

tff(f5137,plain,
    ( spl21_302
    | ~ spl21_91
    | ~ spl21_124 ),
    inference(avatar_split_clause,[],[f1455,f1389,f1107,f5135]) ).

tff(f5135,plain,
    ( spl21_302
  <=> ! [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,sK10(X1,X0)),X2,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_302])]) ).

tff(f1455,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,sK10(X1,X0)),X2,X3)) ) )
    | ~ spl21_91
    | ~ spl21_124 ),
    inference(resolution,[],[f1390,f1108]) ).

tff(f5133,plain,
    ( spl21_301
    | ~ spl21_55
    | ~ spl21_191 ),
    inference(avatar_split_clause,[],[f3098,f2684,f826,f5131]) ).

tff(f826,plain,
    ( spl21_55
  <=> ! [X0: $tType,X3: nat,X2: X0,X1: X0] : ( huffma1401021291ibling(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_55])]) ).

tff(f3098,plain,
    ( ! [X0: a1] : ( huffma1401021291ibling(a1,t_2,X0) = X0 )
    | ~ spl21_55
    | ~ spl21_191 ),
    inference(superposition,[],[f827,f2686]) ).

tff(f827,plain,
    ( ! [X0: $tType,X2: X0,X3: nat,X1: X0] : ( huffma1401021291ibling(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) = X1 )
    | ~ spl21_55 ),
    inference(avatar_component_clause,[],[f826]) ).

tff(f5073,plain,
    ( spl21_300
    | ~ spl21_92
    | ~ spl21_123 ),
    inference(avatar_split_clause,[],[f1385,f1361,f1111,f5071]) ).

tff(f5071,plain,
    ( spl21_300
  <=> ! [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,sK11(X0)),X3,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_300])]) ).

tff(f1385,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,sK11(X0)),X3,X2)) ) )
    | ~ spl21_92
    | ~ spl21_123 ),
    inference(resolution,[],[f1362,f1112]) ).

tff(f5069,plain,
    ( spl21_299
    | ~ spl21_92
    | ~ spl21_121 ),
    inference(avatar_split_clause,[],[f1371,f1353,f1111,f5067]) ).

tff(f5067,plain,
    ( spl21_299
  <=> ! [X0: fun(int,bool),X3: nat,X2: nat,X1: int] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK7(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,[spl21_299])]) ).

tff(f1371,plain,
    ( ! [X2: nat,X3: nat,X0: fun(int,bool),X1: int] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK7(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)) ) )
    | ~ spl21_92
    | ~ spl21_121 ),
    inference(resolution,[],[f1354,f1112]) ).

tff(f5065,plain,
    ( spl21_298
    | ~ spl21_92
    | ~ spl21_120 ),
    inference(avatar_split_clause,[],[f1366,f1349,f1111,f5063]) ).

tff(f5063,plain,
    ( spl21_298
  <=> ! [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,sK4(X1))),X3,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_298])]) ).

tff(f1366,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,sK4(X1))),X3,X2)) ) )
    | ~ spl21_92
    | ~ spl21_120 ),
    inference(resolution,[],[f1350,f1112]) ).

tff(f5001,plain,
    ( spl21_106
    | ~ spl21_53
    | ~ spl21_191 ),
    inference(avatar_split_clause,[],[f3097,f2684,f818,f1212]) ).

tff(f1212,plain,
    ( spl21_106
  <=> ( zero_zero(nat) = huffma945805758height(a1,t_2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_106])]) ).

tff(f818,plain,
    ( spl21_53
  <=> ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_53])]) ).

tff(f3097,plain,
    ( ( zero_zero(nat) = huffma945805758height(a1,t_2) )
    | ~ spl21_53
    | ~ spl21_191 ),
    inference(superposition,[],[f819,f2686]) ).

tff(f819,plain,
    ( ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X2,X1)) )
    | ~ spl21_53 ),
    inference(avatar_component_clause,[],[f818]) ).

tff(f4949,plain,
    ( spl21_297
    | ~ spl21_144 ),
    inference(avatar_split_clause,[],[f1699,f1682,f4947]) ).

tff(f4947,plain,
    ( spl21_297
  <=> ! [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,[spl21_297])]) ).

tff(f1699,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 ) )
    | ~ spl21_144 ),
    inference(factoring,[],[f1683]) ).

tff(f4924,plain,
    ( ~ spl21_18
    | spl21_296
    | ~ spl21_40
    | ~ spl21_142 ),
    inference(avatar_split_clause,[],[f1660,f1655,f763,f4922,f661]) ).

tff(f4922,plain,
    ( spl21_296
  <=> ! [X0: $tType,X2: fun(X0,nat),X1: fun(X0,nat)] :
        ( ord_less_eq(fun(X0,nat),X1,X2)
        | ord_less_eq(nat,aa(X0,nat,X2,sK8(nat,X0,X2,X1)),aa(X0,nat,X1,sK8(nat,X0,X2,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_296])]) ).

tff(f763,plain,
    ( spl21_40
  <=> ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ord_less_eq(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_40])]) ).

tff(f1660,plain,
    ( ! [X0: $tType,X2: fun(X0,nat),X1: fun(X0,nat)] :
        ( ord_less_eq(fun(X0,nat),X1,X2)
        | ~ ord(nat)
        | ord_less_eq(nat,aa(X0,nat,X2,sK8(nat,X0,X2,X1)),aa(X0,nat,X1,sK8(nat,X0,X2,X1))) )
    | ~ spl21_40
    | ~ spl21_142 ),
    inference(resolution,[],[f1656,f764]) ).

tff(f764,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,X0,X1)
        | ord_less_eq(nat,X1,X0) )
    | ~ spl21_40 ),
    inference(avatar_component_clause,[],[f763]) ).

tff(f4920,plain,
    ( spl21_295
    | ~ spl21_111
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1500,f1449,f1293,f4918]) ).

tff(f4918,plain,
    ( spl21_295
  <=> ! [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,[spl21_295])]) ).

tff(f1500,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)) )
    | ~ spl21_111
    | ~ spl21_126 ),
    inference(superposition,[],[f1294,f1450]) ).

tff(f4916,plain,
    ( spl21_294
    | ~ spl21_111
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1477,f1445,f1293,f4914]) ).

tff(f4914,plain,
    ( spl21_294
  <=> ! [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,[spl21_294])]) ).

tff(f1477,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)) )
    | ~ spl21_111
    | ~ spl21_125 ),
    inference(superposition,[],[f1294,f1446]) ).

tff(f4912,plain,
    ( spl21_293
    | ~ spl21_92
    | ~ spl21_118 ),
    inference(avatar_split_clause,[],[f1344,f1332,f1111,f4910]) ).

tff(f4910,plain,
    ( spl21_293
  <=> ! [X0: fun(nat,bool),X3: nat,X2: nat,X1: nat] :
        ( ord_less(nat,zero_zero(nat),sK11(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,[spl21_293])]) ).

tff(f1344,plain,
    ( ! [X2: nat,X3: nat,X0: fun(nat,bool),X1: nat] :
        ( ord_less(nat,zero_zero(nat),sK11(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)) ) )
    | ~ spl21_92
    | ~ spl21_118 ),
    inference(resolution,[],[f1333,f1112]) ).

tff(f4908,plain,
    ( spl21_292
    | ~ spl21_92
    | ~ spl21_117 ),
    inference(avatar_split_clause,[],[f1340,f1328,f1111,f4906]) ).

tff(f4906,plain,
    ( spl21_292
  <=> ! [X0: nat,X3: nat,X2: nat,X1: fun(nat,bool)] :
        ( ord_less_eq(nat,sK10(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,[spl21_292])]) ).

tff(f1340,plain,
    ( ! [X2: nat,X3: nat,X0: nat,X1: fun(nat,bool)] :
        ( ord_less_eq(nat,sK10(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)) ) )
    | ~ spl21_92
    | ~ spl21_117 ),
    inference(resolution,[],[f1329,f1112]) ).

tff(f4862,plain,
    ( spl21_291
    | ~ spl21_52
    | ~ spl21_191 ),
    inference(avatar_split_clause,[],[f3096,f2684,f814,f4859]) ).

tff(f4859,plain,
    ( spl21_291
  <=> ( zero_zero(nat) = huffma1134658180e_cost(a1,t_2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_291])]) ).

tff(f814,plain,
    ( spl21_52
  <=> ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma1134658180e_cost(X0,huffma2021818691e_Leaf(X0,X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_52])]) ).

tff(f3096,plain,
    ( ( zero_zero(nat) = huffma1134658180e_cost(a1,t_2) )
    | ~ spl21_52
    | ~ spl21_191 ),
    inference(superposition,[],[f815,f2686]) ).

tff(f815,plain,
    ( ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma1134658180e_cost(X0,huffma2021818691e_Leaf(X0,X2,X1)) )
    | ~ spl21_52 ),
    inference(avatar_component_clause,[],[f814]) ).

tff(f4808,plain,
    ( spl21_290
    | ~ spl21_29
    | ~ spl21_142 ),
    inference(avatar_split_clause,[],[f1671,f1655,f710,f4806]) ).

tff(f4806,plain,
    ( spl21_290
  <=> ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
        ( ~ ord_less_eq(X0,aa(bool,X0,X2,fTrue),aa(bool,X0,X1,fTrue))
        | ord_less_eq(fun(bool,X0),X2,X1)
        | ~ ord(X0)
        | ( fFalse = sK8(X0,bool,X1,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_290])]) ).

tff(f1671,plain,
    ( ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
        ( ~ ord_less_eq(X0,aa(bool,X0,X2,fTrue),aa(bool,X0,X1,fTrue))
        | ord_less_eq(fun(bool,X0),X2,X1)
        | ~ ord(X0)
        | ( fFalse = sK8(X0,bool,X1,X2) ) )
    | ~ spl21_29
    | ~ spl21_142 ),
    inference(superposition,[],[f1656,f711]) ).

tff(f4804,plain,
    ( spl21_289
    | ~ spl21_124
    | ~ spl21_134 ),
    inference(avatar_split_clause,[],[f1597,f1582,f1389,f4802]) ).

tff(f4802,plain,
    ( spl21_289
  <=> ! [X2: nat,X0: nat,X1: fun(nat,bool)] :
        ( ~ ord_less(nat,sK10(X0,X1),sK10(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,[spl21_289])]) ).

tff(f1597,plain,
    ( ! [X2: nat,X0: nat,X1: fun(nat,bool)] :
        ( ~ ord_less(nat,sK10(X0,X1),sK10(X2,X1))
        | ~ pp(aa(nat,bool,X1,X2))
        | pp(aa(nat,bool,X1,zero_zero(nat)))
        | ~ pp(aa(nat,bool,X1,X0)) )
    | ~ spl21_124
    | ~ spl21_134 ),
    inference(duplicate_literal_removal,[],[f1589]) ).

tff(f1589,plain,
    ( ! [X2: nat,X0: nat,X1: fun(nat,bool)] :
        ( ~ ord_less(nat,sK10(X0,X1),sK10(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))) )
    | ~ spl21_124
    | ~ spl21_134 ),
    inference(resolution,[],[f1583,f1390]) ).

tff(f4800,plain,
    ( spl21_288
    | ~ spl21_29
    | ~ spl21_133 ),
    inference(avatar_split_clause,[],[f1578,f1561,f710,f4798]) ).

tff(f4798,plain,
    ( spl21_288
  <=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
        ( ( fTrue != aa(X0,bool,X2,sK20(bool,X0,X1,X2)) )
        | ( X1 = X2 )
        | ( fFalse = aa(X0,bool,X1,sK20(bool,X0,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_288])]) ).

tff(f1578,plain,
    ( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
        ( ( fTrue != aa(X0,bool,X2,sK20(bool,X0,X1,X2)) )
        | ( X1 = X2 )
        | ( fFalse = aa(X0,bool,X1,sK20(bool,X0,X1,X2)) ) )
    | ~ spl21_29
    | ~ spl21_133 ),
    inference(superposition,[],[f1562,f711]) ).

tff(f4796,plain,
    ( spl21_287
    | ~ spl21_29
    | ~ spl21_133 ),
    inference(avatar_split_clause,[],[f1573,f1561,f710,f4794]) ).

tff(f4794,plain,
    ( spl21_287
  <=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
        ( ( fTrue != aa(X0,bool,X2,sK20(bool,X0,X2,X1)) )
        | ( X1 = X2 )
        | ( fFalse = aa(X0,bool,X1,sK20(bool,X0,X2,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_287])]) ).

tff(f1573,plain,
    ( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
        ( ( fTrue != aa(X0,bool,X2,sK20(bool,X0,X2,X1)) )
        | ( X1 = X2 )
        | ( fFalse = aa(X0,bool,X1,sK20(bool,X0,X2,X1)) ) )
    | ~ spl21_29
    | ~ spl21_133 ),
    inference(superposition,[],[f1562,f711]) ).

tff(f4792,plain,
    ( spl21_286
    | ~ spl21_110
    | ~ spl21_131 ),
    inference(avatar_split_clause,[],[f1552,f1536,f1289,f4790]) ).

tff(f4790,plain,
    ( spl21_286
  <=> ! [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,[spl21_286])]) ).

tff(f1552,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) ) )
    | ~ spl21_110
    | ~ spl21_131 ),
    inference(resolution,[],[f1537,f1290]) ).

tff(f4788,plain,
    ( spl21_94
    | ~ spl21_136
    | ~ spl21_258 ),
    inference(avatar_split_clause,[],[f4069,f4001,f1599,f1119]) ).

tff(f1119,plain,
    ( spl21_94
  <=> ( a = huffma1401021291ibling(a1,t_1,a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_94])]) ).

tff(f4772,plain,
    ( spl21_285
    | ~ spl21_85
    | ~ spl21_127 ),
    inference(avatar_split_clause,[],[f1510,f1503,f1038,f4770]) ).

tff(f4770,plain,
    ( spl21_285
  <=> ! [X0: nat,X3: nat,X2: fun(nat,nat),X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less(nat,sK18(X2),sK19(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,[spl21_285])]) ).

tff(f1038,plain,
    ( spl21_85
  <=> ! [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,[spl21_85])]) ).

tff(f1510,plain,
    ( ! [X2: fun(nat,nat),X3: nat,X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less(nat,sK18(X2),sK19(X2))
        | ~ ord_less_eq(nat,aa(nat,nat,X2,X1),X3)
        | ord_less_eq(nat,aa(nat,nat,X2,X0),X3) )
    | ~ spl21_85
    | ~ spl21_127 ),
    inference(resolution,[],[f1504,f1039]) ).

tff(f1039,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) )
    | ~ spl21_85 ),
    inference(avatar_component_clause,[],[f1038]) ).

tff(f4680,plain,
    ( spl21_284
    | ~ spl21_50
    | ~ spl21_141 ),
    inference(avatar_split_clause,[],[f1650,f1626,f806,f4678]) ).

tff(f4678,plain,
    ( spl21_284
  <=> ! [X0: $tType,X4: huffma1450048681e_tree(X0),X3: nat,X2: huffma1450048681e_tree(X0),X1: X0] :
        ( ~ member(X0,X1,huffma675207370phabet(X0,X2))
        | ( huffma1401021291ibling(X0,X2,X1) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X2,X4),X1) )
        | ( zero_zero(nat) = huffma945805758height(X0,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_284])]) ).

tff(f806,plain,
    ( spl21_50
  <=> ! [X0: nat] :
        ( ord_less(nat,zero_zero(nat),X0)
        | ( zero_zero(nat) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_50])]) ).

tff(f1626,plain,
    ( spl21_141
  <=> ! [X0: $tType,X4: huffma1450048681e_tree(X0),X3: X0,X2: nat,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,X4,X3) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) )
        | ~ member(X0,X3,huffma675207370phabet(X0,X4))
        | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_141])]) ).

tff(f1650,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: X0,X4: huffma1450048681e_tree(X0)] :
        ( ~ member(X0,X1,huffma675207370phabet(X0,X2))
        | ( huffma1401021291ibling(X0,X2,X1) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X2,X4),X1) )
        | ( zero_zero(nat) = huffma945805758height(X0,X2) ) )
    | ~ spl21_50
    | ~ spl21_141 ),
    inference(resolution,[],[f1627,f807]) ).

tff(f807,plain,
    ( ! [X0: nat] :
        ( ord_less(nat,zero_zero(nat),X0)
        | ( zero_zero(nat) = X0 ) )
    | ~ spl21_50 ),
    inference(avatar_component_clause,[],[f806]) ).

tff(f1627,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0)] :
        ( ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4))
        | ~ member(X0,X3,huffma675207370phabet(X0,X4))
        | ( huffma1401021291ibling(X0,X4,X3) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) ) )
    | ~ spl21_141 ),
    inference(avatar_component_clause,[],[f1626]) ).

tff(f4676,plain,
    ( spl21_283
    | ~ spl21_50
    | ~ spl21_140 ),
    inference(avatar_split_clause,[],[f1644,f1622,f806,f4674]) ).

tff(f4674,plain,
    ( spl21_283
  <=> ! [X0: $tType,X4: huffma1450048681e_tree(X0),X3: nat,X2: huffma1450048681e_tree(X0),X1: X0] :
        ( ~ member(X0,X1,huffma675207370phabet(X0,X2))
        | ( huffma1401021291ibling(X0,X2,X1) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X2,X4),X1) )
        | ( zero_zero(nat) = huffma945805758height(X0,X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_283])]) ).

tff(f1622,plain,
    ( spl21_140
  <=> ! [X0: $tType,X4: huffma1450048681e_tree(X0),X3: X0,X2: huffma1450048681e_tree(X0),X1: nat] :
        ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) = huffma1401021291ibling(X0,X2,X3) )
        | ~ member(X0,X3,huffma675207370phabet(X0,X2))
        | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_140])]) ).

tff(f1644,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: X0,X4: huffma1450048681e_tree(X0)] :
        ( ~ member(X0,X1,huffma675207370phabet(X0,X2))
        | ( huffma1401021291ibling(X0,X2,X1) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X3,X2,X4),X1) )
        | ( zero_zero(nat) = huffma945805758height(X0,X4) ) )
    | ~ spl21_50
    | ~ spl21_140 ),
    inference(resolution,[],[f1623,f807]) ).

tff(f1623,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: X0,X1: nat,X4: huffma1450048681e_tree(X0)] :
        ( ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4))
        | ~ member(X0,X3,huffma675207370phabet(X0,X2))
        | ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) = huffma1401021291ibling(X0,X2,X3) ) )
    | ~ spl21_140 ),
    inference(avatar_component_clause,[],[f1622]) ).

tff(f4672,plain,
    ( spl21_282
    | ~ spl21_50
    | ~ spl21_139 ),
    inference(avatar_split_clause,[],[f1638,f1618,f806,f4670]) ).

tff(f4670,plain,
    ( spl21_282
  <=> ! [X0: $tType,X4: nat,X3: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X1: X0] :
        ( member(X0,X1,huffma675207370phabet(X0,X2))
        | ( huffma1401021291ibling(X0,X3,X1) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X2,X3),X1) )
        | ( zero_zero(nat) = huffma945805758height(X0,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_282])]) ).

tff(f1618,plain,
    ( spl21_139
  <=> ! [X0: $tType,X4: huffma1450048681e_tree(X0),X3: X0,X2: nat,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma1401021291ibling(X0,X1,X3) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) )
        | member(X0,X3,huffma675207370phabet(X0,X4))
        | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_139])]) ).

tff(f1638,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X1: X0,X4: nat] :
        ( member(X0,X1,huffma675207370phabet(X0,X2))
        | ( huffma1401021291ibling(X0,X3,X1) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X2,X3),X1) )
        | ( zero_zero(nat) = huffma945805758height(X0,X2) ) )
    | ~ spl21_50
    | ~ spl21_139 ),
    inference(resolution,[],[f1619,f807]) ).

tff(f1619,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0)] :
        ( ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4))
        | member(X0,X3,huffma675207370phabet(X0,X4))
        | ( huffma1401021291ibling(X0,X1,X3) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) ) )
    | ~ spl21_139 ),
    inference(avatar_component_clause,[],[f1618]) ).

tff(f4668,plain,
    ( spl21_281
    | ~ spl21_50
    | ~ spl21_138 ),
    inference(avatar_split_clause,[],[f1632,f1614,f806,f4666]) ).

tff(f4666,plain,
    ( spl21_281
  <=> ! [X0: $tType,X4: nat,X3: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X1: X0] :
        ( member(X0,X1,huffma675207370phabet(X0,X2))
        | ( huffma1401021291ibling(X0,X3,X1) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X2,X3),X1) )
        | ( zero_zero(nat) = huffma945805758height(X0,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_281])]) ).

tff(f1614,plain,
    ( spl21_138
  <=> ! [X0: $tType,X4: huffma1450048681e_tree(X0),X3: X0,X2: huffma1450048681e_tree(X0),X1: nat] :
        ( ( huffma1401021291ibling(X0,X4,X3) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) )
        | member(X0,X3,huffma675207370phabet(X0,X2))
        | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_138])]) ).

tff(f1632,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X1: X0,X4: nat] :
        ( member(X0,X1,huffma675207370phabet(X0,X2))
        | ( huffma1401021291ibling(X0,X3,X1) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X4,X2,X3),X1) )
        | ( zero_zero(nat) = huffma945805758height(X0,X3) ) )
    | ~ spl21_50
    | ~ spl21_138 ),
    inference(resolution,[],[f1615,f807]) ).

tff(f1615,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: X0,X1: nat,X4: huffma1450048681e_tree(X0)] :
        ( ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4))
        | member(X0,X3,huffma675207370phabet(X0,X2))
        | ( huffma1401021291ibling(X0,X4,X3) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) ) )
    | ~ spl21_138 ),
    inference(avatar_component_clause,[],[f1614]) ).

tff(f4664,plain,
    ( spl21_280
    | ~ spl21_114
    | ~ spl21_135 ),
    inference(avatar_split_clause,[],[f1607,f1586,f1305,f4662]) ).

tff(f4662,plain,
    ( spl21_280
  <=> ! [X0: $tType,X4: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X2: nat,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma1146269203erNode(X0,X2,X3,X4) != X1 )
        | ( sK14(X0,X1) = X4 )
        | ( huffma2021818691e_Leaf(X0,sK15(X0,X1),sK16(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_280])]) ).

tff(f1305,plain,
    ( spl21_114
  <=> ! [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,[spl21_114])]) ).

tff(f1607,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0)] :
        ( ( huffma1146269203erNode(X0,X2,X3,X4) != X1 )
        | ( sK14(X0,X1) = X4 )
        | ( huffma2021818691e_Leaf(X0,sK15(X0,X1),sK16(X0,X1)) = X1 ) )
    | ~ spl21_114
    | ~ spl21_135 ),
    inference(superposition,[],[f1306,f1587]) ).

tff(f1306,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 ) )
    | ~ spl21_114 ),
    inference(avatar_component_clause,[],[f1305]) ).

tff(f4660,plain,
    ( spl21_279
    | ~ spl21_113
    | ~ spl21_135 ),
    inference(avatar_split_clause,[],[f1605,f1586,f1301,f4658]) ).

tff(f4658,plain,
    ( spl21_279
  <=> ! [X0: $tType,X4: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X2: nat,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma1146269203erNode(X0,X2,X3,X4) != X1 )
        | ( sK13(X0,X1) = X3 )
        | ( huffma2021818691e_Leaf(X0,sK15(X0,X1),sK16(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_279])]) ).

tff(f1301,plain,
    ( spl21_113
  <=> ! [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,[spl21_113])]) ).

tff(f1605,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0)] :
        ( ( huffma1146269203erNode(X0,X2,X3,X4) != X1 )
        | ( sK13(X0,X1) = X3 )
        | ( huffma2021818691e_Leaf(X0,sK15(X0,X1),sK16(X0,X1)) = X1 ) )
    | ~ spl21_113
    | ~ spl21_135 ),
    inference(superposition,[],[f1302,f1587]) ).

tff(f1302,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 ) )
    | ~ spl21_113 ),
    inference(avatar_component_clause,[],[f1301]) ).

tff(f4656,plain,
    ( spl21_278
    | ~ spl21_29
    | ~ spl21_128 ),
    inference(avatar_split_clause,[],[f1523,f1507,f710,f4654]) ).

tff(f4654,plain,
    ( spl21_278
  <=> ! [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,[spl21_278])]) ).

tff(f1507,plain,
    ( spl21_128
  <=> ! [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,[spl21_128])]) ).

tff(f1523,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) ) )
    | ~ spl21_29
    | ~ spl21_128 ),
    inference(superposition,[],[f1508,f711]) ).

tff(f1508,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 ) )
    | ~ spl21_128 ),
    inference(avatar_component_clause,[],[f1507]) ).

tff(f4646,plain,
    ( ~ spl21_18
    | spl21_277
    | ~ spl21_112
    | ~ spl21_122 ),
    inference(avatar_split_clause,[],[f1383,f1357,f1297,f4644,f661]) ).

tff(f4644,plain,
    ( spl21_277
  <=> ! [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,[spl21_277])]) ).

tff(f1383,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 ) )
    | ~ spl21_112
    | ~ spl21_122 ),
    inference(superposition,[],[f1358,f1298]) ).

tff(f4642,plain,
    ( spl21_276
    | ~ spl21_92
    | ~ spl21_111 ),
    inference(avatar_split_clause,[],[f1314,f1293,f1111,f4640]) ).

tff(f4640,plain,
    ( spl21_276
  <=> ! [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,[spl21_276])]) ).

tff(f1314,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)) ) )
    | ~ spl21_92
    | ~ spl21_111 ),
    inference(resolution,[],[f1294,f1112]) ).

tff(f4638,plain,
    ( spl21_275
    | ~ spl21_33
    | ~ spl21_191 ),
    inference(avatar_split_clause,[],[f3095,f2684,f726,f4635]) ).

tff(f4635,plain,
    ( spl21_275
  <=> huffma1518433673istent(a1,t_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_275])]) ).

tff(f726,plain,
    ( spl21_33
  <=> ! [X0: $tType,X2: nat,X1: X0] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_33])]) ).

tff(f3095,plain,
    ( huffma1518433673istent(a1,t_2)
    | ~ spl21_33
    | ~ spl21_191 ),
    inference(superposition,[],[f727,f2686]) ).

tff(f727,plain,
    ( ! [X0: $tType,X2: nat,X1: X0] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1))
    | ~ spl21_33 ),
    inference(avatar_component_clause,[],[f726]) ).

tff(f4390,plain,
    ( spl21_25
    | ~ spl21_270 ),
    inference(avatar_contradiction_clause,[],[f4389]) ).

tff(f4389,plain,
    ( $false
    | spl21_25
    | ~ spl21_270 ),
    inference(trivial_inequality_removal,[],[f4387]) ).

tff(f4387,plain,
    ( ( huffma1401021291ibling(a1,t_2,a) != huffma1401021291ibling(a1,t_2,a) )
    | spl21_25
    | ~ spl21_270 ),
    inference(superposition,[],[f694,f4164]) ).

tff(f4164,plain,
    ( ! [X0: nat] : ( huffma1401021291ibling(a1,t_2,a) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,t_2),a) )
    | ~ spl21_270 ),
    inference(avatar_component_clause,[],[f4163]) ).

tff(f4163,plain,
    ( spl21_270
  <=> ! [X0: nat] : ( huffma1401021291ibling(a1,t_2,a) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,t_2),a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_270])]) ).

tff(f4181,plain,
    ( spl21_274
    | ~ spl21_109
    | ~ spl21_135 ),
    inference(avatar_split_clause,[],[f1603,f1586,f1274,f4179]) ).

tff(f4179,plain,
    ( spl21_274
  <=> ! [X0: $tType,X4: huffma1450048681e_tree(X0),X3: huffma1450048681e_tree(X0),X2: nat,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma1146269203erNode(X0,X2,X3,X4) != X1 )
        | ( sK12(X0,X1) = X2 )
        | ( huffma2021818691e_Leaf(X0,sK15(X0,X1),sK16(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_274])]) ).

tff(f1274,plain,
    ( spl21_109
  <=> ! [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,[spl21_109])]) ).

tff(f1603,plain,
    ( ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0)] :
        ( ( huffma1146269203erNode(X0,X2,X3,X4) != X1 )
        | ( sK12(X0,X1) = X2 )
        | ( huffma2021818691e_Leaf(X0,sK15(X0,X1),sK16(X0,X1)) = X1 ) )
    | ~ spl21_109
    | ~ spl21_135 ),
    inference(superposition,[],[f1275,f1587]) ).

tff(f1275,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 ) )
    | ~ spl21_109 ),
    inference(avatar_component_clause,[],[f1274]) ).

tff(f4177,plain,
    ( spl21_273
    | ~ spl21_71
    | ~ spl21_131 ),
    inference(avatar_split_clause,[],[f1551,f1536,f923,f4175]) ).

tff(f4175,plain,
    ( spl21_273
  <=> ! [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)),sK9(X0,X2)) = huffma1401021291ibling(X0,X2,sK9(X0,X2)) )
        | ~ huffma1518433673istent(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_273])]) ).

tff(f1551,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)),sK9(X0,X2)) = huffma1401021291ibling(X0,X2,sK9(X0,X2)) )
        | ~ huffma1518433673istent(X0,X2) )
    | ~ spl21_71
    | ~ spl21_131 ),
    inference(resolution,[],[f1537,f924]) ).

tff(f4173,plain,
    ( spl21_272
    | ~ spl21_104
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1491,f1449,f1175,f4171]) ).

tff(f4171,plain,
    ( spl21_272
  <=> ! [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),sK5(aa(nat,fun(int,bool),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_272])]) ).

tff(f1175,plain,
    ( spl21_104
  <=> ! [X0: fun(int,bool),X3: nat] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,X3)))
        | ord_less_eq(int,zero_zero(int),sK5(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_104])]) ).

tff(f1491,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),sK5(aa(nat,fun(int,bool),X0,X1))) )
    | ~ spl21_104
    | ~ spl21_126 ),
    inference(superposition,[],[f1176,f1450]) ).

tff(f1176,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),sK5(X0)) )
    | ~ spl21_104 ),
    inference(avatar_component_clause,[],[f1175]) ).

tff(f4169,plain,
    ( spl21_271
    | ~ spl21_105
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1490,f1449,f1179,f4167]) ).

tff(f4167,plain,
    ( spl21_271
  <=> ! [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),sK6(aa(nat,fun(int,bool),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_271])]) ).

tff(f1179,plain,
    ( spl21_105
  <=> ! [X2: nat,X0: fun(int,bool)] :
        ( ord_less_eq(int,zero_zero(int),sK6(X0))
        | ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_105])]) ).

tff(f1490,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),sK6(aa(nat,fun(int,bool),X0,X1))) )
    | ~ spl21_105
    | ~ spl21_126 ),
    inference(superposition,[],[f1180,f1450]) ).

tff(f1180,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),sK6(X0)) )
    | ~ spl21_105 ),
    inference(avatar_component_clause,[],[f1179]) ).

tff(f4165,plain,
    ( spl21_270
    | spl21_24
    | ~ spl21_215 ),
    inference(avatar_split_clause,[],[f3341,f3057,f687,f4163]) ).

tff(f3057,plain,
    ( spl21_215
  <=> ! [X2: nat,X0: a1,X1: huffma1450048681e_tree(a1)] :
        ( member(a1,X0,huffma675207370phabet(a1,X1))
        | ( huffma1401021291ibling(a1,t_2,X0) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X2,X1,t_2),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_215])]) ).

tff(f3341,plain,
    ( ! [X0: nat] : ( huffma1401021291ibling(a1,t_2,a) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,t_2),a) )
    | spl21_24
    | ~ spl21_215 ),
    inference(resolution,[],[f3058,f689]) ).

tff(f689,plain,
    ( ~ member(a1,a,huffma675207370phabet(a1,t_1))
    | spl21_24 ),
    inference(avatar_component_clause,[],[f687]) ).

tff(f3058,plain,
    ( ! [X2: nat,X0: a1,X1: huffma1450048681e_tree(a1)] :
        ( member(a1,X0,huffma675207370phabet(a1,X1))
        | ( huffma1401021291ibling(a1,t_2,X0) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X2,X1,t_2),X0) ) )
    | ~ spl21_215 ),
    inference(avatar_component_clause,[],[f3057]) ).

tff(f4161,plain,
    ( spl21_269
    | ~ spl21_29
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1483,f1449,f710,f4159]) ).

tff(f4159,plain,
    ( spl21_269
  <=> ! [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,[spl21_269])]) ).

tff(f1483,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)) ) )
    | ~ spl21_29
    | ~ spl21_126 ),
    inference(superposition,[],[f1450,f711]) ).

tff(f4157,plain,
    ( spl21_268
    | ~ spl21_29
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1482,f1449,f710,f4155]) ).

tff(f4155,plain,
    ( spl21_268
  <=> ! [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,[spl21_268])]) ).

tff(f1482,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) ) )
    | ~ spl21_29
    | ~ spl21_126 ),
    inference(superposition,[],[f1450,f711]) ).

tff(f4153,plain,
    ( spl21_267
    | ~ spl21_104
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1468,f1445,f1175,f4151]) ).

tff(f4151,plain,
    ( spl21_267
  <=> ! [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),sK5(aa(nat,fun(int,bool),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_267])]) ).

tff(f1468,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),sK5(aa(nat,fun(int,bool),X0,X1))) )
    | ~ spl21_104
    | ~ spl21_125 ),
    inference(superposition,[],[f1176,f1446]) ).

tff(f4149,plain,
    ( spl21_266
    | ~ spl21_105
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1467,f1445,f1179,f4147]) ).

tff(f4147,plain,
    ( spl21_266
  <=> ! [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),sK6(aa(nat,fun(int,bool),X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_266])]) ).

tff(f1467,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),sK6(aa(nat,fun(int,bool),X0,X1))) )
    | ~ spl21_105
    | ~ spl21_125 ),
    inference(superposition,[],[f1180,f1446]) ).

tff(f4145,plain,
    ( spl21_265
    | ~ spl21_29
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1461,f1445,f710,f4143]) ).

tff(f4143,plain,
    ( spl21_265
  <=> ! [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,[spl21_265])]) ).

tff(f1461,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) ) )
    | ~ spl21_29
    | ~ spl21_125 ),
    inference(superposition,[],[f1446,f711]) ).

tff(f4141,plain,
    ( spl21_264
    | ~ spl21_29
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1458,f1445,f710,f4139]) ).

tff(f4139,plain,
    ( spl21_264
  <=> ! [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,[spl21_264])]) ).

tff(f1458,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)) ) )
    | ~ spl21_29
    | ~ spl21_125 ),
    inference(superposition,[],[f1446,f711]) ).

tff(f4121,plain,
    ( ~ spl21_18
    | spl21_263
    | ~ spl21_85
    | ~ spl21_122 ),
    inference(avatar_split_clause,[],[f1374,f1357,f1038,f4119,f661]) ).

tff(f4119,plain,
    ( spl21_263
  <=> ! [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,[spl21_263])]) ).

tff(f1374,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) )
    | ~ spl21_85
    | ~ spl21_122 ),
    inference(resolution,[],[f1358,f1039]) ).

tff(f4117,plain,
    ( spl21_262
    | ~ spl21_92
    | ~ spl21_108 ),
    inference(avatar_split_clause,[],[f1283,f1270,f1111,f4115]) ).

tff(f4115,plain,
    ( spl21_262
  <=> ! [X0: fun(int,bool),X3: nat,X2: nat,X1: nat] :
        ( pp(aa(int,bool,X0,sK6(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,[spl21_262])]) ).

tff(f1283,plain,
    ( ! [X2: nat,X3: nat,X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,sK6(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)) ) )
    | ~ spl21_92
    | ~ spl21_108 ),
    inference(resolution,[],[f1271,f1112]) ).

tff(f4113,plain,
    ( spl21_261
    | ~ spl21_92
    | ~ spl21_107 ),
    inference(avatar_split_clause,[],[f1278,f1266,f1111,f4111]) ).

tff(f4111,plain,
    ( spl21_261
  <=> ! [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,sK5(X0)),X3,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_261])]) ).

tff(f1278,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,sK5(X0)),X3,X2)) ) )
    | ~ spl21_92
    | ~ spl21_107 ),
    inference(resolution,[],[f1267,f1112]) ).

tff(f4048,plain,
    ( spl21_260
    | ~ spl21_61
    | ~ spl21_134 ),
    inference(avatar_split_clause,[],[f1591,f1582,f871,f4046]) ).

tff(f4046,plain,
    ( spl21_260
  <=> ! [X2: fun(nat,bool),X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,sK10(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,[spl21_260])]) ).

tff(f1591,plain,
    ( ! [X2: fun(nat,bool),X0: nat,X1: nat] :
        ( ~ ord_less(nat,X0,sK10(X1,X2))
        | ~ pp(aa(nat,bool,X2,X1))
        | pp(aa(nat,bool,X2,zero_zero(nat)))
        | ~ member(nat,X0,X2) )
    | ~ spl21_61
    | ~ spl21_134 ),
    inference(resolution,[],[f1583,f872]) ).

tff(f4015,plain,
    ( spl21_25
    | ~ spl21_252 ),
    inference(avatar_contradiction_clause,[],[f4014]) ).

tff(f4014,plain,
    ( $false
    | spl21_25
    | ~ spl21_252 ),
    inference(trivial_inequality_removal,[],[f4010]) ).

tff(f4010,plain,
    ( ( huffma1401021291ibling(a1,t_2,a) != huffma1401021291ibling(a1,t_2,a) )
    | spl21_25
    | ~ spl21_252 ),
    inference(superposition,[],[f694,f3925]) ).

tff(f3925,plain,
    ( ! [X0: huffma1450048681e_tree(a1),X1: nat] : ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,X1,t_1,X0),a) = huffma1401021291ibling(a1,X0,a) )
    | ~ spl21_252 ),
    inference(avatar_component_clause,[],[f3924]) ).

tff(f3924,plain,
    ( spl21_252
  <=> ! [X0: huffma1450048681e_tree(a1),X1: nat] : ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,X1,t_1,X0),a) = huffma1401021291ibling(a1,X0,a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_252])]) ).

tff(f4007,plain,
    ( spl21_259
    | ~ spl21_29
    | ~ spl21_133 ),
    inference(avatar_split_clause,[],[f1575,f1561,f710,f4005]) ).

tff(f4005,plain,
    ( spl21_259
  <=> ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
        ( ( aa(bool,X0,X2,fTrue) != aa(bool,X0,X1,fTrue) )
        | ( X1 = X2 )
        | ( fFalse = sK20(X0,bool,X1,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_259])]) ).

tff(f1575,plain,
    ( ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
        ( ( aa(bool,X0,X2,fTrue) != aa(bool,X0,X1,fTrue) )
        | ( X1 = X2 )
        | ( fFalse = sK20(X0,bool,X1,X2) ) )
    | ~ spl21_29
    | ~ spl21_133 ),
    inference(superposition,[],[f1562,f711]) ).

tff(f4003,plain,
    ( spl21_258
    | ~ spl21_86
    | ~ spl21_131 ),
    inference(avatar_split_clause,[],[f1553,f1536,f1042,f4001]) ).

tff(f1553,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 ) )
    | ~ spl21_86
    | ~ spl21_131 ),
    inference(resolution,[],[f1537,f1043]) ).

tff(f3999,plain,
    ( spl21_257
    | ~ spl21_117
    | ~ spl21_124 ),
    inference(avatar_split_clause,[],[f1457,f1389,f1328,f3997]) ).

tff(f3997,plain,
    ( spl21_257
  <=> ! [X0: fun(nat,bool),X1: nat] :
        ( ~ pp(aa(nat,bool,X0,X1))
        | pp(aa(nat,bool,X0,zero_zero(nat)))
        | ord_less_eq(nat,sK10(sK10(X1,X0),X0),sK10(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_257])]) ).

tff(f1457,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,sK10(sK10(X1,X0),X0),sK10(X1,X0)) )
    | ~ spl21_117
    | ~ spl21_124 ),
    inference(duplicate_literal_removal,[],[f1453]) ).

tff(f1453,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,sK10(sK10(X1,X0),X0),sK10(X1,X0))
        | pp(aa(nat,bool,X0,zero_zero(nat))) )
    | ~ spl21_117
    | ~ spl21_124 ),
    inference(resolution,[],[f1390,f1329]) ).

tff(f3986,plain,
    ( ~ spl21_14
    | spl21_256
    | ~ spl21_29
    | ~ spl21_122 ),
    inference(avatar_split_clause,[],[f1381,f1357,f710,f3984,f641]) ).

tff(f3984,plain,
    ( spl21_256
  <=> ! [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,[spl21_256])]) ).

tff(f1381,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) ) )
    | ~ spl21_29
    | ~ spl21_122 ),
    inference(superposition,[],[f1358,f711]) ).

tff(f3973,plain,
    ( ~ spl21_14
    | spl21_255
    | ~ spl21_29
    | ~ spl21_122 ),
    inference(avatar_split_clause,[],[f1378,f1357,f710,f3971,f641]) ).

tff(f3971,plain,
    ( spl21_255
  <=> ! [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,[spl21_255])]) ).

tff(f1378,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) ) )
    | ~ spl21_29
    | ~ spl21_122 ),
    inference(superposition,[],[f1358,f711]) ).

tff(f3969,plain,
    ( spl21_254
    | ~ spl21_92
    | ~ spl21_105 ),
    inference(avatar_split_clause,[],[f1261,f1179,f1111,f3967]) ).

tff(f3967,plain,
    ( spl21_254
  <=> ! [X0: fun(int,bool),X3: nat,X2: nat,X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK6(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,[spl21_254])]) ).

tff(f1261,plain,
    ( ! [X2: nat,X3: nat,X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK6(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)) ) )
    | ~ spl21_92
    | ~ spl21_105 ),
    inference(resolution,[],[f1180,f1112]) ).

tff(f3965,plain,
    ( spl21_253
    | ~ spl21_91
    | ~ spl21_104 ),
    inference(avatar_split_clause,[],[f1256,f1175,f1107,f3963]) ).

tff(f3963,plain,
    ( spl21_253
  <=> ! [X0: fun(int,bool),X3: nat,X2: nat,X1: nat] :
        ( ord_less_eq(int,zero_zero(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)),X1,X3)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_253])]) ).

tff(f1256,plain,
    ( ! [X2: nat,X3: nat,X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(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)),X1,X3)) ) )
    | ~ spl21_91
    | ~ spl21_104 ),
    inference(resolution,[],[f1176,f1108]) ).

tff(f3926,plain,
    ( spl21_252
    | spl21_24
    | ~ spl21_216 ),
    inference(avatar_split_clause,[],[f3351,f3073,f687,f3924]) ).

tff(f3073,plain,
    ( spl21_216
  <=> ! [X2: nat,X0: a1,X1: huffma1450048681e_tree(a1)] :
        ( member(a1,X0,huffma675207370phabet(a1,t_1))
        | ( huffma1401021291ibling(a1,X1,X0) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X2,t_1,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_216])]) ).

tff(f3351,plain,
    ( ! [X0: huffma1450048681e_tree(a1),X1: nat] : ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,X1,t_1,X0),a) = huffma1401021291ibling(a1,X0,a) )
    | spl21_24
    | ~ spl21_216 ),
    inference(resolution,[],[f3074,f689]) ).

tff(f3074,plain,
    ( ! [X2: nat,X0: a1,X1: huffma1450048681e_tree(a1)] :
        ( member(a1,X0,huffma675207370phabet(a1,t_1))
        | ( huffma1401021291ibling(a1,X1,X0) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X2,t_1,X1),X0) ) )
    | ~ spl21_216 ),
    inference(avatar_component_clause,[],[f3073]) ).

tff(f3804,plain,
    ( spl21_251
    | ~ spl21_61
    | ~ spl21_132 ),
    inference(avatar_split_clause,[],[f1565,f1557,f871,f3802]) ).

tff(f3802,plain,
    ( spl21_251
  <=> ! [X2: nat,X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ ord_less(nat,X1,sK11(X0))
        | pp(aa(nat,bool,X0,X2))
        | ~ member(nat,zero_zero(nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_251])]) ).

tff(f1565,plain,
    ( ! [X2: nat,X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ ord_less(nat,X1,sK11(X0))
        | pp(aa(nat,bool,X0,X2))
        | ~ member(nat,zero_zero(nat),X0) )
    | ~ spl21_61
    | ~ spl21_132 ),
    inference(resolution,[],[f1558,f872]) ).

tff(f3800,plain,
    ( spl21_250
    | ~ spl21_29
    | ~ spl21_119 ),
    inference(avatar_split_clause,[],[f1347,f1336,f710,f3798]) ).

tff(f3798,plain,
    ( spl21_250
  <=> ! [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,[spl21_250])]) ).

tff(f1336,plain,
    ( spl21_119
  <=> ! [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,[spl21_119])]) ).

tff(f1347,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) ) )
    | ~ spl21_29
    | ~ spl21_119 ),
    inference(superposition,[],[f1337,f711]) ).

tff(f1337,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 ) )
    | ~ spl21_119 ),
    inference(avatar_component_clause,[],[f1336]) ).

tff(f3796,plain,
    ( spl21_249
    | ~ spl21_91
    | ~ spl21_92 ),
    inference(avatar_split_clause,[],[f1134,f1111,f1107,f3794]) ).

tff(f3794,plain,
    ( spl21_249
  <=> ! [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,[spl21_249])]) ).

tff(f1134,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)) ) )
    | ~ spl21_91
    | ~ spl21_92 ),
    inference(resolution,[],[f1112,f1108]) ).

tff(f3732,plain,
    ( spl21_248
    | ~ spl21_149 ),
    inference(avatar_split_clause,[],[f1748,f1739,f3730]) ).

tff(f3730,plain,
    ( spl21_248
  <=> ! [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,[spl21_248])]) ).

tff(f1748,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)) )
    | ~ spl21_149 ),
    inference(superposition,[],[f1740,f1740]) ).

tff(f3728,plain,
    ( spl21_247
    | ~ spl21_43
    | ~ spl21_131 ),
    inference(avatar_split_clause,[],[f1550,f1536,f776,f3726]) ).

tff(f3726,plain,
    ( spl21_247
  <=> ! [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)),sK17(X0,X2)) = huffma1401021291ibling(X0,X2,sK17(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_247])]) ).

tff(f1550,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)),sK17(X0,X2)) = huffma1401021291ibling(X0,X2,sK17(X0,X2)) )
    | ~ spl21_43
    | ~ spl21_131 ),
    inference(resolution,[],[f1537,f777]) ).

tff(f3724,plain,
    ( spl21_246
    | ~ spl21_125
    | ~ spl21_129 ),
    inference(avatar_split_clause,[],[f1549,f1527,f1445,f3722]) ).

tff(f3722,plain,
    ( spl21_246
  <=> ! [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,[spl21_246])]) ).

tff(f1549,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) )
    | ~ spl21_125
    | ~ spl21_129 ),
    inference(superposition,[],[f1528,f1446]) ).

tff(f3720,plain,
    ( spl21_245
    | ~ spl21_126
    | ~ spl21_129 ),
    inference(avatar_split_clause,[],[f1548,f1527,f1449,f3718]) ).

tff(f3718,plain,
    ( spl21_245
  <=> ! [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,[spl21_245])]) ).

tff(f1548,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) )
    | ~ spl21_126
    | ~ spl21_129 ),
    inference(superposition,[],[f1528,f1450]) ).

tff(f3716,plain,
    ( spl21_244
    | ~ spl21_62
    | ~ spl21_129 ),
    inference(avatar_split_clause,[],[f1543,f1527,f875,f3714]) ).

tff(f3714,plain,
    ( spl21_244
  <=> ! [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,[spl21_244])]) ).

tff(f1543,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)) )
    | ~ spl21_62
    | ~ spl21_129 ),
    inference(resolution,[],[f1528,f876]) ).

tff(f3702,plain,
    ( ~ spl21_18
    | spl21_243
    | ~ spl21_88
    | ~ spl21_122 ),
    inference(avatar_split_clause,[],[f1382,f1357,f1050,f3700,f661]) ).

tff(f3700,plain,
    ( spl21_243
  <=> ! [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,[spl21_243])]) ).

tff(f1382,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) )
    | ~ spl21_88
    | ~ spl21_122 ),
    inference(superposition,[],[f1358,f1051]) ).

tff(f3688,plain,
    ( ~ spl21_18
    | spl21_242
    | ~ spl21_88
    | ~ spl21_122 ),
    inference(avatar_split_clause,[],[f1379,f1357,f1050,f3686,f661]) ).

tff(f3686,plain,
    ( spl21_242
  <=> ! [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,[spl21_242])]) ).

tff(f1379,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) )
    | ~ spl21_88
    | ~ spl21_122 ),
    inference(superposition,[],[f1358,f1051]) ).

tff(f3679,plain,
    ( spl21_241
    | spl21_24
    | ~ spl21_94
    | ~ spl21_212 ),
    inference(avatar_split_clause,[],[f3340,f3027,f1119,f687,f3677]) ).

tff(f3677,plain,
    ( spl21_241
  <=> ! [X0: nat] : ( a = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,t_1),a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_241])]) ).

tff(f3027,plain,
    ( spl21_212
  <=> ! [X2: nat,X0: a1,X1: huffma1450048681e_tree(a1)] :
        ( member(a1,X0,huffma675207370phabet(a1,X1))
        | ( huffma1401021291ibling(a1,t_1,X0) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X2,X1,t_1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_212])]) ).

tff(f3340,plain,
    ( ! [X0: nat] : ( a = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,t_1),a) )
    | spl21_24
    | ~ spl21_94
    | ~ spl21_212 ),
    inference(forward_demodulation,[],[f3335,f1121]) ).

tff(f1121,plain,
    ( ( a = huffma1401021291ibling(a1,t_1,a) )
    | ~ spl21_94 ),
    inference(avatar_component_clause,[],[f1119]) ).

tff(f3335,plain,
    ( ! [X0: nat] : ( huffma1401021291ibling(a1,t_1,a) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,t_1),a) )
    | spl21_24
    | ~ spl21_212 ),
    inference(resolution,[],[f3028,f689]) ).

tff(f3028,plain,
    ( ! [X2: nat,X0: a1,X1: huffma1450048681e_tree(a1)] :
        ( member(a1,X0,huffma675207370phabet(a1,X1))
        | ( huffma1401021291ibling(a1,t_1,X0) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X2,X1,t_1),X0) ) )
    | ~ spl21_212 ),
    inference(avatar_component_clause,[],[f3027]) ).

tff(f3675,plain,
    ( ~ spl21_9
    | spl21_240
    | ~ spl21_72
    | ~ spl21_103 ),
    inference(avatar_split_clause,[],[f1244,f1171,f927,f3673,f616]) ).

tff(f616,plain,
    ( spl21_9
  <=> linordered_semidom(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_9])]) ).

tff(f3673,plain,
    ( spl21_240
  <=> ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ord_less(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,[spl21_240])]) ).

tff(f1171,plain,
    ( spl21_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,[spl21_103])]) ).

tff(f1244,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less_eq(nat,X0,X1)
        | ~ linordered_semidom(nat)
        | ( 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)) )
    | ~ spl21_72
    | ~ spl21_103 ),
    inference(resolution,[],[f1172,f928]) ).

tff(f1172,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) )
    | ~ spl21_103 ),
    inference(avatar_component_clause,[],[f1171]) ).

tff(f3658,plain,
    ( ~ spl21_9
    | spl21_239
    | ~ spl21_73
    | ~ spl21_103 ),
    inference(avatar_split_clause,[],[f1243,f1171,f931,f3656,f616]) ).

tff(f3656,plain,
    ( spl21_239
  <=> ! [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,[spl21_239])]) ).

tff(f1243,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) ) )
    | ~ spl21_73
    | ~ spl21_103 ),
    inference(resolution,[],[f1172,f932]) ).

tff(f3649,plain,
    ( ~ spl21_9
    | spl21_238
    | ~ spl21_70
    | ~ spl21_101 ),
    inference(avatar_split_clause,[],[f1217,f1163,f919,f3647,f616]) ).

tff(f3647,plain,
    ( spl21_238
  <=> ! [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,[spl21_238])]) ).

tff(f919,plain,
    ( spl21_70
  <=> ! [X0: nat,X1: nat] :
        ( ord_less(nat,X0,X1)
        | ord_less(nat,X1,X0)
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_70])]) ).

tff(f1163,plain,
    ( spl21_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,[spl21_101])]) ).

tff(f1217,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) ) )
    | ~ spl21_70
    | ~ spl21_101 ),
    inference(resolution,[],[f1164,f920]) ).

tff(f920,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less(nat,X1,X0)
        | ord_less(nat,X0,X1)
        | ( X0 = X1 ) )
    | ~ spl21_70 ),
    inference(avatar_component_clause,[],[f919]) ).

tff(f1164,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) )
    | ~ spl21_101 ),
    inference(avatar_component_clause,[],[f1163]) ).

tff(f3615,plain,
    ( spl21_237
    | ~ spl21_61
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1488,f1449,f871,f3613]) ).

tff(f3613,plain,
    ( spl21_237
  <=> ! [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,[spl21_237])]) ).

tff(f1488,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)) )
    | ~ spl21_61
    | ~ spl21_126 ),
    inference(superposition,[],[f872,f1450]) ).

tff(f3611,plain,
    ( spl21_236
    | ~ spl21_62
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1487,f1449,f875,f3609]) ).

tff(f3609,plain,
    ( spl21_236
  <=> ! [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,[spl21_236])]) ).

tff(f1487,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)) )
    | ~ spl21_62
    | ~ spl21_126 ),
    inference(superposition,[],[f876,f1450]) ).

tff(f3607,plain,
    ( spl21_235
    | ~ spl21_61
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1465,f1445,f871,f3605]) ).

tff(f3605,plain,
    ( spl21_235
  <=> ! [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,[spl21_235])]) ).

tff(f1465,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)) )
    | ~ spl21_61
    | ~ spl21_125 ),
    inference(superposition,[],[f872,f1446]) ).

tff(f3603,plain,
    ( spl21_234
    | ~ spl21_62
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1464,f1445,f875,f3601]) ).

tff(f3601,plain,
    ( spl21_234
  <=> ! [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,[spl21_234])]) ).

tff(f1464,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)) )
    | ~ spl21_62
    | ~ spl21_125 ),
    inference(superposition,[],[f876,f1446]) ).

tff(f3523,plain,
    ( spl21_233
    | ~ spl21_97
    | ~ spl21_141 ),
    inference(avatar_split_clause,[],[f1649,f1626,f1142,f3521]) ).

tff(f3521,plain,
    ( spl21_233
  <=> ! [X2: huffma1450048681e_tree(a1),X0: a1,X1: nat] :
        ( ~ member(a1,X0,huffma675207370phabet(a1,t_2))
        | ( huffma1401021291ibling(a1,t_2,X0) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X1,t_2,X2),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_233])]) ).

tff(f1142,plain,
    ( spl21_97
  <=> ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_97])]) ).

tff(f1649,plain,
    ( ! [X2: huffma1450048681e_tree(a1),X0: a1,X1: nat] :
        ( ~ member(a1,X0,huffma675207370phabet(a1,t_2))
        | ( huffma1401021291ibling(a1,t_2,X0) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X1,t_2,X2),X0) ) )
    | ~ spl21_97
    | ~ spl21_141 ),
    inference(resolution,[],[f1627,f1144]) ).

tff(f1144,plain,
    ( ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_2))
    | ~ spl21_97 ),
    inference(avatar_component_clause,[],[f1142]) ).

tff(f3513,plain,
    ( ~ spl21_94
    | spl21_23
    | ~ spl21_221 ),
    inference(avatar_split_clause,[],[f3334,f3217,f683,f1119]) ).

tff(f3217,plain,
    ( spl21_221
  <=> ! [X0: nat] : ( a = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,t_2),a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_221])]) ).

tff(f3334,plain,
    ( ( a != huffma1401021291ibling(a1,t_1,a) )
    | spl21_23
    | ~ spl21_221 ),
    inference(superposition,[],[f685,f3218]) ).

tff(f3218,plain,
    ( ! [X0: nat] : ( a = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,t_2),a) )
    | ~ spl21_221 ),
    inference(avatar_component_clause,[],[f3217]) ).

tff(f3419,plain,
    ( spl21_232
    | ~ spl21_125
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1481,f1449,f1445,f3417]) ).

tff(f3417,plain,
    ( spl21_232
  <=> ! [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,[spl21_232])]) ).

tff(f1481,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)) )
    | ~ spl21_125
    | ~ spl21_126 ),
    inference(superposition,[],[f1450,f1446]) ).

tff(f3415,plain,
    ( spl21_231
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1480,f1449,f3413]) ).

tff(f3413,plain,
    ( spl21_231
  <=> ! [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,[spl21_231])]) ).

tff(f1480,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)) )
    | ~ spl21_126 ),
    inference(superposition,[],[f1450,f1450]) ).

tff(f3411,plain,
    ( spl21_230
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1460,f1445,f3409]) ).

tff(f3409,plain,
    ( spl21_230
  <=> ! [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,[spl21_230])]) ).

tff(f1460,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)) )
    | ~ spl21_125 ),
    inference(superposition,[],[f1446,f1446]) ).

tff(f3407,plain,
    ( spl21_229
    | ~ spl21_62
    | ~ spl21_124 ),
    inference(avatar_split_clause,[],[f1454,f1389,f875,f3405]) ).

tff(f3405,plain,
    ( spl21_229
  <=> ! [X0: fun(nat,bool),X1: nat] :
        ( ~ pp(aa(nat,bool,X0,X1))
        | pp(aa(nat,bool,X0,zero_zero(nat)))
        | member(nat,sK10(X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_229])]) ).

tff(f1454,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( ~ pp(aa(nat,bool,X0,X1))
        | pp(aa(nat,bool,X0,zero_zero(nat)))
        | member(nat,sK10(X1,X0),X0) )
    | ~ spl21_62
    | ~ spl21_124 ),
    inference(resolution,[],[f1390,f876]) ).

tff(f3403,plain,
    ( ~ spl21_228
    | spl21_25
    | ~ spl21_221 ),
    inference(avatar_split_clause,[],[f3333,f3217,f692,f3400]) ).

tff(f3333,plain,
    ( ( a != huffma1401021291ibling(a1,t_2,a) )
    | spl21_25
    | ~ spl21_221 ),
    inference(superposition,[],[f694,f3218]) ).

tff(f3398,plain,
    ( spl21_227
    | ~ spl21_29
    | ~ spl21_115 ),
    inference(avatar_split_clause,[],[f1326,f1309,f710,f3396]) ).

tff(f3396,plain,
    ( spl21_227
  <=> ! [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,[spl21_227])]) ).

tff(f1309,plain,
    ( spl21_115
  <=> ! [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,[spl21_115])]) ).

tff(f1326,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) ) )
    | ~ spl21_29
    | ~ spl21_115 ),
    inference(superposition,[],[f1310,f711]) ).

tff(f1310,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 )
    | ~ spl21_115 ),
    inference(avatar_component_clause,[],[f1309]) ).

tff(f3394,plain,
    ( spl21_226
    | ~ spl21_62
    | ~ spl21_92 ),
    inference(avatar_split_clause,[],[f1133,f1111,f875,f3392]) ).

tff(f3392,plain,
    ( spl21_226
  <=> ! [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,[spl21_226])]) ).

tff(f1133,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) )
    | ~ spl21_62
    | ~ spl21_92 ),
    inference(resolution,[],[f1112,f876]) ).

tff(f3390,plain,
    ( spl21_225
    | ~ spl21_61
    | ~ spl21_91 ),
    inference(avatar_split_clause,[],[f1131,f1107,f871,f3388]) ).

tff(f3388,plain,
    ( spl21_225
  <=> ! [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,[spl21_225])]) ).

tff(f1131,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) )
    | ~ spl21_61
    | ~ spl21_91 ),
    inference(resolution,[],[f1108,f872]) ).

tff(f3386,plain,
    ( spl21_224
    | ~ spl21_74
    | ~ spl21_83 ),
    inference(avatar_split_clause,[],[f1086,f1029,f935,f3384]) ).

tff(f3384,plain,
    ( spl21_224
  <=> ! [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,[spl21_224])]) ).

tff(f1029,plain,
    ( spl21_83
  <=> ! [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,[spl21_83])]) ).

tff(f1086,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)) )
    | ~ spl21_74
    | ~ spl21_83 ),
    inference(resolution,[],[f1030,f936]) ).

tff(f1030,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) )
    | ~ spl21_83 ),
    inference(avatar_component_clause,[],[f1029]) ).

tff(f3316,plain,
    ( spl21_94
    | spl21_24
    | ~ spl21_86 ),
    inference(avatar_split_clause,[],[f3283,f1042,f687,f1119]) ).

tff(f3283,plain,
    ( ( a = huffma1401021291ibling(a1,t_1,a) )
    | spl21_24
    | ~ spl21_86 ),
    inference(resolution,[],[f689,f1043]) ).

tff(f3304,plain,
    ( spl21_223
    | ~ spl21_97
    | ~ spl21_140 ),
    inference(avatar_split_clause,[],[f1643,f1622,f1142,f3302]) ).

tff(f3302,plain,
    ( spl21_223
  <=> ! [X2: nat,X0: a1,X1: huffma1450048681e_tree(a1)] :
        ( ~ member(a1,X0,huffma675207370phabet(a1,X1))
        | ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,X2,X1,t_2),X0) = huffma1401021291ibling(a1,X1,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_223])]) ).

tff(f1643,plain,
    ( ! [X2: nat,X0: a1,X1: huffma1450048681e_tree(a1)] :
        ( ~ member(a1,X0,huffma675207370phabet(a1,X1))
        | ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,X2,X1,t_2),X0) = huffma1401021291ibling(a1,X1,X0) ) )
    | ~ spl21_97
    | ~ spl21_140 ),
    inference(resolution,[],[f1623,f1144]) ).

tff(f3273,plain,
    ( spl21_222
    | ~ spl21_96
    | ~ spl21_141 ),
    inference(avatar_split_clause,[],[f1648,f1626,f1138,f3271]) ).

tff(f1138,plain,
    ( spl21_96
  <=> ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_96])]) ).

tff(f1648,plain,
    ( ! [X2: huffma1450048681e_tree(a1),X0: a1,X1: nat] :
        ( ~ member(a1,X0,huffma675207370phabet(a1,t_1))
        | ( huffma1401021291ibling(a1,t_1,X0) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X1,t_1,X2),X0) ) )
    | ~ spl21_96
    | ~ spl21_141 ),
    inference(resolution,[],[f1627,f1140]) ).

tff(f1140,plain,
    ( ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_1))
    | ~ spl21_96 ),
    inference(avatar_component_clause,[],[f1138]) ).

tff(f3259,plain,
    ( spl21_136
    | ~ spl21_94
    | ~ spl21_147 ),
    inference(avatar_split_clause,[],[f2489,f1710,f1119,f1599]) ).

tff(f1710,plain,
    ( spl21_147
  <=> ! [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,[spl21_147])]) ).

tff(f2489,plain,
    ( ! [X2: huffma1450048681e_tree(a1),X3: huffma1450048681e_tree(a1),X0: nat,X1: nat] : ( a = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,huffma1146269203erNode(a1,X1,X2,X3)),a) )
    | ~ spl21_94
    | ~ spl21_147 ),
    inference(forward_demodulation,[],[f1711,f1121]) ).

tff(f1711,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) )
    | ~ spl21_147 ),
    inference(avatar_component_clause,[],[f1710]) ).

tff(f3231,plain,
    ( spl21_218
    | ~ spl21_87
    | ~ spl21_106
    | ~ spl21_215 ),
    inference(avatar_split_clause,[],[f3076,f3057,f1212,f1046,f3131]) ).

tff(f3131,plain,
    ( spl21_218
  <=> ! [X2: nat,X0: a1,X1: huffma1450048681e_tree(a1)] :
        ( ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,X2,X1,t_2),X0) = X0 )
        | member(a1,X0,huffma675207370phabet(a1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_218])]) ).

tff(f1046,plain,
    ( spl21_87
  <=> ! [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,[spl21_87])]) ).

tff(f3076,plain,
    ( ! [X2: nat,X0: a1,X1: huffma1450048681e_tree(a1)] :
        ( ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,X2,X1,t_2),X0) = X0 )
        | member(a1,X0,huffma675207370phabet(a1,X1)) )
    | ~ spl21_87
    | ~ spl21_106
    | ~ spl21_215 ),
    inference(forward_demodulation,[],[f3058,f3070]) ).

tff(f3070,plain,
    ( ! [X0: a1] : ( huffma1401021291ibling(a1,t_2,X0) = X0 )
    | ~ spl21_87
    | ~ spl21_106 ),
    inference(trivial_inequality_removal,[],[f3063]) ).

tff(f3063,plain,
    ( ! [X0: a1] :
        ( ( zero_zero(nat) != zero_zero(nat) )
        | ( huffma1401021291ibling(a1,t_2,X0) = X0 ) )
    | ~ spl21_87
    | ~ spl21_106 ),
    inference(superposition,[],[f1047,f1214]) ).

tff(f1214,plain,
    ( ( zero_zero(nat) = huffma945805758height(a1,t_2) )
    | ~ spl21_106 ),
    inference(avatar_component_clause,[],[f1212]) ).

tff(f1047,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X1: X0] :
        ( ( zero_zero(nat) != huffma945805758height(X0,X2) )
        | ( huffma1401021291ibling(X0,X2,X1) = X1 ) )
    | ~ spl21_87 ),
    inference(avatar_component_clause,[],[f1046]) ).

tff(f3219,plain,
    ( spl21_221
    | spl21_24
    | ~ spl21_218 ),
    inference(avatar_split_clause,[],[f3185,f3131,f687,f3217]) ).

tff(f3185,plain,
    ( ! [X0: nat] : ( a = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,t_2),a) )
    | spl21_24
    | ~ spl21_218 ),
    inference(resolution,[],[f3132,f689]) ).

tff(f3132,plain,
    ( ! [X2: nat,X0: a1,X1: huffma1450048681e_tree(a1)] :
        ( member(a1,X0,huffma675207370phabet(a1,X1))
        | ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,X2,X1,t_2),X0) = X0 ) )
    | ~ spl21_218 ),
    inference(avatar_component_clause,[],[f3131]) ).

tff(f3215,plain,
    ( spl21_94
    | spl21_24
    | ~ spl21_86 ),
    inference(avatar_split_clause,[],[f3175,f1042,f687,f1119]) ).

tff(f3175,plain,
    ( ( a = huffma1401021291ibling(a1,t_1,a) )
    | spl21_24
    | ~ spl21_86 ),
    inference(resolution,[],[f689,f1043]) ).

tff(f3205,plain,
    ( spl21_220
    | ~ spl21_97
    | ~ spl21_139 ),
    inference(avatar_split_clause,[],[f1637,f1618,f1142,f3203]) ).

tff(f3203,plain,
    ( spl21_220
  <=> ! [X2: nat,X0: a1,X1: huffma1450048681e_tree(a1)] :
        ( member(a1,X0,huffma675207370phabet(a1,t_2))
        | ( huffma1401021291ibling(a1,X1,X0) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X2,t_2,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_220])]) ).

tff(f1637,plain,
    ( ! [X2: nat,X0: a1,X1: huffma1450048681e_tree(a1)] :
        ( member(a1,X0,huffma675207370phabet(a1,t_2))
        | ( huffma1401021291ibling(a1,X1,X0) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X2,t_2,X1),X0) ) )
    | ~ spl21_97
    | ~ spl21_139 ),
    inference(resolution,[],[f1619,f1144]) ).

tff(f3201,plain,
    ( spl21_215
    | ~ spl21_97
    | ~ spl21_138 ),
    inference(avatar_split_clause,[],[f1631,f1614,f1142,f3057]) ).

tff(f1631,plain,
    ( ! [X2: nat,X0: a1,X1: huffma1450048681e_tree(a1)] :
        ( member(a1,X0,huffma675207370phabet(a1,X1))
        | ( huffma1401021291ibling(a1,t_2,X0) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X2,X1,t_2),X0) ) )
    | ~ spl21_97
    | ~ spl21_138 ),
    inference(resolution,[],[f1615,f1144]) ).

tff(f3176,plain,
    ( spl21_116
    | ~ spl21_152
    | ~ spl21_177 ),
    inference(avatar_split_clause,[],[f2791,f2484,f1850,f1318]) ).

tff(f1318,plain,
    ( spl21_116
  <=> ( zero_zero(nat) = aa(a1,nat,huffma1352802255e_freq(a1,t_1),a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_116])]) ).

tff(f1850,plain,
    ( spl21_152
  <=> ! [X0: $tType,X1: fun(X0,nat)] : ord_less_eq(fun(X0,nat),X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_152])]) ).

tff(f2484,plain,
    ( spl21_177
  <=> ! [X0: fun(a1,nat)] :
        ( ~ ord_less_eq(fun(a1,nat),X0,huffma1352802255e_freq(a1,t_1))
        | ( zero_zero(nat) = aa(a1,nat,X0,a) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_177])]) ).

tff(f2791,plain,
    ( ( zero_zero(nat) = aa(a1,nat,huffma1352802255e_freq(a1,t_1),a) )
    | ~ spl21_152
    | ~ spl21_177 ),
    inference(resolution,[],[f2485,f1851]) ).

tff(f1851,plain,
    ( ! [X0: $tType,X1: fun(X0,nat)] : ord_less_eq(fun(X0,nat),X1,X1)
    | ~ spl21_152 ),
    inference(avatar_component_clause,[],[f1850]) ).

tff(f2485,plain,
    ( ! [X0: fun(a1,nat)] :
        ( ~ ord_less_eq(fun(a1,nat),X0,huffma1352802255e_freq(a1,t_1))
        | ( zero_zero(nat) = aa(a1,nat,X0,a) ) )
    | ~ spl21_177 ),
    inference(avatar_component_clause,[],[f2484]) ).

tff(f3171,plain,
    ( spl21_217
    | ~ spl21_53
    | ~ spl21_97
    | ~ spl21_191 ),
    inference(avatar_split_clause,[],[f3161,f2684,f1142,f818,f3085]) ).

tff(f3085,plain,
    ( spl21_217
  <=> ord_less(nat,zero_zero(nat),zero_zero(nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_217])]) ).

tff(f3161,plain,
    ( ord_less(nat,zero_zero(nat),zero_zero(nat))
    | ~ spl21_53
    | ~ spl21_97
    | ~ spl21_191 ),
    inference(forward_demodulation,[],[f1144,f3097]) ).

tff(f3169,plain,
    ( ~ spl21_26
    | ~ spl21_217 ),
    inference(avatar_contradiction_clause,[],[f3165]) ).

tff(f3165,plain,
    ( $false
    | ~ spl21_26
    | ~ spl21_217 ),
    inference(resolution,[],[f3087,f698]) ).

tff(f698,plain,
    ( ! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat))
    | ~ spl21_26 ),
    inference(avatar_component_clause,[],[f697]) ).

tff(f697,plain,
    ( spl21_26
  <=> ! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_26])]) ).

tff(f3087,plain,
    ( ord_less(nat,zero_zero(nat),zero_zero(nat))
    | ~ spl21_217 ),
    inference(avatar_component_clause,[],[f3085]) ).

tff(f3168,plain,
    ( ~ spl21_20
    | ~ spl21_217 ),
    inference(avatar_contradiction_clause,[],[f3166]) ).

tff(f3166,plain,
    ( $false
    | ~ spl21_20
    | ~ spl21_217 ),
    inference(resolution,[],[f3087,f672]) ).

tff(f672,plain,
    ( ! [X0: nat] : ~ ord_less(nat,X0,X0)
    | ~ spl21_20 ),
    inference(avatar_component_clause,[],[f671]) ).

tff(f671,plain,
    ( spl21_20
  <=> ! [X0: nat] : ~ ord_less(nat,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_20])]) ).

tff(f3152,plain,
    ( spl21_219
    | ~ spl21_96
    | ~ spl21_140 ),
    inference(avatar_split_clause,[],[f1642,f1622,f1138,f3150]) ).

tff(f3150,plain,
    ( spl21_219
  <=> ! [X2: nat,X0: a1,X1: huffma1450048681e_tree(a1)] :
        ( ~ member(a1,X0,huffma675207370phabet(a1,X1))
        | ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,X2,X1,t_1),X0) = huffma1401021291ibling(a1,X1,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_219])]) ).

tff(f1642,plain,
    ( ! [X2: nat,X0: a1,X1: huffma1450048681e_tree(a1)] :
        ( ~ member(a1,X0,huffma675207370phabet(a1,X1))
        | ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,X2,X1,t_1),X0) = huffma1401021291ibling(a1,X1,X0) ) )
    | ~ spl21_96
    | ~ spl21_140 ),
    inference(resolution,[],[f1623,f1140]) ).

tff(f3142,plain,
    ( spl21_217
    | ~ spl21_96
    | ~ spl21_214 ),
    inference(avatar_split_clause,[],[f3141,f3046,f1138,f3085]) ).

tff(f3046,plain,
    ( spl21_214
  <=> ( zero_zero(nat) = huffma945805758height(a1,t_1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_214])]) ).

tff(f3141,plain,
    ( ord_less(nat,zero_zero(nat),zero_zero(nat))
    | ~ spl21_96
    | ~ spl21_214 ),
    inference(forward_demodulation,[],[f1140,f3048]) ).

tff(f3048,plain,
    ( ( zero_zero(nat) = huffma945805758height(a1,t_1) )
    | ~ spl21_214 ),
    inference(avatar_component_clause,[],[f3046]) ).

tff(f3133,plain,
    ( spl21_218
    | ~ spl21_55
    | ~ spl21_191
    | ~ spl21_215 ),
    inference(avatar_split_clause,[],[f3129,f3057,f2684,f826,f3131]) ).

tff(f3129,plain,
    ( ! [X2: nat,X0: a1,X1: huffma1450048681e_tree(a1)] :
        ( ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,X2,X1,t_2),X0) = X0 )
        | member(a1,X0,huffma675207370phabet(a1,X1)) )
    | ~ spl21_55
    | ~ spl21_191
    | ~ spl21_215 ),
    inference(forward_demodulation,[],[f3058,f3098]) ).

tff(f3128,plain,
    ( spl21_215
    | ~ spl21_97
    | ~ spl21_138 ),
    inference(avatar_split_clause,[],[f1631,f1614,f1142,f3057]) ).

tff(f3088,plain,
    ( spl21_217
    | ~ spl21_97
    | ~ spl21_106 ),
    inference(avatar_split_clause,[],[f3081,f1212,f1142,f3085]) ).

tff(f3081,plain,
    ( ord_less(nat,zero_zero(nat),zero_zero(nat))
    | ~ spl21_97
    | ~ spl21_106 ),
    inference(forward_demodulation,[],[f1144,f1214]) ).

tff(f3075,plain,
    ( spl21_216
    | ~ spl21_96
    | ~ spl21_139 ),
    inference(avatar_split_clause,[],[f1636,f1618,f1138,f3073]) ).

tff(f1636,plain,
    ( ! [X2: nat,X0: a1,X1: huffma1450048681e_tree(a1)] :
        ( member(a1,X0,huffma675207370phabet(a1,t_1))
        | ( huffma1401021291ibling(a1,X1,X0) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X2,t_1,X1),X0) ) )
    | ~ spl21_96
    | ~ spl21_139 ),
    inference(resolution,[],[f1619,f1140]) ).

tff(f3059,plain,
    ( spl21_215
    | ~ spl21_97
    | ~ spl21_138 ),
    inference(avatar_split_clause,[],[f1631,f1614,f1142,f3057]) ).

tff(f3049,plain,
    ( spl21_214
    | ~ spl21_50
    | spl21_96 ),
    inference(avatar_split_clause,[],[f3034,f1138,f806,f3046]) ).

tff(f3034,plain,
    ( ( zero_zero(nat) = huffma945805758height(a1,t_1) )
    | ~ spl21_50
    | spl21_96 ),
    inference(resolution,[],[f1139,f807]) ).

tff(f1139,plain,
    ( ~ ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_1))
    | spl21_96 ),
    inference(avatar_component_clause,[],[f1138]) ).

tff(f3043,plain,
    ( spl21_116
    | ~ spl21_152
    | ~ spl21_177 ),
    inference(avatar_split_clause,[],[f2791,f2484,f1850,f1318]) ).

tff(f3042,plain,
    ( spl21_147
    | ~ spl21_24
    | ~ spl21_131 ),
    inference(avatar_split_clause,[],[f3021,f1536,f687,f1710]) ).

tff(f3021,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) )
    | ~ spl21_24
    | ~ spl21_131 ),
    inference(resolution,[],[f688,f1537]) ).

tff(f3041,plain,
    ( spl21_213
    | ~ spl21_24
    | ~ spl21_94
    | ~ spl21_148 ),
    inference(avatar_split_clause,[],[f3030,f1727,f1119,f687,f3039]) ).

tff(f3039,plain,
    ( spl21_213
  <=> ! [X0: nat,X3: huffma1450048681e_tree(a1),X2: huffma1450048681e_tree(a1),X1: nat] :
        ( ( 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,[spl21_213])]) ).

tff(f3030,plain,
    ( ! [X2: huffma1450048681e_tree(a1),X3: huffma1450048681e_tree(a1),X0: nat,X1: nat] :
        ( ( a = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,huffma1146269203erNode(a1,X1,X2,X3),t_1),a) )
        | member(a1,a,huffma675207370phabet(a1,huffma1146269203erNode(a1,X1,X2,X3))) )
    | ~ spl21_24
    | ~ spl21_94
    | ~ spl21_148 ),
    inference(forward_demodulation,[],[f3020,f1121]) ).

tff(f3020,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))) )
    | ~ spl21_24
    | ~ spl21_148 ),
    inference(resolution,[],[f688,f1728]) ).

tff(f3029,plain,
    ( spl21_212
    | ~ spl21_96
    | ~ spl21_138 ),
    inference(avatar_split_clause,[],[f1630,f1614,f1138,f3027]) ).

tff(f1630,plain,
    ( ! [X2: nat,X0: a1,X1: huffma1450048681e_tree(a1)] :
        ( member(a1,X0,huffma675207370phabet(a1,X1))
        | ( huffma1401021291ibling(a1,t_1,X0) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X2,X1,t_1),X0) ) )
    | ~ spl21_96
    | ~ spl21_138 ),
    inference(resolution,[],[f1615,f1140]) ).

tff(f3023,plain,
    ( spl21_136
    | ~ spl21_94
    | ~ spl21_147 ),
    inference(avatar_split_clause,[],[f2489,f1710,f1119,f1599]) ).

tff(f2992,plain,
    ( spl21_211
    | ~ spl21_88
    | ~ spl21_158 ),
    inference(avatar_split_clause,[],[f2392,f2160,f1050,f2990]) ).

tff(f2990,plain,
    ( spl21_211
  <=> ! [X0: nat] :
        ( ord_less_eq(nat,X0,zero_zero(nat))
        | ~ ord_less_eq(fun(a1,nat),huffma1352802255e_freq(a1,huffma2021818691e_Leaf(a1,X0,a)),huffma1352802255e_freq(a1,t_1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_211])]) ).

tff(f2160,plain,
    ( spl21_158
  <=> ! [X0: fun(a1,nat)] :
        ( ord_less_eq(nat,aa(a1,nat,X0,a),zero_zero(nat))
        | ~ ord_less_eq(fun(a1,nat),X0,huffma1352802255e_freq(a1,t_1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_158])]) ).

tff(f2392,plain,
    ( ! [X0: nat] :
        ( ord_less_eq(nat,X0,zero_zero(nat))
        | ~ ord_less_eq(fun(a1,nat),huffma1352802255e_freq(a1,huffma2021818691e_Leaf(a1,X0,a)),huffma1352802255e_freq(a1,t_1)) )
    | ~ spl21_88
    | ~ spl21_158 ),
    inference(superposition,[],[f2161,f1051]) ).

tff(f2161,plain,
    ( ! [X0: fun(a1,nat)] :
        ( ord_less_eq(nat,aa(a1,nat,X0,a),zero_zero(nat))
        | ~ ord_less_eq(fun(a1,nat),X0,huffma1352802255e_freq(a1,t_1)) )
    | ~ spl21_158 ),
    inference(avatar_component_clause,[],[f2160]) ).

tff(f2956,plain,
    ( spl21_210
    | ~ spl21_75
    | ~ spl21_135 ),
    inference(avatar_split_clause,[],[f1602,f1586,f940,f2954]) ).

tff(f2954,plain,
    ( spl21_210
  <=> ! [X0: $tType,X3: X0,X2: nat,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma2021818691e_Leaf(X0,X2,X3) != X1 )
        | ( huffma2021818691e_Leaf(X0,sK15(X0,X1),sK16(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_210])]) ).

tff(f1602,plain,
    ( ! [X0: $tType,X2: nat,X3: X0,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma2021818691e_Leaf(X0,X2,X3) != X1 )
        | ( huffma2021818691e_Leaf(X0,sK15(X0,X1),sK16(X0,X1)) = X1 ) )
    | ~ spl21_75
    | ~ spl21_135 ),
    inference(superposition,[],[f941,f1587]) ).

tff(f2952,plain,
    ( spl21_209
    | ~ spl21_61
    | ~ spl21_123 ),
    inference(avatar_split_clause,[],[f1384,f1361,f871,f2950]) ).

tff(f2950,plain,
    ( spl21_209
  <=> ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ pp(aa(nat,bool,X0,zero_zero(nat)))
        | ~ member(nat,sK11(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_209])]) ).

tff(f1384,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( pp(aa(nat,bool,X0,X1))
        | ~ pp(aa(nat,bool,X0,zero_zero(nat)))
        | ~ member(nat,sK11(X0),X0) )
    | ~ spl21_61
    | ~ spl21_123 ),
    inference(resolution,[],[f1362,f872]) ).

tff(f2948,plain,
    ( spl21_208
    | ~ spl21_61
    | ~ spl21_121 ),
    inference(avatar_split_clause,[],[f1370,f1353,f871,f2946]) ).

tff(f2946,plain,
    ( spl21_208
  <=> ! [X0: fun(int,bool),X1: int] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK7(X0))))
        | ~ ord_less_eq(int,zero_zero(int),X1)
        | ~ member(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_208])]) ).

tff(f1370,plain,
    ( ! [X0: fun(int,bool),X1: int] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK7(X0))))
        | ~ ord_less_eq(int,zero_zero(int),X1)
        | ~ member(int,X1,X0) )
    | ~ spl21_61
    | ~ spl21_121 ),
    inference(resolution,[],[f1354,f872]) ).

tff(f2944,plain,
    ( spl21_207
    | ~ spl21_61
    | ~ spl21_120 ),
    inference(avatar_split_clause,[],[f1365,f1349,f871,f2942]) ).

tff(f2942,plain,
    ( spl21_207
  <=> ! [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,sK4(X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_207])]) ).

tff(f1365,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,sK4(X1)),X1) )
    | ~ spl21_61
    | ~ spl21_120 ),
    inference(resolution,[],[f1350,f872]) ).

tff(f2928,plain,
    ( ~ spl21_9
    | spl21_206
    | ~ spl21_85
    | ~ spl21_103 ),
    inference(avatar_split_clause,[],[f1242,f1171,f1038,f2926,f616]) ).

tff(f2926,plain,
    ( spl21_206
  <=> ! [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,[spl21_206])]) ).

tff(f1242,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) )
    | ~ spl21_85
    | ~ spl21_103 ),
    inference(resolution,[],[f1172,f1039]) ).

tff(f2848,plain,
    ( spl21_205
    | ~ spl21_104
    | ~ spl21_120 ),
    inference(avatar_split_clause,[],[f1364,f1349,f1175,f2846]) ).

tff(f2846,plain,
    ( spl21_205
  <=> ! [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),sK5(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_205])]) ).

tff(f1364,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),sK5(X1)) )
    | ~ spl21_104
    | ~ spl21_120 ),
    inference(resolution,[],[f1350,f1176]) ).

tff(f2844,plain,
    ( spl21_204
    | ~ spl21_61
    | ~ spl21_118 ),
    inference(avatar_split_clause,[],[f1343,f1332,f871,f2842]) ).

tff(f2842,plain,
    ( spl21_204
  <=> ! [X0: fun(nat,bool),X1: nat] :
        ( ord_less(nat,zero_zero(nat),sK11(X0))
        | pp(aa(nat,bool,X0,X1))
        | ~ member(nat,zero_zero(nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_204])]) ).

tff(f1343,plain,
    ( ! [X0: fun(nat,bool),X1: nat] :
        ( ord_less(nat,zero_zero(nat),sK11(X0))
        | pp(aa(nat,bool,X0,X1))
        | ~ member(nat,zero_zero(nat),X0) )
    | ~ spl21_61
    | ~ spl21_118 ),
    inference(resolution,[],[f1333,f872]) ).

tff(f2840,plain,
    ( spl21_203
    | ~ spl21_61
    | ~ spl21_117 ),
    inference(avatar_split_clause,[],[f1339,f1328,f871,f2838]) ).

tff(f2838,plain,
    ( spl21_203
  <=> ! [X0: nat,X1: fun(nat,bool)] :
        ( ord_less_eq(nat,sK10(X0,X1),X0)
        | pp(aa(nat,bool,X1,zero_zero(nat)))
        | ~ member(nat,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_203])]) ).

tff(f1339,plain,
    ( ! [X0: nat,X1: fun(nat,bool)] :
        ( ord_less_eq(nat,sK10(X0,X1),X0)
        | pp(aa(nat,bool,X1,zero_zero(nat)))
        | ~ member(nat,X0,X1) )
    | ~ spl21_61
    | ~ spl21_117 ),
    inference(resolution,[],[f1329,f872]) ).

tff(f2836,plain,
    ( spl21_202
    | ~ spl21_54
    | ~ spl21_73 ),
    inference(avatar_split_clause,[],[f985,f931,f822,f2834]) ).

tff(f2834,plain,
    ( spl21_202
  <=> ! [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,[spl21_202])]) ).

tff(f822,plain,
    ( spl21_54
  <=> ! [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,[spl21_54])]) ).

tff(f985,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) ) )
    | ~ spl21_54
    | ~ spl21_73 ),
    inference(resolution,[],[f932,f823]) ).

tff(f823,plain,
    ( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X1: X0] : ord_less_eq(nat,huffma410068972_depth(X0,X2,X1),huffma945805758height(X0,X2))
    | ~ spl21_54 ),
    inference(avatar_component_clause,[],[f822]) ).

tff(f2832,plain,
    ( spl21_201
    | ~ spl21_54
    | ~ spl21_72 ),
    inference(avatar_split_clause,[],[f975,f927,f822,f2830]) ).

tff(f2830,plain,
    ( spl21_201
  <=> ! [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,[spl21_201])]) ).

tff(f975,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)) )
    | ~ spl21_54
    | ~ spl21_72 ),
    inference(resolution,[],[f928,f823]) ).

tff(f2790,plain,
    ( spl21_200
    | ~ spl21_56
    | ~ spl21_102 ),
    inference(avatar_split_clause,[],[f1234,f1167,f850,f2788]) ).

tff(f2788,plain,
    ( spl21_200
  <=> ! [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,[spl21_200])]) ).

tff(f1167,plain,
    ( spl21_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,[spl21_102])]) ).

tff(f1234,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) )
    | ~ spl21_56
    | ~ spl21_102 ),
    inference(resolution,[],[f1168,f851]) ).

tff(f1168,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) )
    | ~ spl21_102 ),
    inference(avatar_component_clause,[],[f1167]) ).

tff(f2777,plain,
    ( spl21_199
    | ~ spl21_66
    | ~ spl21_78 ),
    inference(avatar_split_clause,[],[f1062,f1009,f903,f2775]) ).

tff(f2775,plain,
    ( spl21_199
  <=> ! [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,[spl21_199])]) ).

tff(f903,plain,
    ( spl21_66
  <=> ! [X0: int] :
        ( ( semiring_1_of_nat(int,sK1(X0)) = X0 )
        | ~ ord_less(int,zero_zero(int),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_66])]) ).

tff(f1009,plain,
    ( spl21_78
  <=> ! [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,[spl21_78])]) ).

tff(f1062,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))) ) )
    | ~ spl21_66
    | ~ spl21_78 ),
    inference(resolution,[],[f1010,f904]) ).

tff(f904,plain,
    ( ! [X0: int] :
        ( ~ ord_less(int,zero_zero(int),X0)
        | ( semiring_1_of_nat(int,sK1(X0)) = X0 ) )
    | ~ spl21_66 ),
    inference(avatar_component_clause,[],[f903]) ).

tff(f1010,plain,
    ( ! [X0: nat] :
        ( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0))
        | ~ ord_less(nat,zero_zero(nat),X0) )
    | ~ spl21_78 ),
    inference(avatar_component_clause,[],[f1009]) ).

tff(f2773,plain,
    ( ~ spl21_197
    | spl21_198
    | ~ spl21_29
    | ~ spl21_76 ),
    inference(avatar_split_clause,[],[f1053,f1001,f710,f2771,f2767]) ).

tff(f2767,plain,
    ( spl21_197
  <=> semiring_char_0(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_197])]) ).

tff(f2771,plain,
    ( spl21_198
  <=> ! [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,[spl21_198])]) ).

tff(f1001,plain,
    ( spl21_76
  <=> ! [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,[spl21_76])]) ).

tff(f1053,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) ) )
    | ~ spl21_29
    | ~ spl21_76 ),
    inference(superposition,[],[f1002,f711]) ).

tff(f1002,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) )
    | ~ spl21_76 ),
    inference(avatar_component_clause,[],[f1001]) ).

tff(f2727,plain,
    ( spl21_196
    | ~ spl21_111
    | ~ spl21_126 ),
    inference(avatar_split_clause,[],[f1495,f1449,f1293,f2725]) ).

tff(f2725,plain,
    ( spl21_196
  <=> ! [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,[spl21_196])]) ).

tff(f1495,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) )
    | ~ spl21_111
    | ~ spl21_126 ),
    inference(superposition,[],[f1294,f1450]) ).

tff(f2723,plain,
    ( spl21_195
    | ~ spl21_111
    | ~ spl21_125 ),
    inference(avatar_split_clause,[],[f1472,f1445,f1293,f2721]) ).

tff(f2721,plain,
    ( spl21_195
  <=> ! [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,[spl21_195])]) ).

tff(f1472,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) )
    | ~ spl21_111
    | ~ spl21_125 ),
    inference(superposition,[],[f1294,f1446]) ).

tff(f2719,plain,
    ( spl21_194
    | ~ spl21_61
    | ~ spl21_111 ),
    inference(avatar_split_clause,[],[f1313,f1293,f871,f2717]) ).

tff(f2717,plain,
    ( spl21_194
  <=> ! [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,[spl21_194])]) ).

tff(f1313,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)) )
    | ~ spl21_61
    | ~ spl21_111 ),
    inference(resolution,[],[f1294,f872]) ).

tff(f2715,plain,
    ( spl21_193
    | ~ spl21_34
    | ~ spl21_108 ),
    inference(avatar_split_clause,[],[f1285,f1270,f733,f2713]) ).

tff(f2713,plain,
    ( spl21_193
  <=> ! [X0: fun(int,bool)] :
        ( ~ pp(aa(int,bool,X0,zero_zero(int)))
        | pp(aa(int,bool,X0,sK6(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_193])]) ).

tff(f733,plain,
    ( spl21_34
  <=> ( zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_34])]) ).

tff(f1285,plain,
    ( ! [X0: fun(int,bool)] :
        ( ~ pp(aa(int,bool,X0,zero_zero(int)))
        | pp(aa(int,bool,X0,sK6(X0))) )
    | ~ spl21_34
    | ~ spl21_108 ),
    inference(superposition,[],[f1271,f735]) ).

tff(f735,plain,
    ( ( zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)) )
    | ~ spl21_34 ),
    inference(avatar_component_clause,[],[f733]) ).

tff(f2704,plain,
    ( ~ spl21_9
    | spl21_192
    | ~ spl21_40
    | ~ spl21_102 ),
    inference(avatar_split_clause,[],[f1229,f1167,f763,f2702,f616]) ).

tff(f2702,plain,
    ( spl21_192
  <=> ! [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,[spl21_192])]) ).

tff(f1229,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)) )
    | ~ spl21_40
    | ~ spl21_102 ),
    inference(resolution,[],[f1168,f764]) ).

tff(f2687,plain,
    ( spl21_191
    | spl21_23
    | ~ spl21_161 ),
    inference(avatar_split_clause,[],[f2600,f2247,f683,f2684]) ).

tff(f2247,plain,
    ( spl21_161
  <=> ! [X0: huffma1450048681e_tree(a1),X1: nat] :
        ( ( huffma1401021291ibling(a1,t_1,a) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X1,t_1,X0),a) )
        | ( huffma2021818691e_Leaf(a1,sK15(a1,X0),sK16(a1,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_161])]) ).

tff(f2600,plain,
    ( ( t_2 = huffma2021818691e_Leaf(a1,sK15(a1,t_2),sK16(a1,t_2)) )
    | spl21_23
    | ~ spl21_161 ),
    inference(trivial_inequality_removal,[],[f2578]) ).

tff(f2578,plain,
    ( ( huffma1401021291ibling(a1,t_1,a) != huffma1401021291ibling(a1,t_1,a) )
    | ( t_2 = huffma2021818691e_Leaf(a1,sK15(a1,t_2),sK16(a1,t_2)) )
    | spl21_23
    | ~ spl21_161 ),
    inference(superposition,[],[f685,f2248]) ).

tff(f2248,plain,
    ( ! [X0: huffma1450048681e_tree(a1),X1: nat] :
        ( ( huffma1401021291ibling(a1,t_1,a) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X1,t_1,X0),a) )
        | ( huffma2021818691e_Leaf(a1,sK15(a1,X0),sK16(a1,X0)) = X0 ) )
    | ~ spl21_161 ),
    inference(avatar_component_clause,[],[f2247]) ).

tff(f2682,plain,
    ( ~ spl21_9
    | spl21_190
    | ~ spl21_41
    | ~ spl21_100 ),
    inference(avatar_split_clause,[],[f1203,f1159,f767,f2680,f616]) ).

tff(f2680,plain,
    ( spl21_190
  <=> ! [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,[spl21_190])]) ).

tff(f767,plain,
    ( spl21_41
  <=> ! [X0: nat,X1: nat] :
        ( ord_less_eq(nat,X1,X0)
        | ~ ord_less(nat,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_41])]) ).

tff(f1159,plain,
    ( spl21_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,[spl21_100])]) ).

tff(f1203,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)) )
    | ~ spl21_41
    | ~ spl21_100 ),
    inference(resolution,[],[f1160,f768]) ).

tff(f768,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ord_less(nat,X1,X0)
        | ord_less_eq(nat,X1,X0) )
    | ~ spl21_41 ),
    inference(avatar_component_clause,[],[f767]) ).

tff(f1160,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) )
    | ~ spl21_100 ),
    inference(avatar_component_clause,[],[f1159]) ).

tff(f2663,plain,
    ( ~ spl21_11
    | spl21_189
    | ~ spl21_56
    | ~ spl21_82 ),
    inference(avatar_split_clause,[],[f1081,f1025,f850,f2661,f626]) ).

tff(f626,plain,
    ( spl21_11
  <=> linorder(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_11])]) ).

tff(f2661,plain,
    ( spl21_189
  <=> ! [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,[spl21_189])]) ).

tff(f1025,plain,
    ( spl21_82
  <=> ! [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,[spl21_82])]) ).

tff(f1081,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) )
    | ~ spl21_56
    | ~ spl21_82 ),
    inference(resolution,[],[f1026,f851]) ).

tff(f1026,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) )
    | ~ spl21_82 ),
    inference(avatar_component_clause,[],[f1025]) ).

tff(f2659,plain,
    ( spl21_188
    | ~ spl21_29
    | ~ spl21_71 ),
    inference(avatar_split_clause,[],[f970,f923,f710,f2657]) ).

tff(f2657,plain,
    ( spl21_188
  <=> ! [X0: huffma1450048681e_tree(bool)] :
        ( member(bool,fTrue,huffma675207370phabet(bool,X0))
        | ~ huffma1518433673istent(bool,X0)
        | ( fFalse = sK9(bool,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_188])]) ).

tff(f970,plain,
    ( ! [X0: huffma1450048681e_tree(bool)] :
        ( member(bool,fTrue,huffma675207370phabet(bool,X0))
        | ~ huffma1518433673istent(bool,X0)
        | ( fFalse = sK9(bool,X0) ) )
    | ~ spl21_29
    | ~ spl21_71 ),
    inference(superposition,[],[f924,f711]) ).

tff(f2567,plain,
    ( spl21_187
    | ~ spl21_61
    | ~ spl21_108 ),
    inference(avatar_split_clause,[],[f1282,f1270,f871,f2565]) ).

tff(f2565,plain,
    ( spl21_187
  <=> ! [X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,sK6(X0)))
        | ~ member(int,semiring_1_of_nat(int,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_187])]) ).

tff(f1282,plain,
    ( ! [X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,sK6(X0)))
        | ~ member(int,semiring_1_of_nat(int,X1),X0) )
    | ~ spl21_61
    | ~ spl21_108 ),
    inference(resolution,[],[f1271,f872]) ).

tff(f2563,plain,
    ( spl21_186
    | ~ spl21_104
    | ~ spl21_108 ),
    inference(avatar_split_clause,[],[f1281,f1270,f1175,f2561]) ).

tff(f2561,plain,
    ( spl21_186
  <=> ! [X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,sK6(X0)))
        | ord_less_eq(int,zero_zero(int),sK5(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_186])]) ).

tff(f1281,plain,
    ( ! [X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,sK6(X0)))
        | ord_less_eq(int,zero_zero(int),sK5(X0)) )
    | ~ spl21_104
    | ~ spl21_108 ),
    inference(resolution,[],[f1271,f1176]) ).

tff(f2559,plain,
    ( spl21_185
    | ~ spl21_61
    | ~ spl21_107 ),
    inference(avatar_split_clause,[],[f1277,f1266,f871,f2557]) ).

tff(f2557,plain,
    ( spl21_185
  <=> ! [X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,X1)))
        | ~ member(int,sK5(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_185])]) ).

tff(f1277,plain,
    ( ! [X0: fun(int,bool),X1: nat] :
        ( pp(aa(int,bool,X0,semiring_1_of_nat(int,X1)))
        | ~ member(int,sK5(X0),X0) )
    | ~ spl21_61
    | ~ spl21_107 ),
    inference(resolution,[],[f1267,f872]) ).

tff(f2555,plain,
    ( spl21_184
    | ~ spl21_34
    | ~ spl21_105 ),
    inference(avatar_split_clause,[],[f1263,f1179,f733,f2553]) ).

tff(f2553,plain,
    ( spl21_184
  <=> ! [X0: fun(int,bool)] :
        ( ~ pp(aa(int,bool,X0,zero_zero(int)))
        | ord_less_eq(int,zero_zero(int),sK6(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_184])]) ).

tff(f1263,plain,
    ( ! [X0: fun(int,bool)] :
        ( ~ pp(aa(int,bool,X0,zero_zero(int)))
        | ord_less_eq(int,zero_zero(int),sK6(X0)) )
    | ~ spl21_34
    | ~ spl21_105 ),
    inference(superposition,[],[f1180,f735]) ).

tff(f2551,plain,
    ( spl21_183
    | ~ spl21_34
    | ~ spl21_104 ),
    inference(avatar_split_clause,[],[f1257,f1175,f733,f2549]) ).

tff(f2549,plain,
    ( spl21_183
  <=> ! [X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,zero_zero(int)))
        | ord_less_eq(int,zero_zero(int),sK5(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_183])]) ).

tff(f1257,plain,
    ( ! [X0: fun(int,bool)] :
        ( pp(aa(int,bool,X0,zero_zero(int)))
        | ord_less_eq(int,zero_zero(int),sK5(X0)) )
    | ~ spl21_34
    | ~ spl21_104 ),
    inference(superposition,[],[f1176,f735]) ).

tff(f2538,plain,
    ( spl21_94
    | ~ spl21_24
    | ~ spl21_131
    | ~ spl21_136 ),
    inference(avatar_split_clause,[],[f2532,f1599,f1536,f687,f1119]) ).

tff(f2532,plain,
    ( ( a = huffma1401021291ibling(a1,t_1,a) )
    | ~ spl21_24
    | ~ spl21_131
    | ~ spl21_136 ),
    inference(forward_demodulation,[],[f2493,f1600]) ).

tff(f2493,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) )
    | ~ spl21_24
    | ~ spl21_131 ),
    inference(resolution,[],[f688,f1537]) ).

tff(f2531,plain,
    ( spl21_182
    | ~ spl21_94
    | ~ spl21_161 ),
    inference(avatar_split_clause,[],[f2487,f2247,f1119,f2529]) ).

tff(f2529,plain,
    ( spl21_182
  <=> ! [X0: huffma1450048681e_tree(a1),X1: nat] :
        ( ( a = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X1,t_1,X0),a) )
        | ( huffma2021818691e_Leaf(a1,sK15(a1,X0),sK16(a1,X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_182])]) ).

tff(f2487,plain,
    ( ! [X0: huffma1450048681e_tree(a1),X1: nat] :
        ( ( a = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X1,t_1,X0),a) )
        | ( huffma2021818691e_Leaf(a1,sK15(a1,X0),sK16(a1,X0)) = X0 ) )
    | ~ spl21_94
    | ~ spl21_161 ),
    inference(forward_demodulation,[],[f2248,f1121]) ).

tff(f2527,plain,
    ( ~ spl21_9
    | spl21_181
    | ~ spl21_50
    | ~ spl21_98 ),
    inference(avatar_split_clause,[],[f1182,f1151,f806,f2525,f616]) ).

tff(f2525,plain,
    ( spl21_181
  <=> ! [X0: nat] :
        ( ord_less(nat,zero_zero(nat),X0)
        | ( zero_zero(nat) = semiring_1_of_nat(nat,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_181])]) ).

tff(f1151,plain,
    ( spl21_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,[spl21_98])]) ).

tff(f1182,plain,
    ( ! [X0: nat] :
        ( ord_less(nat,zero_zero(nat),X0)
        | ~ linordered_semidom(nat)
        | ( zero_zero(nat) = semiring_1_of_nat(nat,X0) ) )
    | ~ spl21_50
    | ~ spl21_98 ),
    inference(resolution,[],[f1152,f807]) ).

tff(f1152,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) )
    | ~ spl21_98 ),
    inference(avatar_component_clause,[],[f1151]) ).

tff(f2523,plain,
    ( spl21_180
    | ~ spl21_54
    | ~ spl21_85 ),
    inference(avatar_split_clause,[],[f1093,f1038,f822,f2521]) ).

tff(f2521,plain,
    ( spl21_180
  <=> ! [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,[spl21_180])]) ).

tff(f1093,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) )
    | ~ spl21_54
    | ~ spl21_85 ),
    inference(resolution,[],[f1039,f823]) ).

tff(f2510,plain,
    ( ~ spl21_11
    | spl21_179
    | ~ spl21_56
    | ~ spl21_74 ),
    inference(avatar_split_clause,[],[f997,f935,f850,f2508,f626]) ).

tff(f2508,plain,
    ( spl21_179
  <=> ! [X0: int,X1: int] :
        ( ( X0 = X1 )
        | ord_less_eq(int,X0,X1)
        | ord_less(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_179])]) ).

tff(f997,plain,
    ( ! [X0: int,X1: int] :
        ( ( X0 = X1 )
        | ord_less(int,X1,X0)
        | ord_less_eq(int,X0,X1)
        | ~ linorder(int) )
    | ~ spl21_56
    | ~ spl21_74 ),
    inference(resolution,[],[f936,f851]) ).

tff(f2506,plain,
    ( spl21_178
    | ~ spl21_37
    | ~ spl21_74 ),
    inference(avatar_split_clause,[],[f994,f935,f746,f2504]) ).

tff(f2504,plain,
    ( spl21_178
  <=> ! [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,[spl21_178])]) ).

tff(f746,plain,
    ( spl21_37
  <=> ! [X0: nat] : ord_less_eq(int,zero_zero(int),semiring_1_of_nat(int,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_37])]) ).

tff(f994,plain,
    ( ! [X0: nat] :
        ( ( zero_zero(int) = semiring_1_of_nat(int,X0) )
        | ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) )
    | ~ spl21_37
    | ~ spl21_74 ),
    inference(resolution,[],[f936,f747]) ).

tff(f747,plain,
    ( ! [X0: nat] : ord_less_eq(int,zero_zero(int),semiring_1_of_nat(int,X0))
    | ~ spl21_37 ),
    inference(avatar_component_clause,[],[f746]) ).

tff(f2495,plain,
    ( spl21_136
    | ~ spl21_94
    | ~ spl21_147 ),
    inference(avatar_split_clause,[],[f2489,f1710,f1119,f1599]) ).

tff(f2486,plain,
    ( spl21_177
    | ~ spl21_51
    | ~ spl21_158 ),
    inference(avatar_split_clause,[],[f2387,f2160,f810,f2484]) ).

tff(f810,plain,
    ( spl21_51
  <=> ! [X0: nat] :
        ( ( zero_zero(nat) = X0 )
        | ~ ord_less_eq(nat,X0,zero_zero(nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_51])]) ).

tff(f2387,plain,
    ( ! [X0: fun(a1,nat)] :
        ( ~ ord_less_eq(fun(a1,nat),X0,huffma1352802255e_freq(a1,t_1))
        | ( zero_zero(nat) = aa(a1,nat,X0,a) ) )
    | ~ spl21_51
    | ~ spl21_158 ),
    inference(resolution,[],[f2161,f811]) ).

tff(f811,plain,
    ( ! [X0: nat] :
        ( ~ ord_less_eq(nat,X0,zero_zero(nat))
        | ( zero_zero(nat) = X0 ) )
    | ~ spl21_51 ),
    inference(avatar_component_clause,[],[f810]) ).

tff(f2482,plain,
    ( ~ spl21_11
    | spl21_176
    | ~ spl21_56
    | ~ spl21_68 ),
    inference(avatar_split_clause,[],[f956,f911,f850,f2480,f626]) ).

tff(f2480,plain,
    ( spl21_176
  <=> ! [X0: int] :
        ( ( semiring_1_of_nat(int,sK3(X0)) = X0 )
        | ord_less_eq(int,X0,zero_zero(int)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_176])]) ).

tff(f911,plain,
    ( spl21_68
  <=> ! [X0: int] :
        ( ( semiring_1_of_nat(int,sK3(X0)) = X0 )
        | ~ ord_less_eq(int,zero_zero(int),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_68])]) ).

tff(f956,plain,
    ( ! [X0: int] :
        ( ( semiring_1_of_nat(int,sK3(X0)) = X0 )
        | ord_less_eq(int,X0,zero_zero(int))
        | ~ linorder(int) )
    | ~ spl21_56
    | ~ spl21_68 ),
    inference(resolution,[],[f912,f851]) ).

tff(f912,plain,
    ( ! [X0: int] :
        ( ~ ord_less_eq(int,zero_zero(int),X0)
        | ( semiring_1_of_nat(int,sK3(X0)) = X0 ) )
    | ~ spl21_68 ),
    inference(avatar_component_clause,[],[f911]) ).

tff(f2472,plain,
    ( ~ spl21_11
    | spl21_175
    | ~ spl21_56
    | ~ spl21_67 ),
    inference(avatar_split_clause,[],[f949,f907,f850,f2470,f626]) ).

tff(f2470,plain,
    ( spl21_175
  <=> ! [X0: int] :
        ( ( semiring_1_of_nat(int,sK2(X0)) = X0 )
        | ord_less_eq(int,X0,zero_zero(int)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_175])]) ).

tff(f907,plain,
    ( spl21_67
  <=> ! [X0: int] :
        ( ( semiring_1_of_nat(int,sK2(X0)) = X0 )
        | ~ ord_less_eq(int,zero_zero(int),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_67])]) ).

tff(f949,plain,
    ( ! [X0: int] :
        ( ( semiring_1_of_nat(int,sK2(X0)) = X0 )
        | ord_less_eq(int,X0,zero_zero(int))
        | ~ linorder(int) )
    | ~ spl21_56
    | ~ spl21_67 ),
    inference(resolution,[],[f908,f851]) ).

tff(f908,plain,
    ( ! [X0: int] :
        ( ~ ord_less_eq(int,zero_zero(int),X0)
        | ( semiring_1_of_nat(int,sK2(X0)) = X0 ) )
    | ~ spl21_67 ),
    inference(avatar_component_clause,[],[f907]) ).

tff(f2379,plain,
    ( spl21_174
    | ~ spl21_61
    | ~ spl21_105 ),
    inference(avatar_split_clause,[],[f1260,f1179,f871,f2377]) ).

tff(f2377,plain,
    ( spl21_174
  <=> ! [X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK6(X0))
        | ~ member(int,semiring_1_of_nat(int,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_174])]) ).

tff(f1260,plain,
    ( ! [X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK6(X0))
        | ~ member(int,semiring_1_of_nat(int,X1),X0) )
    | ~ spl21_61
    | ~ spl21_105 ),
    inference(resolution,[],[f1180,f872]) ).

tff(f2375,plain,
    ( spl21_173
    | ~ spl21_104
    | ~ spl21_105 ),
    inference(avatar_split_clause,[],[f1259,f1179,f1175,f2373]) ).

tff(f2373,plain,
    ( spl21_173
  <=> ! [X0: fun(int,bool)] :
        ( ord_less_eq(int,zero_zero(int),sK6(X0))
        | ord_less_eq(int,zero_zero(int),sK5(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_173])]) ).

tff(f1259,plain,
    ( ! [X0: fun(int,bool)] :
        ( ord_less_eq(int,zero_zero(int),sK6(X0))
        | ord_less_eq(int,zero_zero(int),sK5(X0)) )
    | ~ spl21_104
    | ~ spl21_105 ),
    inference(resolution,[],[f1180,f1176]) ).

tff(f2371,plain,
    ( spl21_172
    | ~ spl21_62
    | ~ spl21_104 ),
    inference(avatar_split_clause,[],[f1255,f1175,f875,f2369]) ).

tff(f2369,plain,
    ( spl21_172
  <=> ! [X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK5(X0))
        | member(int,semiring_1_of_nat(int,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_172])]) ).

tff(f1255,plain,
    ( ! [X0: fun(int,bool),X1: nat] :
        ( ord_less_eq(int,zero_zero(int),sK5(X0))
        | member(int,semiring_1_of_nat(int,X1),X0) )
    | ~ spl21_62
    | ~ spl21_104 ),
    inference(resolution,[],[f1176,f876]) ).

tff(f2367,plain,
    ( spl21_171
    | ~ spl21_40
    | ~ spl21_85 ),
    inference(avatar_split_clause,[],[f1091,f1038,f763,f2365]) ).

tff(f2365,plain,
    ( spl21_171
  <=> ! [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,[spl21_171])]) ).

tff(f1091,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) )
    | ~ spl21_40
    | ~ spl21_85 ),
    inference(resolution,[],[f1039,f764]) ).

tff(f2363,plain,
    ( spl21_170
    | ~ spl21_34
    | ~ spl21_83 ),
    inference(avatar_split_clause,[],[f1088,f1029,f733,f2361]) ).

tff(f2361,plain,
    ( spl21_170
  <=> ! [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,[spl21_170])]) ).

tff(f1088,plain,
    ( ! [X0: nat] :
        ( ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int))
        | ~ ord_less_eq(nat,X0,zero_zero(nat)) )
    | ~ spl21_34
    | ~ spl21_83 ),
    inference(superposition,[],[f1030,f735]) ).

tff(f2359,plain,
    ( spl21_169
    | ~ spl21_34
    | ~ spl21_82 ),
    inference(avatar_split_clause,[],[f1084,f1025,f733,f2357]) ).

tff(f2357,plain,
    ( spl21_169
  <=> ! [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,[spl21_169])]) ).

tff(f1084,plain,
    ( ! [X0: nat] :
        ( ~ ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int))
        | ord_less_eq(nat,X0,zero_zero(nat)) )
    | ~ spl21_34
    | ~ spl21_82 ),
    inference(superposition,[],[f1026,f735]) ).

tff(f2355,plain,
    ( spl21_168
    | ~ spl21_42
    | ~ spl21_81 ),
    inference(avatar_split_clause,[],[f1071,f1021,f772,f2353]) ).

tff(f2353,plain,
    ( spl21_168
  <=> ! [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,[spl21_168])]) ).

tff(f772,plain,
    ( spl21_42
  <=> ! [X0: int,X1: int] :
        ( ord_less_eq(int,X1,X0)
        | ~ ord_less(int,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_42])]) ).

tff(f1021,plain,
    ( spl21_81
  <=> ! [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,[spl21_81])]) ).

tff(f1071,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)) )
    | ~ spl21_42
    | ~ spl21_81 ),
    inference(resolution,[],[f1022,f773]) ).

tff(f773,plain,
    ( ! [X0: int,X1: int] :
        ( ~ ord_less(int,X1,X0)
        | ord_less_eq(int,X1,X0) )
    | ~ spl21_42 ),
    inference(avatar_component_clause,[],[f772]) ).

tff(f1022,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) )
    | ~ spl21_81 ),
    inference(avatar_component_clause,[],[f1021]) ).

tff(f2351,plain,
    ( spl21_167
    | ~ spl21_29
    | ~ spl21_55 ),
    inference(avatar_split_clause,[],[f848,f826,f710,f2349]) ).

tff(f2349,plain,
    ( spl21_167
  <=> ! [X2: bool,X0: nat,X1: bool] :
        ( ( fTrue = X2 )
        | ( fFalse = huffma1401021291ibling(bool,huffma2021818691e_Leaf(bool,X0,X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_167])]) ).

tff(f848,plain,
    ( ! [X2: bool,X0: nat,X1: bool] :
        ( ( fTrue = X2 )
        | ( fFalse = huffma1401021291ibling(bool,huffma2021818691e_Leaf(bool,X0,X1),X2) ) )
    | ~ spl21_29
    | ~ spl21_55 ),
    inference(superposition,[],[f827,f711]) ).

tff(f2337,plain,
    ( spl21_164
    | ~ spl21_165
    | ~ spl21_166
    | ~ spl21_29
    | ~ spl21_46 ),
    inference(avatar_split_clause,[],[f831,f790,f710,f2334,f2330,f2327]) ).

tff(f2327,plain,
    ( spl21_164
  <=> ! [X0: nat] : ( fFalse = semiring_1_of_nat(bool,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_164])]) ).

tff(f2330,plain,
    ( spl21_165
  <=> linordered_semidom(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_165])]) ).

tff(f2334,plain,
    ( spl21_166
  <=> ord_less(bool,fTrue,zero_zero(bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_166])]) ).

tff(f790,plain,
    ( spl21_46
  <=> ! [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,[spl21_46])]) ).

tff(f831,plain,
    ( ! [X0: nat] :
        ( ~ ord_less(bool,fTrue,zero_zero(bool))
        | ~ linordered_semidom(bool)
        | ( fFalse = semiring_1_of_nat(bool,X0) ) )
    | ~ spl21_29
    | ~ spl21_46 ),
    inference(superposition,[],[f791,f711]) ).

tff(f791,plain,
    ( ! [X0: $tType,X1: nat] :
        ( ~ ord_less(X0,semiring_1_of_nat(X0,X1),zero_zero(X0))
        | ~ linordered_semidom(X0) )
    | ~ spl21_46 ),
    inference(avatar_component_clause,[],[f790]) ).

tff(f2305,plain,
    ( spl21_163
    | ~ spl21_41
    | ~ spl21_70 ),
    inference(avatar_split_clause,[],[f963,f919,f767,f2303]) ).

tff(f2303,plain,
    ( spl21_163
  <=> ! [X0: nat,X1: nat] :
        ( ord_less(nat,X1,X0)
        | ( X0 = X1 )
        | ord_less_eq(nat,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_163])]) ).

tff(f963,plain,
    ( ! [X0: nat,X1: nat] :
        ( ord_less(nat,X1,X0)
        | ( X0 = X1 )
        | ord_less_eq(nat,X0,X1) )
    | ~ spl21_41
    | ~ spl21_70 ),
    inference(resolution,[],[f920,f768]) ).

tff(f2301,plain,
    ( spl21_162
    | ~ spl21_29
    | ~ spl21_43 ),
    inference(avatar_split_clause,[],[f784,f776,f710,f2299]) ).

tff(f2299,plain,
    ( spl21_162
  <=> ! [X0: huffma1450048681e_tree(bool)] :
        ( member(bool,fTrue,huffma675207370phabet(bool,X0))
        | ( fFalse = sK17(bool,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_162])]) ).

tff(f784,plain,
    ( ! [X0: huffma1450048681e_tree(bool)] :
        ( member(bool,fTrue,huffma675207370phabet(bool,X0))
        | ( fFalse = sK17(bool,X0) ) )
    | ~ spl21_29
    | ~ spl21_43 ),
    inference(superposition,[],[f777,f711]) ).

tff(f2249,plain,
    ( spl21_161
    | ~ spl21_135
    | ~ spl21_147 ),
    inference(avatar_split_clause,[],[f2165,f1710,f1586,f2247]) ).

tff(f2165,plain,
    ( ! [X0: huffma1450048681e_tree(a1),X1: nat] :
        ( ( huffma1401021291ibling(a1,t_1,a) = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X1,t_1,X0),a) )
        | ( huffma2021818691e_Leaf(a1,sK15(a1,X0),sK16(a1,X0)) = X0 ) )
    | ~ spl21_135
    | ~ spl21_147 ),
    inference(superposition,[],[f1711,f1587]) ).

tff(f2173,plain,
    ( spl21_160
    | ~ spl21_30
    | ~ spl21_142 ),
    inference(avatar_split_clause,[],[f1664,f1655,f714,f2171]) ).

tff(f2171,plain,
    ( spl21_160
  <=> ! [X1: $tType,X0: $tType,X2: fun(X0,X1)] :
        ( ord_less_eq(fun(X0,X1),X2,X2)
        | ~ ord(X1)
        | ~ preorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_160])]) ).

tff(f714,plain,
    ( spl21_30
  <=> ! [X0: $tType,X1: X0] :
        ( ord_less_eq(X0,X1,X1)
        | ~ preorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_30])]) ).

tff(f1664,plain,
    ( ! [X1: $tType,X0: $tType,X2: fun(X0,X1)] :
        ( ord_less_eq(fun(X0,X1),X2,X2)
        | ~ ord(X1)
        | ~ preorder(X1) )
    | ~ spl21_30
    | ~ spl21_142 ),
    inference(resolution,[],[f1656,f715]) ).

tff(f715,plain,
    ( ! [X0: $tType,X1: X0] :
        ( ord_less_eq(X0,X1,X1)
        | ~ preorder(X0) )
    | ~ spl21_30 ),
    inference(avatar_component_clause,[],[f714]) ).

tff(f2169,plain,
    ( spl21_159
    | ~ spl21_37
    | ~ spl21_68 ),
    inference(avatar_split_clause,[],[f952,f911,f746,f2167]) ).

tff(f2167,plain,
    ( spl21_159
  <=> ! [X0: nat] : ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,sK3(semiring_1_of_nat(int,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_159])]) ).

tff(f952,plain,
    ( ! [X0: nat] : ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,sK3(semiring_1_of_nat(int,X0))) )
    | ~ spl21_37
    | ~ spl21_68 ),
    inference(resolution,[],[f912,f747]) ).

tff(f2162,plain,
    ( ~ spl21_18
    | spl21_158
    | ~ spl21_116
    | ~ spl21_122 ),
    inference(avatar_split_clause,[],[f1795,f1357,f1318,f2160,f661]) ).

tff(f1795,plain,
    ( ! [X0: fun(a1,nat)] :
        ( ord_less_eq(nat,aa(a1,nat,X0,a),zero_zero(nat))
        | ~ ord_less_eq(fun(a1,nat),X0,huffma1352802255e_freq(a1,t_1))
        | ~ ord(nat) )
    | ~ spl21_116
    | ~ spl21_122 ),
    inference(superposition,[],[f1358,f1320]) ).

tff(f1320,plain,
    ( ( zero_zero(nat) = aa(a1,nat,huffma1352802255e_freq(a1,t_1),a) )
    | ~ spl21_116 ),
    inference(avatar_component_clause,[],[f1318]) ).

tff(f2158,plain,
    ( spl21_157
    | ~ spl21_37
    | ~ spl21_67 ),
    inference(avatar_split_clause,[],[f945,f907,f746,f2156]) ).

tff(f2156,plain,
    ( spl21_157
  <=> ! [X0: nat] : ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,sK2(semiring_1_of_nat(int,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_157])]) ).

tff(f945,plain,
    ( ! [X0: nat] : ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,sK2(semiring_1_of_nat(int,X0))) )
    | ~ spl21_37
    | ~ spl21_67 ),
    inference(resolution,[],[f908,f747]) ).

tff(f2154,plain,
    ( spl21_156
    | ~ spl21_29
    | ~ spl21_39 ),
    inference(avatar_split_clause,[],[f761,f754,f710,f2152]) ).

tff(f2152,plain,
    ( spl21_156
  <=> ! [X0: bool,X1: bool] :
        ( ( fTrue = X1 )
        | ( fFalse = if(bool,fFalse,X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_156])]) ).

tff(f754,plain,
    ( spl21_39
  <=> ! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fFalse,X2,X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_39])]) ).

tff(f761,plain,
    ( ! [X0: bool,X1: bool] :
        ( ( fTrue = X1 )
        | ( fFalse = if(bool,fFalse,X0,X1) ) )
    | ~ spl21_29
    | ~ spl21_39 ),
    inference(superposition,[],[f755,f711]) ).

tff(f755,plain,
    ( ! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fFalse,X2,X1) = X1 )
    | ~ spl21_39 ),
    inference(avatar_component_clause,[],[f754]) ).

tff(f2150,plain,
    ( spl21_155
    | ~ spl21_29
    | ~ spl21_38 ),
    inference(avatar_split_clause,[],[f760,f750,f710,f2148]) ).

tff(f2148,plain,
    ( spl21_155
  <=> ! [X0: bool,X1: bool] :
        ( ( fTrue = X0 )
        | ( fFalse = if(bool,fTrue,X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_155])]) ).

tff(f750,plain,
    ( spl21_38
  <=> ! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fTrue,X2,X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_38])]) ).

tff(f760,plain,
    ( ! [X0: bool,X1: bool] :
        ( ( fTrue = X0 )
        | ( fFalse = if(bool,fTrue,X0,X1) ) )
    | ~ spl21_29
    | ~ spl21_38 ),
    inference(superposition,[],[f751,f711]) ).

tff(f751,plain,
    ( ! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fTrue,X2,X1) = X2 )
    | ~ spl21_38 ),
    inference(avatar_component_clause,[],[f750]) ).

tff(f2146,plain,
    ( spl21_154
    | ~ spl21_29
    | ~ spl21_38 ),
    inference(avatar_split_clause,[],[f759,f750,f710,f2144]) ).

tff(f2144,plain,
    ( spl21_154
  <=> ! [X1: $tType,X0: bool,X3: X1,X2: X1] :
        ( ( if(X1,X0,X2,X3) = X2 )
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_154])]) ).

tff(f759,plain,
    ( ! [X1: $tType,X2: X1,X3: X1,X0: bool] :
        ( ( if(X1,X0,X2,X3) = X2 )
        | ( fFalse = X0 ) )
    | ~ spl21_29
    | ~ spl21_38 ),
    inference(superposition,[],[f751,f711]) ).

tff(f1858,plain,
    ( spl21_153
    | ~ spl21_29 ),
    inference(avatar_split_clause,[],[f729,f710,f1856]) ).

tff(f1856,plain,
    ( spl21_153
  <=> ! [X0: bool,X1: bool] :
        ( ( X0 = X1 )
        | ( fFalse = X1 )
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_153])]) ).

tff(f729,plain,
    ( ! [X0: bool,X1: bool] :
        ( ( X0 = X1 )
        | ( fFalse = X1 )
        | ( fFalse = X0 ) )
    | ~ spl21_29 ),
    inference(superposition,[],[f711,f711]) ).

tff(f1852,plain,
    ( ~ spl21_18
    | spl21_152
    | ~ spl21_21
    | ~ spl21_142 ),
    inference(avatar_split_clause,[],[f1659,f1655,f675,f1850,f661]) ).

tff(f675,plain,
    ( spl21_21
  <=> ! [X0: nat] : ord_less_eq(nat,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_21])]) ).

tff(f1659,plain,
    ( ! [X0: $tType,X1: fun(X0,nat)] :
        ( ord_less_eq(fun(X0,nat),X1,X1)
        | ~ ord(nat) )
    | ~ spl21_21
    | ~ spl21_142 ),
    inference(resolution,[],[f1656,f676]) ).

tff(f676,plain,
    ( ! [X0: nat] : ord_less_eq(nat,X0,X0)
    | ~ spl21_21 ),
    inference(avatar_component_clause,[],[f675]) ).

tff(f1774,plain,
    spl21_151,
    inference(avatar_split_clause,[],[f531,f1772]) ).

tff(f531,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,[],[f222]) ).

tff(f222,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,[],[f54]) ).

tff(f54,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/sandbox/benchmark/theBenchmark.p',fact_53_tree_Orecs_I2_J) ).

tff(f1761,plain,
    spl21_150,
    inference(avatar_split_clause,[],[f536,f1759]) ).

tff(f536,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,[],[f291]) ).

tff(f291,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,[],[f224]) ).

tff(f224,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/sandbox/benchmark/theBenchmark.p',fact_1_sibling_Osimps_I4_J) ).

tff(f1741,plain,
    spl21_149,
    inference(avatar_split_clause,[],[f530,f1739]) ).

tff(f530,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,[],[f221]) ).

tff(f221,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,[],[f17]) ).

tff(f17,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/sandbox/benchmark/theBenchmark.p',fact_16_tree_Osimps_I6_J) ).

tff(f1729,plain,
    spl21_148,
    inference(avatar_split_clause,[],[f539,f1727]) ).

tff(f539,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,[],[f292]) ).

tff(f292,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,[],[f225]) ).

tff(f225,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/sandbox/benchmark/theBenchmark.p',fact_2_sibling_Osimps_I3_J) ).

tff(f1712,plain,
    ( spl21_147
    | ~ spl21_24
    | ~ spl21_131 ),
    inference(avatar_split_clause,[],[f1554,f1536,f687,f1710]) ).

tff(f1554,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) )
    | ~ spl21_24
    | ~ spl21_131 ),
    inference(resolution,[],[f1537,f688]) ).

tff(f1708,plain,
    spl21_146,
    inference(avatar_split_clause,[],[f538,f1706]) ).

tff(f538,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,[],[f292]) ).

tff(f1688,plain,
    spl21_145,
    inference(avatar_split_clause,[],[f540,f1686]) ).

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) = X6 )
      | member(X0,X6,huffma675207370phabet(X0,X1))
      | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X5,X4,X3))) ),
    inference(cnf_transformation,[],[f292]) ).

tff(f1684,plain,
    spl21_144,
    inference(avatar_split_clause,[],[f537,f1682]) ).

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) = X6 )
      | member(X0,X6,huffma675207370phabet(X0,huffma1146269203erNode(X0,X3,X2,X1)))
      | member(X0,X6,huffma675207370phabet(X0,X5)) ),
    inference(cnf_transformation,[],[f291]) ).

tff(f1680,plain,
    spl21_143,
    inference(avatar_split_clause,[],[f511,f1678]) ).

tff(f1678,plain,
    ( spl21_143
  <=> ! [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,sK18(X2)),aa(nat,nat,X2,sK19(X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_143])]) ).

tff(f511,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,sK18(X2)),aa(nat,nat,X2,sK19(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,sK18(X2)),aa(nat,nat,X2,sK19(X2)))
        & ord_less(nat,sK18(X2),sK19(X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19])],[f279,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,sK18(X2)),aa(nat,nat,X2,sK19(X2)))
        & ord_less(nat,sK18(X2),sK19(X2)) ) ),
    introduced(choice_axiom,[]) ).

tff(f279,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,[],[f278]) ).

tff(f278,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,[],[f206]) ).

tff(f206,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,[],[f96]) ).

tff(f96,axiom,
    ! [X64: nat,X65: nat,X55: fun(nat,nat)] :
      ( ! [X66: nat,X67: nat] :
          ( ord_less(nat,X66,X67)
         => ord_less(nat,aa(nat,nat,X55,X66),aa(nat,nat,X55,X67)) )
     => ( ord_less_eq(nat,X65,X64)
       => ord_less_eq(nat,aa(nat,nat,X55,X65),aa(nat,nat,X55,X64)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_less__mono__imp__le__mono) ).

tff(f1657,plain,
    spl21_142,
    inference(avatar_split_clause,[],[f444,f1655]) ).

tff(f444,plain,
    ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
      ( ord_less_eq(fun(X1,X0),X3,X2)
      | ~ ord_less_eq(X0,aa(X1,X0,X3,sK8(X0,X1,X2,X3)),aa(X1,X0,X2,sK8(X0,X1,X2,X3)))
      | ~ ord(X0) ),
    inference(cnf_transformation,[],[f324]) ).

tff(f324,plain,
    ! [X0: $tType,X1: $tType] :
      ( ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
          ( ( ord_less_eq(fun(X1,X0),X3,X2)
            | ~ ord_less_eq(X0,aa(X1,X0,X3,sK8(X0,X1,X2,X3)),aa(X1,X0,X2,sK8(X0,X1,X2,X3))) )
          & ( ! [X5: X1] : ord_less_eq(X0,aa(X1,X0,X3,X5),aa(X1,X0,X2,X5))
            | ~ ord_less_eq(fun(X1,X0),X3,X2) ) )
      | ~ ord(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f322,f323]) ).

tff(f323,plain,
    ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
      ( ? [X4: X1] : ~ ord_less_eq(X0,aa(X1,X0,X3,X4),aa(X1,X0,X2,X4))
     => ~ ord_less_eq(X0,aa(X1,X0,X3,sK8(X0,X1,X2,X3)),aa(X1,X0,X2,sK8(X0,X1,X2,X3))) ),
    introduced(choice_axiom,[]) ).

tff(f322,plain,
    ! [X0: $tType,X1: $tType] :
      ( ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
          ( ( ord_less_eq(fun(X1,X0),X3,X2)
            | ? [X4: X1] : ~ ord_less_eq(X0,aa(X1,X0,X3,X4),aa(X1,X0,X2,X4)) )
          & ( ! [X5: X1] : ord_less_eq(X0,aa(X1,X0,X3,X5),aa(X1,X0,X2,X5))
            | ~ ord_less_eq(fun(X1,X0),X3,X2) ) )
      | ~ ord(X0) ),
    inference(rectify,[],[f321]) ).

tff(f321,plain,
    ! [X0: $tType,X1: $tType] :
      ( ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
          ( ( ord_less_eq(fun(X1,X0),X3,X2)
            | ? [X4: X1] : ~ ord_less_eq(X0,aa(X1,X0,X3,X4),aa(X1,X0,X2,X4)) )
          & ( ! [X4: X1] : ord_less_eq(X0,aa(X1,X0,X3,X4),aa(X1,X0,X2,X4))
            | ~ ord_less_eq(fun(X1,X0),X3,X2) ) )
      | ~ ord(X0) ),
    inference(nnf_transformation,[],[f248]) ).

tff(f248,plain,
    ! [X0: $tType,X1: $tType] :
      ( ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
          ( ord_less_eq(fun(X1,X0),X3,X2)
        <=> ! [X4: X1] : ord_less_eq(X0,aa(X1,X0,X3,X4),aa(X1,X0,X2,X4)) )
      | ~ ord(X0) ),
    inference(ennf_transformation,[],[f165]) ).

tff(f165,plain,
    ! [X0: $tType,X1: $tType] :
      ( ord(X0)
     => ! [X2: fun(X1,X0),X3: fun(X1,X0)] :
          ( ord_less_eq(fun(X1,X0),X3,X2)
        <=> ! [X4: X1] : ord_less_eq(X0,aa(X1,X0,X3,X4),aa(X1,X0,X2,X4)) ) ),
    inference(rectify,[],[f98]) ).

tff(f98,axiom,
    ! [X23: $tType,X2: $tType] :
      ( ord(X23)
     => ! [X54: fun(X2,X23),X55: fun(X2,X23)] :
          ( ord_less_eq(fun(X2,X23),X55,X54)
        <=> ! [X61: X2] : ord_less_eq(X23,aa(X2,X23,X55,X61),aa(X2,X23,X54,X61)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_le__fun__def) ).

tff(f1628,plain,
    spl21_141,
    inference(avatar_split_clause,[],[f522,f1626]) ).

tff(f522,plain,
    ! [X0: $tType,X2: nat,X3: X0,X1: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0)] :
      ( ( huffma1401021291ibling(X0,X4,X3) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) )
      | ~ member(X0,X3,huffma675207370phabet(X0,X4))
      | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
    inference(cnf_transformation,[],[f289]) ).

tff(f289,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: nat,X3: X0,X4: huffma1450048681e_tree(X0)] :
      ( ( huffma1401021291ibling(X0,X4,X3) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) )
      | ~ member(X0,X3,huffma675207370phabet(X0,X4))
      | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
    inference(flattening,[],[f288]) ).

tff(f288,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: nat,X3: X0,X4: huffma1450048681e_tree(X0)] :
      ( ( huffma1401021291ibling(X0,X4,X3) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) )
      | ~ member(X0,X3,huffma675207370phabet(X0,X4))
      | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
    inference(ennf_transformation,[],[f215]) ).

tff(f215,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: nat,X3: X0,X4: huffma1450048681e_tree(X0)] :
      ( ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4))
     => ( member(X0,X3,huffma675207370phabet(X0,X4))
       => ( huffma1401021291ibling(X0,X4,X3) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) ) ) ),
    inference(rectify,[],[f7]) ).

tff(f7,axiom,
    ! [X2: $tType,X15: huffma1450048681e_tree(X2),X12: nat,X14: X2,X13: huffma1450048681e_tree(X2)] :
      ( ord_less(nat,zero_zero(nat),huffma945805758height(X2,X13))
     => ( member(X2,X14,huffma675207370phabet(X2,X13))
       => ( huffma1401021291ibling(X2,X13,X14) = huffma1401021291ibling(X2,huffma1146269203erNode(X2,X12,X13,X15),X14) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_height__gt__0__in__alphabet__imp__sibling__left) ).

tff(f1624,plain,
    spl21_140,
    inference(avatar_split_clause,[],[f521,f1622]) ).

tff(f521,plain,
    ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: X0,X1: nat,X4: huffma1450048681e_tree(X0)] :
      ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) = huffma1401021291ibling(X0,X2,X3) )
      | ~ member(X0,X3,huffma675207370phabet(X0,X2))
      | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
    inference(cnf_transformation,[],[f287]) ).

tff(f287,plain,
    ! [X0: $tType,X1: nat,X2: huffma1450048681e_tree(X0),X3: X0,X4: huffma1450048681e_tree(X0)] :
      ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) = huffma1401021291ibling(X0,X2,X3) )
      | ~ member(X0,X3,huffma675207370phabet(X0,X2))
      | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
    inference(flattening,[],[f286]) ).

tff(f286,plain,
    ! [X0: $tType,X1: nat,X2: huffma1450048681e_tree(X0),X3: X0,X4: huffma1450048681e_tree(X0)] :
      ( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) = huffma1401021291ibling(X0,X2,X3) )
      | ~ member(X0,X3,huffma675207370phabet(X0,X2))
      | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
    inference(ennf_transformation,[],[f214]) ).

tff(f214,plain,
    ! [X0: $tType,X1: nat,X2: huffma1450048681e_tree(X0),X3: X0,X4: huffma1450048681e_tree(X0)] :
      ( ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4))
     => ( member(X0,X3,huffma675207370phabet(X0,X2))
       => ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) = huffma1401021291ibling(X0,X2,X3) ) ) ),
    inference(rectify,[],[f8]) ).

tff(f8,axiom,
    ! [X2: $tType,X12: nat,X13: huffma1450048681e_tree(X2),X14: X2,X15: huffma1450048681e_tree(X2)] :
      ( ord_less(nat,zero_zero(nat),huffma945805758height(X2,X15))
     => ( member(X2,X14,huffma675207370phabet(X2,X13))
       => ( huffma1401021291ibling(X2,X13,X14) = huffma1401021291ibling(X2,huffma1146269203erNode(X2,X12,X13,X15),X14) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_height__gt__0__in__alphabet__imp__sibling__right) ).

tff(f1620,plain,
    spl21_139,
    inference(avatar_split_clause,[],[f520,f1618]) ).

tff(f520,plain,
    ! [X0: $tType,X2: nat,X3: X0,X1: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0)] :
      ( ( huffma1401021291ibling(X0,X1,X3) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) )
      | member(X0,X3,huffma675207370phabet(X0,X4))
      | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
    inference(cnf_transformation,[],[f285]) ).

tff(f285,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: nat,X3: X0,X4: huffma1450048681e_tree(X0)] :
      ( ( huffma1401021291ibling(X0,X1,X3) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) )
      | member(X0,X3,huffma675207370phabet(X0,X4))
      | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
    inference(flattening,[],[f284]) ).

tff(f284,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: nat,X3: X0,X4: huffma1450048681e_tree(X0)] :
      ( ( huffma1401021291ibling(X0,X1,X3) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) )
      | member(X0,X3,huffma675207370phabet(X0,X4))
      | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
    inference(ennf_transformation,[],[f213]) ).

tff(f213,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: nat,X3: X0,X4: huffma1450048681e_tree(X0)] :
      ( ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4))
     => ( ~ member(X0,X3,huffma675207370phabet(X0,X4))
       => ( huffma1401021291ibling(X0,X1,X3) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) ) ) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X2: $tType,X15: huffma1450048681e_tree(X2),X12: nat,X14: X2,X13: huffma1450048681e_tree(X2)] :
      ( ord_less(nat,zero_zero(nat),huffma945805758height(X2,X13))
     => ( ~ member(X2,X14,huffma675207370phabet(X2,X13))
       => ( huffma1401021291ibling(X2,X15,X14) = huffma1401021291ibling(X2,huffma1146269203erNode(X2,X12,X13,X15),X14) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_height__gt__0__notin__alphabet__imp__sibling__left) ).

tff(f1616,plain,
    spl21_138,
    inference(avatar_split_clause,[],[f519,f1614]) ).

tff(f519,plain,
    ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: X0,X1: nat,X4: huffma1450048681e_tree(X0)] :
      ( ( huffma1401021291ibling(X0,X4,X3) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) )
      | member(X0,X3,huffma675207370phabet(X0,X2))
      | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
    inference(cnf_transformation,[],[f283]) ).

tff(f283,plain,
    ! [X0: $tType,X1: nat,X2: huffma1450048681e_tree(X0),X3: X0,X4: huffma1450048681e_tree(X0)] :
      ( ( huffma1401021291ibling(X0,X4,X3) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) )
      | member(X0,X3,huffma675207370phabet(X0,X2))
      | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
    inference(flattening,[],[f282]) ).

tff(f282,plain,
    ! [X0: $tType,X1: nat,X2: huffma1450048681e_tree(X0),X3: X0,X4: huffma1450048681e_tree(X0)] :
      ( ( huffma1401021291ibling(X0,X4,X3) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) )
      | member(X0,X3,huffma675207370phabet(X0,X2))
      | ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
    inference(ennf_transformation,[],[f212]) ).

tff(f212,plain,
    ! [X0: $tType,X1: nat,X2: huffma1450048681e_tree(X0),X3: X0,X4: huffma1450048681e_tree(X0)] :
      ( ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4))
     => ( ~ member(X0,X3,huffma675207370phabet(X0,X2))
       => ( huffma1401021291ibling(X0,X4,X3) = huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) ) ) ),
    inference(rectify,[],[f6]) ).

tff(f6,axiom,
    ! [X2: $tType,X12: nat,X13: huffma1450048681e_tree(X2),X14: X2,X15: huffma1450048681e_tree(X2)] :
      ( ord_less(nat,zero_zero(nat),huffma945805758height(X2,X15))
     => ( ~ member(X2,X14,huffma675207370phabet(X2,X13))
       => ( huffma1401021291ibling(X2,X15,X14) = huffma1401021291ibling(X2,huffma1146269203erNode(X2,X12,X13,X15),X14) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_height__gt__0__notin__alphabet__imp__sibling__right) ).

tff(f1612,plain,
    spl21_137,
    inference(avatar_split_clause,[],[f503,f1610]) ).

tff(f1610,plain,
    ( spl21_137
  <=> ! [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,[spl21_137])]) ).

tff(f503,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,[],[f275]) ).

tff(f275,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,[],[f274]) ).

tff(f274,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,[],[f204]) ).

tff(f204,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,[],[f13]) ).

tff(f13,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/sandbox/benchmark/theBenchmark.p',fact_12_height__gt__0__alphabet__eq__imp__height__gt__0) ).

tff(f1601,plain,
    ( spl21_136
    | ~ spl21_24
    | ~ spl21_94
    | ~ spl21_131 ),
    inference(avatar_split_clause,[],[f1555,f1536,f1119,f687,f1599]) ).

tff(f1555,plain,
    ( ! [X2: huffma1450048681e_tree(a1),X3: huffma1450048681e_tree(a1),X0: nat,X1: nat] : ( a = huffma1401021291ibling(a1,huffma1146269203erNode(a1,X0,t_1,huffma1146269203erNode(a1,X1,X2,X3)),a) )
    | ~ spl21_24
    | ~ spl21_94
    | ~ spl21_131 ),
    inference(forward_demodulation,[],[f1554,f1121]) ).

tff(f1588,plain,
    spl21_135,
    inference(avatar_split_clause,[],[f464,f1586]) ).

tff(f464,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ( huffma1146269203erNode(X0,sK12(X0,X1),sK13(X0,X1),sK14(X0,X1)) = X1 )
      | ( huffma2021818691e_Leaf(X0,sK15(X0,X1),sK16(X0,X1)) = X1 ) ),
    inference(cnf_transformation,[],[f334]) ).

tff(f334,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ( huffma1146269203erNode(X0,sK12(X0,X1),sK13(X0,X1),sK14(X0,X1)) = X1 )
      | ( huffma2021818691e_Leaf(X0,sK15(X0,X1),sK16(X0,X1)) = X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15,sK16])],[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,sK12(X0,X1),sK13(X0,X1),sK14(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,sK15(X0,X1),sK16(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,[],[f267]) ).

tff(f267,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,[],[f179]) ).

tff(f179,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,[],[f40]) ).

tff(f40,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/sandbox/benchmark/theBenchmark.p',fact_39_tree_Oexhaust) ).

tff(f1584,plain,
    spl21_134,
    inference(avatar_split_clause,[],[f457,f1582]) ).

tff(f457,plain,
    ! [X3: nat,X0: nat,X1: fun(nat,bool)] :
      ( ~ pp(aa(nat,bool,X1,X3))
      | ~ ord_less(nat,X3,sK10(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,sK10(X0,X1)))
        & ! [X3: nat] :
            ( ~ pp(aa(nat,bool,X1,X3))
            | ~ ord_less(nat,X3,sK10(X0,X1)) )
        & ord_less_eq(nat,sK10(X0,X1),X0) )
      | ~ pp(aa(nat,bool,X1,X0))
      | pp(aa(nat,bool,X1,zero_zero(nat))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f263,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,sK10(X0,X1)))
        & ! [X3: nat] :
            ( ~ pp(aa(nat,bool,X1,X3))
            | ~ ord_less(nat,X3,sK10(X0,X1)) )
        & ord_less_eq(nat,sK10(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

tff(f263,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,[],[f262]) ).

tff(f262,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,[],[f176]) ).

tff(f176,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))
       => ? [X57: nat] :
            ( pp(aa(nat,bool,X38,X57))
            & ! [X58: nat] :
                ( ord_less(nat,X58,X57)
               => ~ pp(aa(nat,bool,X38,X58)) )
            & ord_less_eq(nat,X57,X19) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_ex__least__nat__le) ).

tff(f1563,plain,
    spl21_133,
    inference(avatar_split_clause,[],[f518,f1561]) ).

tff(f518,plain,
    ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
      ( ( X2 = X3 )
      | ( aa(X1,X0,X3,sK20(X0,X1,X2,X3)) != aa(X1,X0,X2,sK20(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,sK20(X0,X1,X2,X3)) != aa(X1,X0,X2,sK20(X0,X1,X2,X3)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f281,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,sK20(X0,X1,X2,X3)) != aa(X1,X0,X2,sK20(X0,X1,X2,X3)) ) ),
    introduced(choice_axiom,[]) ).

tff(f281,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,[],[f211]) ).

tff(f211,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,X54: fun(X2,X23),X55: fun(X2,X23)] :
      ( ! [X47: X2] : ( aa(X2,X23,X55,X47) = aa(X2,X23,X54,X47) )
     => ( X54 = X55 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).

tff(f1559,plain,
    spl21_132,
    inference(avatar_split_clause,[],[f461,f1557]) ).

tff(f461,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,sK11(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,sK11(X1)) )
        & ~ pp(aa(nat,bool,X1,sK11(X1)))
        & ord_less(nat,zero_zero(nat),sK11(X1)) )
      | ~ pp(aa(nat,bool,X1,zero_zero(nat))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f265,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,sK11(X1)) )
        & ~ pp(aa(nat,bool,X1,sK11(X1)))
        & ord_less(nat,zero_zero(nat),sK11(X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f265,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,[],[f264]) ).

tff(f264,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,[],[f177]) ).

tff(f177,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,[],[f43]) ).

tff(f43,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/sandbox/benchmark/theBenchmark.p',fact_42_infinite__descent0) ).

tff(f1538,plain,
    spl21_131,
    inference(avatar_split_clause,[],[f535,f1536]) ).

tff(f535,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,[],[f291]) ).

tff(f1534,plain,
    ( spl21_130
    | ~ spl21_57
    | ~ spl21_84 ),
    inference(avatar_split_clause,[],[f1425,f1033,f854,f1531]) ).

tff(f1531,plain,
    ( spl21_130
  <=> ( zero_zero(nat) = sK2(zero_zero(int)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_130])]) ).

tff(f854,plain,
    ( spl21_57
  <=> ! [X0: nat] :
        ( ( zero_zero(nat) = X0 )
        | ( zero_zero(int) != semiring_1_of_nat(int,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_57])]) ).

tff(f1033,plain,
    ( spl21_84
  <=> ( zero_zero(int) = semiring_1_of_nat(int,sK2(zero_zero(int))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_84])]) ).

tff(f1425,plain,
    ( ( zero_zero(nat) = sK2(zero_zero(int)) )
    | ~ spl21_57
    | ~ spl21_84 ),
    inference(trivial_inequality_removal,[],[f1394]) ).

tff(f1394,plain,
    ( ( zero_zero(int) != zero_zero(int) )
    | ( zero_zero(nat) = sK2(zero_zero(int)) )
    | ~ spl21_57
    | ~ spl21_84 ),
    inference(superposition,[],[f855,f1035]) ).

tff(f1035,plain,
    ( ( zero_zero(int) = semiring_1_of_nat(int,sK2(zero_zero(int))) )
    | ~ spl21_84 ),
    inference(avatar_component_clause,[],[f1033]) ).

tff(f855,plain,
    ( ! [X0: nat] :
        ( ( zero_zero(int) != semiring_1_of_nat(int,X0) )
        | ( zero_zero(nat) = X0 ) )
    | ~ spl21_57 ),
    inference(avatar_component_clause,[],[f854]) ).

tff(f1529,plain,
    spl21_129,
    inference(avatar_split_clause,[],[f506,f1527]) ).

tff(f506,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,[],[f294]) ).

tff(f294,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,[],[f277,f293]) ).

tff(f293,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(f277,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,[],[f276]) ).

tff(f276,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,[],[f205]) ).

tff(f205,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,[],[f30]) ).

tff(f30,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/sandbox/benchmark/theBenchmark.p',fact_29_nat__less__cases) ).

tff(f1509,plain,
    spl21_128,
    inference(avatar_split_clause,[],[f534,f1507]) ).

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) = X6 )
      | ( X1 = X6 )
      | ( X5 = X6 ) ),
    inference(cnf_transformation,[],[f290]) ).

tff(f290,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,[],[f223]) ).

tff(f223,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,[],[f19]) ).

tff(f19,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/sandbox/benchmark/theBenchmark.p',fact_18_sibling_Osimps_I2_J) ).

tff(f1505,plain,
    spl21_127,
    inference(avatar_split_clause,[],[f510,f1503]) ).

tff(f510,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,sK18(X2),sK19(X2)) ),
    inference(cnf_transformation,[],[f354]) ).

tff(f1451,plain,
    spl21_126,
    inference(avatar_split_clause,[],[f529,f1449]) ).

tff(f529,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,[],[f220]) ).

tff(f220,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,[],[f53]) ).

tff(f53,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/sandbox/benchmark/theBenchmark.p',fact_52_tree_Orecs_I1_J) ).

tff(f1447,plain,
    spl21_125,
    inference(avatar_split_clause,[],[f528,f1445]) ).

tff(f528,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,[],[f219]) ).

tff(f219,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,[],[f25]) ).

tff(f25,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/sandbox/benchmark/theBenchmark.p',fact_24_tree_Osimps_I5_J) ).

tff(f1391,plain,
    spl21_124,
    inference(avatar_split_clause,[],[f458,f1389]) ).

tff(f458,plain,
    ! [X0: nat,X1: fun(nat,bool)] :
      ( pp(aa(nat,bool,X1,sK10(X0,X1)))
      | ~ pp(aa(nat,bool,X1,X0))
      | pp(aa(nat,bool,X1,zero_zero(nat))) ),
    inference(cnf_transformation,[],[f328]) ).

tff(f1363,plain,
    spl21_123,
    inference(avatar_split_clause,[],[f460,f1361]) ).

tff(f460,plain,
    ! [X0: nat,X1: fun(nat,bool)] :
      ( pp(aa(nat,bool,X1,X0))
      | ~ pp(aa(nat,bool,X1,sK11(X1)))
      | ~ pp(aa(nat,bool,X1,zero_zero(nat))) ),
    inference(cnf_transformation,[],[f330]) ).

tff(f1359,plain,
    spl21_122,
    inference(avatar_split_clause,[],[f443,f1357]) ).

tff(f443,plain,
    ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X5: X1] :
      ( ord_less_eq(X0,aa(X1,X0,X3,X5),aa(X1,X0,X2,X5))
      | ~ ord_less_eq(fun(X1,X0),X3,X2)
      | ~ ord(X0) ),
    inference(cnf_transformation,[],[f324]) ).

tff(f1355,plain,
    spl21_121,
    inference(avatar_split_clause,[],[f437,f1353]) ).

tff(f437,plain,
    ! [X0: fun(int,bool),X4: int] :
      ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK7(X0))))
      | ~ pp(aa(int,bool,X0,X4))
      | ~ ord_less_eq(int,zero_zero(int),X4) ),
    inference(cnf_transformation,[],[f320]) ).

tff(f320,plain,
    ! [X0: fun(int,bool)] :
      ( ( ( pp(aa(int,bool,X0,sK6(X0)))
          & ord_less_eq(int,zero_zero(int),sK6(X0)) )
        | ! [X2: nat] : ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,X2))) )
      & ( pp(aa(int,bool,X0,semiring_1_of_nat(int,sK7(X0))))
        | ! [X4: int] :
            ( ~ pp(aa(int,bool,X0,X4))
            | ~ ord_less_eq(int,zero_zero(int),X4) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f317,f319,f318]) ).

tff(f318,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,sK6(X0)))
        & ord_less_eq(int,zero_zero(int),sK6(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f319,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,sK7(X0)))) ),
    introduced(choice_axiom,[]) ).

tff(f317,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,[],[f316]) ).

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))) )
      & ( ? [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,[],[f161]) ).

tff(f161,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,[],[f84]) ).

tff(f84,axiom,
    ! [X38: fun(int,bool)] :
      ( ? [X61: int] :
          ( pp(aa(int,bool,X38,X61))
          & ord_less_eq(int,zero_zero(int),X61) )
    <=> ? [X61: nat] : pp(aa(int,bool,X38,semiring_1_of_nat(int,X61))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_transfer__int__nat__quantifiers_I2_J) ).

tff(f1351,plain,
    spl21_120,
    inference(avatar_split_clause,[],[f436,f1349]) ).

tff(f436,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,sK4(X0)))) ),
    inference(cnf_transformation,[],[f315]) ).

tff(f315,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,sK4(X0)))) )
      & ( ! [X3: nat] : pp(aa(int,bool,X0,semiring_1_of_nat(int,X3)))
        | ( ~ pp(aa(int,bool,X0,sK5(X0)))
          & ord_less_eq(int,zero_zero(int),sK5(X0)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f312,f314,f313]) ).

tff(f313,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,sK4(X0)))) ),
    introduced(choice_axiom,[]) ).

tff(f314,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,sK5(X0)))
        & ord_less_eq(int,zero_zero(int),sK5(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f312,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,[],[f311]) ).

tff(f311,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,[],[f245]) ).

tff(f245,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,[],[f160]) ).

tff(f160,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,[],[f85]) ).

tff(f85,axiom,
    ! [X38: fun(int,bool)] :
      ( ! [X61: int] :
          ( ord_less_eq(int,zero_zero(int),X61)
         => pp(aa(int,bool,X38,X61)) )
    <=> ! [X61: nat] : pp(aa(int,bool,X38,semiring_1_of_nat(int,X61))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_transfer__int__nat__quantifiers_I1_J) ).

tff(f1338,plain,
    spl21_119,
    inference(avatar_split_clause,[],[f567,f1336]) ).

tff(f567,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,[],[f533]) ).

tff(f533,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,[],[f290]) ).

tff(f1334,plain,
    spl21_118,
    inference(avatar_split_clause,[],[f459,f1332]) ).

tff(f459,plain,
    ! [X0: nat,X1: fun(nat,bool)] :
      ( pp(aa(nat,bool,X1,X0))
      | ord_less(nat,zero_zero(nat),sK11(X1))
      | ~ pp(aa(nat,bool,X1,zero_zero(nat))) ),
    inference(cnf_transformation,[],[f330]) ).

tff(f1330,plain,
    spl21_117,
    inference(avatar_split_clause,[],[f456,f1328]) ).

tff(f456,plain,
    ! [X0: nat,X1: fun(nat,bool)] :
      ( ord_less_eq(nat,sK10(X0,X1),X0)
      | ~ pp(aa(nat,bool,X1,X0))
      | pp(aa(nat,bool,X1,zero_zero(nat))) ),
    inference(cnf_transformation,[],[f328]) ).

tff(f1321,plain,
    ( spl21_116
    | spl21_24
    | ~ spl21_110 ),
    inference(avatar_split_clause,[],[f1312,f1289,f687,f1318]) ).

tff(f1312,plain,
    ( ( zero_zero(nat) = aa(a1,nat,huffma1352802255e_freq(a1,t_1),a) )
    | spl21_24
    | ~ spl21_110 ),
    inference(resolution,[],[f1290,f689]) ).

tff(f1311,plain,
    spl21_115,
    inference(avatar_split_clause,[],[f568,f1309]) ).

tff(f568,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,[],[f532]) ).

tff(f532,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,[],[f290]) ).

tff(f1307,plain,
    spl21_114,
    inference(avatar_split_clause,[],[f543,f1305]) ).

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)] :
      ( ( 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,[],[f226]) ).

tff(f226,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/sandbox/benchmark/theBenchmark.p',fact_0_tree_Osimps_I2_J) ).

tff(f1303,plain,
    spl21_113,
    inference(avatar_split_clause,[],[f542,f1301]) ).

tff(f542,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(f1299,plain,
    spl21_112,
    inference(avatar_split_clause,[],[f517,f1297]) ).

tff(f517,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,[],[f280]) ).

tff(f280,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,[],[f210]) ).

tff(f210,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,[],[f41]) ).

tff(f41,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/sandbox/benchmark/theBenchmark.p',fact_40_freq_Osimps_I1_J) ).

tff(f1295,plain,
    spl21_111,
    inference(avatar_split_clause,[],[f505,f1293]) ).

tff(f505,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,[],[f293]) ).

tff(f1291,plain,
    spl21_110,
    inference(avatar_split_clause,[],[f501,f1289]) ).

tff(f501,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,[],[f272]) ).

tff(f272,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,[],[f202]) ).

tff(f202,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,[],[f50]) ).

tff(f50,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/sandbox/benchmark/theBenchmark.p',fact_49_notin__alphabet__imp__freq__0) ).

tff(f1276,plain,
    spl21_109,
    inference(avatar_split_clause,[],[f541,f1274]) ).

tff(f541,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(f1272,plain,
    spl21_108,
    inference(avatar_split_clause,[],[f439,f1270]) ).

tff(f439,plain,
    ! [X2: nat,X0: fun(int,bool)] :
      ( pp(aa(int,bool,X0,sK6(X0)))
      | ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,X2))) ),
    inference(cnf_transformation,[],[f320]) ).

tff(f1268,plain,
    spl21_107,
    inference(avatar_split_clause,[],[f435,f1266]) ).

tff(f435,plain,
    ! [X3: nat,X0: fun(int,bool)] :
      ( pp(aa(int,bool,X0,semiring_1_of_nat(int,X3)))
      | ~ pp(aa(int,bool,X0,sK5(X0))) ),
    inference(cnf_transformation,[],[f315]) ).

tff(f1215,plain,
    ( spl21_106
    | ~ spl21_50
    | spl21_97 ),
    inference(avatar_split_clause,[],[f1147,f1142,f806,f1212]) ).

tff(f1147,plain,
    ( ( zero_zero(nat) = huffma945805758height(a1,t_2) )
    | ~ spl21_50
    | spl21_97 ),
    inference(resolution,[],[f1143,f807]) ).

tff(f1143,plain,
    ( ~ ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_2))
    | spl21_97 ),
    inference(avatar_component_clause,[],[f1142]) ).

tff(f1181,plain,
    spl21_105,
    inference(avatar_split_clause,[],[f438,f1179]) ).

tff(f438,plain,
    ! [X2: nat,X0: fun(int,bool)] :
      ( ord_less_eq(int,zero_zero(int),sK6(X0))
      | ~ pp(aa(int,bool,X0,semiring_1_of_nat(int,X2))) ),
    inference(cnf_transformation,[],[f320]) ).

tff(f1177,plain,
    spl21_104,
    inference(avatar_split_clause,[],[f434,f1175]) ).

tff(f434,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),sK5(X0)) ),
    inference(cnf_transformation,[],[f315]) ).

tff(f1173,plain,
    spl21_103,
    inference(avatar_split_clause,[],[f416,f1171]) ).

tff(f416,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,[],[f299]) ).

tff(f299,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,[],[f238]) ).

tff(f238,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,[],[f148]) ).

tff(f148,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,[],[f58]) ).

tff(f58,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/sandbox/benchmark/theBenchmark.p',fact_57_of__nat__le__iff) ).

tff(f1169,plain,
    spl21_102,
    inference(avatar_split_clause,[],[f415,f1167]) ).

tff(f415,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,[],[f299]) ).

tff(f1165,plain,
    spl21_101,
    inference(avatar_split_clause,[],[f412,f1163]) ).

tff(f412,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,[],[f236]) ).

tff(f236,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,[],[f146]) ).

tff(f146,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,[],[f49]) ).

tff(f49,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/sandbox/benchmark/theBenchmark.p',fact_48_of__nat__less__imp__less) ).

tff(f1161,plain,
    spl21_100,
    inference(avatar_split_clause,[],[f411,f1159]) ).

tff(f411,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,[],[f235]) ).

tff(f235,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,[],[f145]) ).

tff(f145,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,[],[f48]) ).

tff(f48,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/sandbox/benchmark/theBenchmark.p',fact_47_less__imp__of__nat__less) ).

tff(f1157,plain,
    spl21_99,
    inference(avatar_split_clause,[],[f410,f1155]) ).

tff(f1155,plain,
    ( spl21_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,[spl21_99])]) ).

tff(f410,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,[],[f297]) ).

tff(f297,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,[],[f234]) ).

tff(f234,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,[],[f144]) ).

tff(f144,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,[],[f39]) ).

tff(f39,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/sandbox/benchmark/theBenchmark.p',fact_38_of__nat__0__less__iff) ).

tff(f1153,plain,
    spl21_98,
    inference(avatar_split_clause,[],[f409,f1151]) ).

tff(f409,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,[],[f297]) ).

tff(f1145,plain,
    ( spl21_96
    | spl21_97 ),
    inference(avatar_split_clause,[],[f366,f1142,f1138]) ).

tff(f366,plain,
    ( ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_2))
    | ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_1)) ),
    inference(cnf_transformation,[],[f124]) ).

tff(f124,axiom,
    ( ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_2))
    | ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(f1126,plain,
    spl21_95,
    inference(avatar_split_clause,[],[f524,f1124]) ).

tff(f524,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,[],[f216]) ).

tff(f216,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,[],[f21]) ).

tff(f21,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/sandbox/benchmark/theBenchmark.p',fact_20_tree_Osimps_I1_J) ).

tff(f1122,plain,
    ( spl21_94
    | spl21_24
    | ~ spl21_86 ),
    inference(avatar_split_clause,[],[f1099,f1042,f687,f1119]) ).

tff(f1099,plain,
    ( ( a = huffma1401021291ibling(a1,t_1,a) )
    | spl21_24
    | ~ spl21_86 ),
    inference(resolution,[],[f1043,f689]) ).

tff(f1117,plain,
    spl21_93,
    inference(avatar_split_clause,[],[f523,f1115]) ).

tff(f523,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(f1113,plain,
    spl21_92,
    inference(avatar_split_clause,[],[f498,f1111]) ).

tff(f498,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,[],[f268]) ).

tff(f268,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,[],[f199]) ).

tff(f199,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,[],[f93]) ).

tff(f93,axiom,
    ! [X59: nat,X37: nat,X38: bool] :
      ( ( ~ pp(X38)
       => ( semiring_1_of_nat(int,X59) = semiring_1_of_nat(int,if(nat,X38,X37,X59)) ) )
      & ( pp(X38)
       => ( semiring_1_of_nat(int,X37) = semiring_1_of_nat(int,if(nat,X38,X37,X59)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_int__if__cong) ).

tff(f1109,plain,
    spl21_91,
    inference(avatar_split_clause,[],[f497,f1107]) ).

tff(f497,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,[],[f268]) ).

tff(f1105,plain,
    spl21_90,
    inference(avatar_split_clause,[],[f448,f1103]) ).

tff(f1103,plain,
    ( spl21_90
  <=> ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,sK9(X0,X1)) )
        | ~ huffma1518433673istent(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_90])]) ).

tff(f448,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,sK9(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,sK9(X0,X1)) )
        & member(X0,sK9(X0,X1),huffma675207370phabet(X0,X1)) )
      | ~ huffma1518433673istent(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f252,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,sK9(X0,X1)) )
        & member(X0,sK9(X0,X1),huffma675207370phabet(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f252,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,[],[f168]) ).

tff(f168,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,[],[f42]) ).

tff(f42,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/sandbox/benchmark/theBenchmark.p',fact_41_exists__at__height) ).

tff(f1078,plain,
    ( spl21_89
    | ~ spl21_28
    | ~ spl21_68 ),
    inference(avatar_split_clause,[],[f951,f911,f705,f1075]) ).

tff(f1075,plain,
    ( spl21_89
  <=> ( zero_zero(int) = semiring_1_of_nat(int,sK3(zero_zero(int))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_89])]) ).

tff(f705,plain,
    ( spl21_28
  <=> ord_less_eq(int,zero_zero(int),zero_zero(int)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_28])]) ).

tff(f951,plain,
    ( ( zero_zero(int) = semiring_1_of_nat(int,sK3(zero_zero(int))) )
    | ~ spl21_28
    | ~ spl21_68 ),
    inference(resolution,[],[f912,f707]) ).

tff(f707,plain,
    ( ord_less_eq(int,zero_zero(int),zero_zero(int))
    | ~ spl21_28 ),
    inference(avatar_component_clause,[],[f705]) ).

tff(f1052,plain,
    spl21_88,
    inference(avatar_split_clause,[],[f564,f1050]) ).

tff(f564,plain,
    ! [X0: $tType,X3: X0,X1: nat] : ( aa(X0,nat,huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X3)),X3) = X1 ),
    inference(equality_resolution,[],[f516]) ).

tff(f516,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,[],[f280]) ).

tff(f1048,plain,
    spl21_87,
    inference(avatar_split_clause,[],[f502,f1046]) ).

tff(f502,plain,
    ! [X0: $tType,X2: huffma1450048681e_tree(X0),X1: X0] :
      ( ( huffma1401021291ibling(X0,X2,X1) = X1 )
      | ( zero_zero(nat) != huffma945805758height(X0,X2) ) ),
    inference(cnf_transformation,[],[f273]) ).

tff(f273,plain,
    ! [X0: $tType,X1: X0,X2: huffma1450048681e_tree(X0)] :
      ( ( huffma1401021291ibling(X0,X2,X1) = X1 )
      | ( zero_zero(nat) != huffma945805758height(X0,X2) ) ),
    inference(ennf_transformation,[],[f203]) ).

tff(f203,plain,
    ! [X0: $tType,X1: X0,X2: huffma1450048681e_tree(X0)] :
      ( ( zero_zero(nat) = huffma945805758height(X0,X2) )
     => ( huffma1401021291ibling(X0,X2,X1) = X1 ) ),
    inference(rectify,[],[f9]) ).

tff(f9,axiom,
    ! [X0: $tType,X17: X0,X18: huffma1450048681e_tree(X0)] :
      ( ( zero_zero(nat) = huffma945805758height(X0,X18) )
     => ( huffma1401021291ibling(X0,X18,X17) = X17 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_height__0__imp__sibling__id) ).

tff(f1044,plain,
    spl21_86,
    inference(avatar_split_clause,[],[f500,f1042]) ).

tff(f500,plain,
    ! [X0: $tType,X2: X0,X1: huffma1450048681e_tree(X0)] :
      ( ( huffma1401021291ibling(X0,X1,X2) = X2 )
      | member(X0,X2,huffma675207370phabet(X0,X1)) ),
    inference(cnf_transformation,[],[f271]) ).

tff(f271,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: X0] :
      ( ( huffma1401021291ibling(X0,X1,X2) = X2 )
      | member(X0,X2,huffma675207370phabet(X0,X1)) ),
    inference(ennf_transformation,[],[f201]) ).

tff(f201,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/sandbox/benchmark/theBenchmark.p',fact_3_notin__alphabet__imp__sibling__id) ).

tff(f1040,plain,
    spl21_85,
    inference(avatar_split_clause,[],[f499,f1038]) ).

tff(f499,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,[],[f270]) ).

tff(f270,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,[],[f269]) ).

tff(f269,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,[],[f200]) ).

tff(f200,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,[],[f67]) ).

tff(f67,axiom,
    ! [X51: nat,X52: nat,X53: nat] :
      ( ord_less_eq(nat,X53,X52)
     => ( ord_less_eq(nat,X52,X51)
       => ord_less_eq(nat,X53,X51) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_le__trans) ).

tff(f1036,plain,
    ( spl21_84
    | ~ spl21_28
    | ~ spl21_67 ),
    inference(avatar_split_clause,[],[f944,f907,f705,f1033]) ).

tff(f944,plain,
    ( ( zero_zero(int) = semiring_1_of_nat(int,sK2(zero_zero(int))) )
    | ~ spl21_28
    | ~ spl21_67 ),
    inference(resolution,[],[f908,f707]) ).

tff(f1031,plain,
    spl21_83,
    inference(avatar_split_clause,[],[f486,f1029]) ).

tff(f486,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,[],[f189]) ).

tff(f189,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,[],[f86]) ).

tff(f86,axiom,
    ! [X59: nat,X37: nat] :
      ( ord_less_eq(int,semiring_1_of_nat(int,X37),semiring_1_of_nat(int,X59))
    <=> ord_less_eq(nat,X37,X59) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_transfer__int__nat__relations_I3_J) ).

tff(f1027,plain,
    spl21_82,
    inference(avatar_split_clause,[],[f485,f1025]) ).

tff(f485,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(f1023,plain,
    spl21_81,
    inference(avatar_split_clause,[],[f482,f1021]) ).

tff(f482,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,[],[f187]) ).

tff(f187,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,[],[f81]) ).

tff(f81,axiom,
    ! [X59: nat,X37: nat] :
      ( ord_less(int,semiring_1_of_nat(int,X37),semiring_1_of_nat(int,X59))
    <=> ord_less(nat,X37,X59) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_transfer__int__nat__relations_I2_J) ).

tff(f1019,plain,
    spl21_80,
    inference(avatar_split_clause,[],[f481,f1017]) ).

tff(f1017,plain,
    ( spl21_80
  <=> ! [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,[spl21_80])]) ).

tff(f481,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(f1015,plain,
    spl21_79,
    inference(avatar_split_clause,[],[f455,f1013]) ).

tff(f1013,plain,
    ( spl21_79
  <=> ! [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,[spl21_79])]) ).

tff(f455,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ( zero_zero(nat) = huffma1134658180e_cost(X0,X1) )
      | ( zero_zero(nat) != huffma945805758height(X0,X1) ) ),
    inference(cnf_transformation,[],[f261]) ).

tff(f261,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ( zero_zero(nat) = huffma1134658180e_cost(X0,X1) )
      | ( zero_zero(nat) != huffma945805758height(X0,X1) ) ),
    inference(ennf_transformation,[],[f175]) ).

tff(f175,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ( zero_zero(nat) = huffma945805758height(X0,X1) )
     => ( zero_zero(nat) = huffma1134658180e_cost(X0,X1) ) ),
    inference(rectify,[],[f20]) ).

tff(f20,axiom,
    ! [X0: $tType,X18: huffma1450048681e_tree(X0)] :
      ( ( zero_zero(nat) = huffma945805758height(X0,X18) )
     => ( zero_zero(nat) = huffma1134658180e_cost(X0,X18) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_height__0__imp__cost__0) ).

tff(f1011,plain,
    spl21_78,
    inference(avatar_split_clause,[],[f431,f1009]) ).

tff(f431,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,[],[f309]) ).

tff(f309,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,[],[f158]) ).

tff(f158,plain,
    ! [X0: nat] :
      ( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0))
    <=> ord_less(nat,zero_zero(nat),X0) ),
    inference(rectify,[],[f51]) ).

tff(f51,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/sandbox/benchmark/theBenchmark.p',fact_50_zero__less__int__conv) ).

tff(f1007,plain,
    spl21_77,
    inference(avatar_split_clause,[],[f430,f1005]) ).

tff(f1005,plain,
    ( spl21_77
  <=> ! [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,[spl21_77])]) ).

tff(f430,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,[],[f309]) ).

tff(f1003,plain,
    spl21_76,
    inference(avatar_split_clause,[],[f404,f1001]) ).

tff(f404,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,[],[f296]) ).

tff(f296,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,[],[f230]) ).

tff(f230,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,[],[f140]) ).

tff(f140,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,[],[f44]) ).

tff(f44,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/sandbox/benchmark/theBenchmark.p',fact_43_of__nat__eq__iff) ).

tff(f942,plain,
    spl21_75,
    inference(avatar_split_clause,[],[f526,f940]) ).

tff(f526,plain,
    ! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: X0,X4: huffma1450048681e_tree(X0),X5: nat] : ( huffma2021818691e_Leaf(X0,X2,X1) != huffma1146269203erNode(X0,X5,X4,X3) ),
    inference(cnf_transformation,[],[f217]) ).

tff(f217,plain,
    ! [X0: $tType,X1: X0,X2: nat,X3: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X5: nat] : ( huffma2021818691e_Leaf(X0,X2,X1) != huffma1146269203erNode(X0,X5,X4,X3) ),
    inference(rectify,[],[f26]) ).

tff(f26,axiom,
    ! [X0: $tType,X17: X0,X33: nat,X34: huffma1450048681e_tree(X0),X35: huffma1450048681e_tree(X0),X36: nat] : ( huffma1146269203erNode(X0,X36,X35,X34) != huffma2021818691e_Leaf(X0,X33,X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_tree_Osimps_I4_J) ).

tff(f937,plain,
    spl21_74,
    inference(avatar_split_clause,[],[f470,f935]) ).

tff(f470,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,[],[f182]) ).

tff(f182,plain,
    ! [X0: int,X1: int] :
      ( ord_less(int,X1,X0)
    <=> ( ( X0 != X1 )
        & ord_less_eq(int,X1,X0) ) ),
    inference(rectify,[],[f87]) ).

tff(f87,axiom,
    ! [X12: int,X62: int] :
      ( ord_less(int,X62,X12)
    <=> ( ( X12 != X62 )
        & ord_less_eq(int,X62,X12) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_less__int__def) ).

tff(f933,plain,
    spl21_73,
    inference(avatar_split_clause,[],[f454,f931]) ).

tff(f454,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ ord_less_eq(nat,X0,X1)
      | ~ ord_less_eq(nat,X1,X0) ),
    inference(cnf_transformation,[],[f260]) ).

tff(f260,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ ord_less_eq(nat,X0,X1)
      | ~ ord_less_eq(nat,X1,X0) ),
    inference(flattening,[],[f259]) ).

tff(f259,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ~ ord_less_eq(nat,X0,X1)
      | ~ ord_less_eq(nat,X1,X0) ),
    inference(ennf_transformation,[],[f174]) ).

tff(f174,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less_eq(nat,X1,X0)
     => ( ord_less_eq(nat,X0,X1)
       => ( X0 = X1 ) ) ),
    inference(rectify,[],[f66]) ).

tff(f66,axiom,
    ! [X20: nat,X22: nat] :
      ( ord_less_eq(nat,X22,X20)
     => ( ord_less_eq(nat,X20,X22)
       => ( X20 = X22 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_le__antisym) ).

tff(f929,plain,
    spl21_72,
    inference(avatar_split_clause,[],[f453,f927]) ).

tff(f453,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,X1,X0)
      | ( X0 = X1 )
      | ~ ord_less_eq(nat,X1,X0) ),
    inference(cnf_transformation,[],[f258]) ).

tff(f258,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,X1,X0)
      | ( X0 = X1 )
      | ~ ord_less_eq(nat,X1,X0) ),
    inference(flattening,[],[f257]) ).

tff(f257,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,X1,X0)
      | ( X0 = X1 )
      | ~ ord_less_eq(nat,X1,X0) ),
    inference(ennf_transformation,[],[f173]) ).

tff(f173,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less_eq(nat,X1,X0)
     => ( ( X0 != X1 )
       => ord_less(nat,X1,X0) ) ),
    inference(rectify,[],[f64]) ).

tff(f64,axiom,
    ! [X20: nat,X22: nat] :
      ( ord_less_eq(nat,X22,X20)
     => ( ( X20 != X22 )
       => ord_less(nat,X22,X20) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_le__neq__implies__less) ).

tff(f925,plain,
    spl21_71,
    inference(avatar_split_clause,[],[f447,f923]) ).

tff(f447,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( member(X0,sK9(X0,X1),huffma675207370phabet(X0,X1))
      | ~ huffma1518433673istent(X0,X1) ),
    inference(cnf_transformation,[],[f326]) ).

tff(f921,plain,
    spl21_70,
    inference(avatar_split_clause,[],[f445,f919]) ).

tff(f445,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,X0,X1)
      | ord_less(nat,X1,X0)
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f250]) ).

tff(f250,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,X0,X1)
      | ord_less(nat,X1,X0)
      | ( X0 = X1 ) ),
    inference(flattening,[],[f249]) ).

tff(f249,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,X0,X1)
      | ord_less(nat,X1,X0)
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f166]) ).

tff(f166,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 != X1 )
     => ( ~ ord_less(nat,X1,X0)
       => ord_less(nat,X0,X1) ) ),
    inference(rectify,[],[f34]) ).

tff(f34,axiom,
    ! [X41: nat,X42: nat] :
      ( ( X41 != X42 )
     => ( ~ ord_less(nat,X42,X41)
       => ord_less(nat,X41,X42) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_linorder__neqE__nat) ).

tff(f917,plain,
    spl21_69,
    inference(avatar_split_clause,[],[f432,f915]) ).

tff(f915,plain,
    ( spl21_69
  <=> ! [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,[spl21_69])]) ).

tff(f432,plain,
    ! [X0: nat] :
      ( ( zero_zero(nat) = X0 )
      | ~ ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int)) ),
    inference(cnf_transformation,[],[f310]) ).

tff(f310,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,[],[f159]) ).

tff(f159,plain,
    ! [X0: nat] :
      ( ord_less_eq(int,semiring_1_of_nat(int,X0),zero_zero(int))
    <=> ( zero_zero(nat) = X0 ) ),
    inference(rectify,[],[f91]) ).

tff(f91,axiom,
    ! [X19: nat] :
      ( ord_less_eq(int,semiring_1_of_nat(int,X19),zero_zero(int))
    <=> ( zero_zero(nat) = X19 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_int__le__0__conv) ).

tff(f913,plain,
    spl21_68,
    inference(avatar_split_clause,[],[f423,f911]) ).

tff(f423,plain,
    ! [X0: int] :
      ( ( semiring_1_of_nat(int,sK3(X0)) = X0 )
      | ~ ord_less_eq(int,zero_zero(int),X0) ),
    inference(cnf_transformation,[],[f305]) ).

tff(f305,plain,
    ! [X0: int] :
      ( ( semiring_1_of_nat(int,sK3(X0)) = X0 )
      | ~ ord_less_eq(int,zero_zero(int),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f244,f304]) ).

tff(f304,plain,
    ! [X0: int] :
      ( ? [X1: nat] : ( semiring_1_of_nat(int,X1) = X0 )
     => ( semiring_1_of_nat(int,sK3(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f244,plain,
    ! [X0: int] :
      ( ? [X1: nat] : ( semiring_1_of_nat(int,X1) = X0 )
      | ~ ord_less_eq(int,zero_zero(int),X0) ),
    inference(ennf_transformation,[],[f154]) ).

tff(f154,plain,
    ! [X0: int] :
      ( ord_less_eq(int,zero_zero(int),X0)
     => ? [X1: nat] : ( semiring_1_of_nat(int,X1) = X0 ) ),
    inference(rectify,[],[f95]) ).

tff(f95,axiom,
    ! [X51: int] :
      ( ord_less_eq(int,zero_zero(int),X51)
     => ? [X48: nat] : ( semiring_1_of_nat(int,X48) = X51 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_zero__le__imp__eq__int) ).

tff(f909,plain,
    spl21_67,
    inference(avatar_split_clause,[],[f422,f907]) ).

tff(f422,plain,
    ! [X0: int] :
      ( ( semiring_1_of_nat(int,sK2(X0)) = X0 )
      | ~ ord_less_eq(int,zero_zero(int),X0) ),
    inference(cnf_transformation,[],[f303]) ).

tff(f303,plain,
    ! [X0: int] :
      ( ( semiring_1_of_nat(int,sK2(X0)) = X0 )
      | ~ ord_less_eq(int,zero_zero(int),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f243,f302]) ).

tff(f302,plain,
    ! [X0: int] :
      ( ? [X1: nat] : ( semiring_1_of_nat(int,X1) = X0 )
     => ( semiring_1_of_nat(int,sK2(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f243,plain,
    ! [X0: int] :
      ( ? [X1: nat] : ( semiring_1_of_nat(int,X1) = X0 )
      | ~ ord_less_eq(int,zero_zero(int),X0) ),
    inference(ennf_transformation,[],[f153]) ).

tff(f153,plain,
    ! [X0: int] :
      ( ord_less_eq(int,zero_zero(int),X0)
     => ~ ! [X1: nat] : ( semiring_1_of_nat(int,X1) != X0 ) ),
    inference(rectify,[],[f94]) ).

tff(f94,axiom,
    ! [X60: int] :
      ( ord_less_eq(int,zero_zero(int),X60)
     => ~ ! [X63: nat] : ( semiring_1_of_nat(int,X63) != X60 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_nonneg__eq__int) ).

tff(f905,plain,
    spl21_66,
    inference(avatar_split_clause,[],[f421,f903]) ).

tff(f421,plain,
    ! [X0: int] :
      ( ( semiring_1_of_nat(int,sK1(X0)) = X0 )
      | ~ ord_less(int,zero_zero(int),X0) ),
    inference(cnf_transformation,[],[f301]) ).

tff(f301,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])],[f242,f300]) ).

tff(f300,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(f242,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,[],[f152]) ).

tff(f152,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,[],[f79]) ).

tff(f79,axiom,
    ! [X51: int] :
      ( ord_less(int,zero_zero(int),X51)
     => ? [X48: nat] :
          ( ( semiring_1_of_nat(int,X48) = X51 )
          & ord_less(nat,zero_zero(nat),X48) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_zero__less__imp__eq__int) ).

tff(f901,plain,
    spl21_65,
    inference(avatar_split_clause,[],[f420,f899]) ).

tff(f899,plain,
    ( spl21_65
  <=> ! [X0: int] :
        ( ord_less(nat,zero_zero(nat),sK1(X0))
        | ~ ord_less(int,zero_zero(int),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_65])]) ).

tff(f420,plain,
    ! [X0: int] :
      ( ord_less(nat,zero_zero(nat),sK1(X0))
      | ~ ord_less(int,zero_zero(int),X0) ),
    inference(cnf_transformation,[],[f301]) ).

tff(f897,plain,
    ( spl21_64
    | ~ spl21_56 ),
    inference(avatar_split_clause,[],[f884,f850,f895]) ).

tff(f895,plain,
    ( spl21_64
  <=> ! [X0: $tType,X1: X0] :
        ( ord_less_eq(X0,X1,X1)
        | ~ linorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_64])]) ).

tff(f884,plain,
    ( ! [X0: $tType,X1: X0] :
        ( ord_less_eq(X0,X1,X1)
        | ~ linorder(X0) )
    | ~ spl21_56 ),
    inference(factoring,[],[f851]) ).

tff(f881,plain,
    spl21_63,
    inference(avatar_split_clause,[],[f515,f879]) ).

tff(f515,plain,
    ! [X0: $tType,X2: X0,X3: nat,X1: X0] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) ),
    inference(cnf_transformation,[],[f209]) ).

tff(f209,plain,
    ! [X0: $tType,X1: X0,X2: X0,X3: nat] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) ),
    inference(rectify,[],[f38]) ).

tff(f38,axiom,
    ! [X0: $tType,X17: X0,X31: X0,X30: nat] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X30,X31),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_depth_Osimps_I1_J) ).

tff(f877,plain,
    spl21_62,
    inference(avatar_split_clause,[],[f513,f875]) ).

tff(f513,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,[],[f207]) ).

tff(f207,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,X56: fun(X2,bool),X37: X2] :
      ( member(X2,X37,X56)
    <=> pp(aa(X2,bool,X56,X37)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def) ).

tff(f873,plain,
    spl21_61,
    inference(avatar_split_clause,[],[f512,f871]) ).

tff(f512,plain,
    ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
      ( pp(aa(X0,bool,X1,X2))
      | ~ member(X0,X2,X1) ),
    inference(cnf_transformation,[],[f355]) ).

tff(f869,plain,
    ( spl21_60
    | ~ spl21_5
    | ~ spl21_45 ),
    inference(avatar_split_clause,[],[f830,f786,f596,f866]) ).

tff(f866,plain,
    ( spl21_60
  <=> ( zero_zero(nat) = semiring_1_of_nat(nat,zero_zero(nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_60])]) ).

tff(f596,plain,
    ( spl21_5
  <=> semiring_1(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_5])]) ).

tff(f786,plain,
    ( spl21_45
  <=> ! [X0: $tType] :
        ( ( semiring_1_of_nat(X0,zero_zero(nat)) = zero_zero(X0) )
        | ~ semiring_1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_45])]) ).

tff(f830,plain,
    ( ( zero_zero(nat) = semiring_1_of_nat(nat,zero_zero(nat)) )
    | ~ spl21_5
    | ~ spl21_45 ),
    inference(resolution,[],[f787,f598]) ).

tff(f598,plain,
    ( semiring_1(nat)
    | ~ spl21_5 ),
    inference(avatar_component_clause,[],[f596]) ).

tff(f787,plain,
    ( ! [X0: $tType] :
        ( ~ semiring_1(X0)
        | ( semiring_1_of_nat(X0,zero_zero(nat)) = zero_zero(X0) ) )
    | ~ spl21_45 ),
    inference(avatar_component_clause,[],[f786]) ).

tff(f864,plain,
    spl21_59,
    inference(avatar_split_clause,[],[f496,f862]) ).

tff(f496,plain,
    ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X2,X1)) ),
    inference(cnf_transformation,[],[f198]) ).

tff(f198,plain,
    ! [X0: $tType,X1: X0,X2: nat] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X2,X1)) ),
    inference(rectify,[],[f37]) ).

tff(f37,axiom,
    ! [X0: $tType,X17: X0,X33: nat] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X33,X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_tree_Osize_I3_J) ).

tff(f860,plain,
    spl21_58,
    inference(avatar_split_clause,[],[f477,f858]) ).

tff(f858,plain,
    ( spl21_58
  <=> ! [X0: nat,X1: nat] :
        ( ( X0 = X1 )
        | ( semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_58])]) ).

tff(f477,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,[],[f185]) ).

tff(f185,plain,
    ! [X0: nat,X1: nat] :
      ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
    <=> ( X0 = X1 ) ),
    inference(rectify,[],[f60]) ).

tff(f60,axiom,
    ! [X19: nat,X39: nat] :
      ( ( semiring_1_of_nat(int,X19) = semiring_1_of_nat(int,X39) )
    <=> ( X19 = X39 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_int__int__eq) ).

tff(f856,plain,
    spl21_57,
    inference(avatar_split_clause,[],[f428,f854]) ).

tff(f428,plain,
    ! [X0: nat] :
      ( ( zero_zero(nat) = X0 )
      | ( zero_zero(int) != semiring_1_of_nat(int,X0) ) ),
    inference(cnf_transformation,[],[f308]) ).

tff(f308,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,[],[f157]) ).

tff(f157,plain,
    ! [X0: nat] :
      ( ( zero_zero(int) = semiring_1_of_nat(int,X0) )
    <=> ( zero_zero(nat) = X0 ) ),
    inference(rectify,[],[f74]) ).

tff(f74,axiom,
    ! [X19: nat] :
      ( ( zero_zero(int) = semiring_1_of_nat(int,X19) )
    <=> ( zero_zero(nat) = X19 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_int__eq__0__conv) ).

tff(f852,plain,
    spl21_56,
    inference(avatar_split_clause,[],[f417,f850]) ).

tff(f417,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ord_less_eq(X0,X1,X2)
      | ord_less_eq(X0,X2,X1)
      | ~ linorder(X0) ),
    inference(cnf_transformation,[],[f239]) ).

tff(f239,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ord_less_eq(X0,X1,X2)
          | ord_less_eq(X0,X2,X1) )
      | ~ linorder(X0) ),
    inference(ennf_transformation,[],[f149]) ).

tff(f149,plain,
    ! [X0: $tType] :
      ( linorder(X0)
     => ! [X1: X0,X2: X0] :
          ( ord_less_eq(X0,X1,X2)
          | ord_less_eq(X0,X2,X1) ) ),
    inference(rectify,[],[f99]) ).

tff(f99,axiom,
    ! [X0: $tType] :
      ( linorder(X0)
     => ! [X41: X0,X42: X0] :
          ( ord_less_eq(X0,X41,X42)
          | ord_less_eq(X0,X42,X41) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_linorder__linear) ).

tff(f828,plain,
    spl21_55,
    inference(avatar_split_clause,[],[f514,f826]) ).

tff(f514,plain,
    ! [X0: $tType,X2: X0,X3: nat,X1: X0] : ( huffma1401021291ibling(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) = X1 ),
    inference(cnf_transformation,[],[f208]) ).

tff(f208,plain,
    ! [X0: $tType,X1: X0,X2: X0,X3: nat] : ( huffma1401021291ibling(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) = X1 ),
    inference(rectify,[],[f28]) ).

tff(f28,axiom,
    ! [X0: $tType,X17: X0,X31: X0,X29: nat] : ( huffma1401021291ibling(X0,huffma2021818691e_Leaf(X0,X29,X31),X17) = X17 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_sibling_Osimps_I1_J) ).

tff(f824,plain,
    spl21_54,
    inference(avatar_split_clause,[],[f495,f822]) ).

tff(f495,plain,
    ! [X0: $tType,X2: huffma1450048681e_tree(X0),X1: X0] : ord_less_eq(nat,huffma410068972_depth(X0,X2,X1),huffma945805758height(X0,X2)),
    inference(cnf_transformation,[],[f197]) ).

tff(f197,plain,
    ! [X0: $tType,X1: X0,X2: huffma1450048681e_tree(X0)] : ord_less_eq(nat,huffma410068972_depth(X0,X2,X1),huffma945805758height(X0,X2)),
    inference(rectify,[],[f73]) ).

tff(f73,axiom,
    ! [X0: $tType,X17: X0,X18: huffma1450048681e_tree(X0)] : ord_less_eq(nat,huffma410068972_depth(X0,X18,X17),huffma945805758height(X0,X18)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_depth__le__height) ).

tff(f820,plain,
    spl21_53,
    inference(avatar_split_clause,[],[f494,f818]) ).

tff(f494,plain,
    ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
    inference(cnf_transformation,[],[f196]) ).

tff(f196,plain,
    ! [X0: $tType,X1: X0,X2: nat] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
    inference(rectify,[],[f23]) ).

tff(f23,axiom,
    ! [X0: $tType,X17: X0,X30: nat] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X30,X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_height_Osimps_I1_J) ).

tff(f816,plain,
    spl21_52,
    inference(avatar_split_clause,[],[f493,f814]) ).

tff(f493,plain,
    ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma1134658180e_cost(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
    inference(cnf_transformation,[],[f195]) ).

tff(f195,plain,
    ! [X0: $tType,X1: X0,X2: nat] : ( zero_zero(nat) = huffma1134658180e_cost(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
    inference(rectify,[],[f24]) ).

tff(f24,axiom,
    ! [X0: $tType,X17: X0,X30: nat] : ( zero_zero(nat) = huffma1134658180e_cost(X0,huffma2021818691e_Leaf(X0,X30,X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_cost_Osimps_I1_J) ).

tff(f812,plain,
    spl21_51,
    inference(avatar_split_clause,[],[f426,f810]) ).

tff(f426,plain,
    ! [X0: nat] :
      ( ( zero_zero(nat) = X0 )
      | ~ ord_less_eq(nat,X0,zero_zero(nat)) ),
    inference(cnf_transformation,[],[f307]) ).

tff(f307,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,[],[f156]) ).

tff(f156,plain,
    ! [X0: nat] :
      ( ord_less_eq(nat,X0,zero_zero(nat))
    <=> ( zero_zero(nat) = X0 ) ),
    inference(rectify,[],[f55]) ).

tff(f55,axiom,
    ! [X19: nat] :
      ( ord_less_eq(nat,X19,zero_zero(nat))
    <=> ( zero_zero(nat) = X19 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_le__0__eq) ).

tff(f808,plain,
    spl21_50,
    inference(avatar_split_clause,[],[f419,f806]) ).

tff(f419,plain,
    ! [X0: nat] :
      ( ord_less(nat,zero_zero(nat),X0)
      | ( zero_zero(nat) = X0 ) ),
    inference(cnf_transformation,[],[f241]) ).

tff(f241,plain,
    ! [X0: nat] :
      ( ord_less(nat,zero_zero(nat),X0)
      | ( zero_zero(nat) = X0 ) ),
    inference(ennf_transformation,[],[f151]) ).

tff(f151,plain,
    ! [X0: nat] :
      ( ( zero_zero(nat) != X0 )
     => ord_less(nat,zero_zero(nat),X0) ),
    inference(rectify,[],[f16]) ).

tff(f16,axiom,
    ! [X20: nat] :
      ( ( zero_zero(nat) != X20 )
     => ord_less(nat,zero_zero(nat),X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_gr0I) ).

tff(f804,plain,
    spl21_49,
    inference(avatar_split_clause,[],[f407,f802]) ).

tff(f802,plain,
    ( spl21_49
  <=> ! [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,[spl21_49])]) ).

tff(f407,plain,
    ! [X0: $tType,X1: nat] :
      ( ord_less_eq(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
      | ~ linordered_semidom(X0) ),
    inference(cnf_transformation,[],[f232]) ).

tff(f232,plain,
    ! [X0: $tType] :
      ( ! [X1: nat] : ord_less_eq(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
      | ~ linordered_semidom(X0) ),
    inference(ennf_transformation,[],[f142]) ).

tff(f142,plain,
    ! [X0: $tType] :
      ( linordered_semidom(X0)
     => ! [X1: nat] : ord_less_eq(X0,zero_zero(X0),semiring_1_of_nat(X0,X1)) ),
    inference(rectify,[],[f71]) ).

tff(f71,axiom,
    ! [X0: $tType] :
      ( linordered_semidom(X0)
     => ! [X20: nat] : ord_less_eq(X0,zero_zero(X0),semiring_1_of_nat(X0,X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_of__nat__0__le__iff) ).

tff(f800,plain,
    ( spl21_47
    | ~ spl21_48
    | ~ spl21_29 ),
    inference(avatar_split_clause,[],[f731,f710,f797,f794]) ).

tff(f794,plain,
    ( spl21_47
  <=> ! [X0: bool] : ( fFalse = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_47])]) ).

tff(f797,plain,
    ( spl21_48
  <=> ( fTrue = fFalse ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_48])]) ).

tff(f731,plain,
    ( ! [X0: bool] :
        ( ( fTrue != fFalse )
        | ( fFalse = X0 ) )
    | ~ spl21_29 ),
    inference(equality_factoring,[],[f711]) ).

tff(f792,plain,
    spl21_46,
    inference(avatar_split_clause,[],[f406,f790]) ).

tff(f406,plain,
    ! [X0: $tType,X1: nat] :
      ( ~ ord_less(X0,semiring_1_of_nat(X0,X1),zero_zero(X0))
      | ~ linordered_semidom(X0) ),
    inference(cnf_transformation,[],[f231]) ).

tff(f231,plain,
    ! [X0: $tType] :
      ( ! [X1: nat] : ~ ord_less(X0,semiring_1_of_nat(X0,X1),zero_zero(X0))
      | ~ linordered_semidom(X0) ),
    inference(ennf_transformation,[],[f141]) ).

tff(f141,plain,
    ! [X0: $tType] :
      ( linordered_semidom(X0)
     => ! [X1: nat] : ~ ord_less(X0,semiring_1_of_nat(X0,X1),zero_zero(X0)) ),
    inference(rectify,[],[f47]) ).

tff(f47,axiom,
    ! [X0: $tType] :
      ( linordered_semidom(X0)
     => ! [X22: nat] : ~ ord_less(X0,semiring_1_of_nat(X0,X22),zero_zero(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_of__nat__less__0__iff) ).

tff(f788,plain,
    spl21_45,
    inference(avatar_split_clause,[],[f401,f786]) ).

tff(f401,plain,
    ! [X0: $tType] :
      ( ( semiring_1_of_nat(X0,zero_zero(nat)) = zero_zero(X0) )
      | ~ semiring_1(X0) ),
    inference(cnf_transformation,[],[f228]) ).

tff(f228,plain,
    ! [X0: $tType] :
      ( ( semiring_1_of_nat(X0,zero_zero(nat)) = zero_zero(X0) )
      | ~ semiring_1(X0) ),
    inference(ennf_transformation,[],[f45]) ).

tff(f45,axiom,
    ! [X0: $tType] :
      ( semiring_1(X0)
     => ( semiring_1_of_nat(X0,zero_zero(nat)) = zero_zero(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_of__nat__0) ).

tff(f782,plain,
    spl21_44,
    inference(avatar_split_clause,[],[f504,f780]) ).

tff(f780,plain,
    ( spl21_44
  <=> ! [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,[spl21_44])]) ).

tff(f504,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(f778,plain,
    spl21_43,
    inference(avatar_split_clause,[],[f489,f776]) ).

tff(f489,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] : member(X0,sK17(X0,X1),huffma675207370phabet(X0,X1)),
    inference(cnf_transformation,[],[f350]) ).

tff(f350,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] : member(X0,sK17(X0,X1),huffma675207370phabet(X0,X1)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f191,f349]) ).

tff(f349,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ? [X2: X0] : member(X0,X2,huffma675207370phabet(X0,X1))
     => member(X0,sK17(X0,X1),huffma675207370phabet(X0,X1)) ),
    introduced(choice_axiom,[]) ).

tff(f191,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
    ? [X2: X0] : member(X0,X2,huffma675207370phabet(X0,X1)),
    inference(rectify,[],[f18]) ).

tff(f18,axiom,
    ! [X2: $tType,X16: huffma1450048681e_tree(X2)] :
    ? [X26: X2] : member(X2,X26,huffma675207370phabet(X2,X16)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_exists__in__alphabet) ).

tff(f774,plain,
    spl21_42,
    inference(avatar_split_clause,[],[f468,f772]) ).

tff(f468,plain,
    ! [X0: int,X1: int] :
      ( ord_less_eq(int,X1,X0)
      | ~ ord_less(int,X1,X0) ),
    inference(cnf_transformation,[],[f338]) ).

tff(f769,plain,
    spl21_41,
    inference(avatar_split_clause,[],[f452,f767]) ).

tff(f452,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less_eq(nat,X1,X0)
      | ~ ord_less(nat,X1,X0) ),
    inference(cnf_transformation,[],[f256]) ).

tff(f256,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less_eq(nat,X1,X0)
      | ~ ord_less(nat,X1,X0) ),
    inference(ennf_transformation,[],[f172]) ).

tff(f172,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less(nat,X1,X0)
     => ord_less_eq(nat,X1,X0) ),
    inference(rectify,[],[f63]) ).

tff(f63,axiom,
    ! [X20: nat,X22: nat] :
      ( ord_less(nat,X22,X20)
     => ord_less_eq(nat,X22,X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_less__imp__le__nat) ).

tff(f765,plain,
    spl21_40,
    inference(avatar_split_clause,[],[f440,f763]) ).

tff(f440,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less_eq(nat,X0,X1)
      | ord_less_eq(nat,X1,X0) ),
    inference(cnf_transformation,[],[f162]) ).

tff(f162,plain,
    ! [X0: nat,X1: nat] :
      ( ord_less_eq(nat,X0,X1)
      | ord_less_eq(nat,X1,X0) ),
    inference(rectify,[],[f69]) ).

tff(f69,axiom,
    ! [X20: nat,X22: nat] :
      ( ord_less_eq(nat,X20,X22)
      | ord_less_eq(nat,X22,X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_nat__le__linear) ).

tff(f756,plain,
    spl21_39,
    inference(avatar_split_clause,[],[f492,f754]) ).

tff(f492,plain,
    ! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fFalse,X2,X1) = X1 ),
    inference(cnf_transformation,[],[f194]) ).

tff(f194,plain,
    ! [X0: $tType,X1: X0,X2: X0] : ( if(X0,fFalse,X2,X1) = X1 ),
    inference(rectify,[],[f120]) ).

tff(f120,axiom,
    ! [X0: $tType,X41: X0,X42: X0] : ( if(X0,fFalse,X42,X41) = X41 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).

tff(f752,plain,
    spl21_38,
    inference(avatar_split_clause,[],[f491,f750]) ).

tff(f491,plain,
    ! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fTrue,X2,X1) = X2 ),
    inference(cnf_transformation,[],[f193]) ).

tff(f193,plain,
    ! [X0: $tType,X1: X0,X2: X0] : ( if(X0,fTrue,X2,X1) = X2 ),
    inference(rectify,[],[f119]) ).

tff(f119,axiom,
    ! [X0: $tType,X41: X0,X42: X0] : ( if(X0,fTrue,X42,X41) = X42 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).

tff(f748,plain,
    spl21_37,
    inference(avatar_split_clause,[],[f398,f746]) ).

tff(f398,plain,
    ! [X0: nat] : ord_less_eq(int,zero_zero(int),semiring_1_of_nat(int,X0)),
    inference(cnf_transformation,[],[f136]) ).

tff(f136,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/sandbox/benchmark/theBenchmark.p',fact_88_zero__zle__int) ).

tff(f744,plain,
    ( spl21_36
    | ~ spl21_19
    | ~ spl21_29 ),
    inference(avatar_split_clause,[],[f730,f710,f666,f742]) ).

tff(f742,plain,
    ( spl21_36
  <=> ! [X0: bool] :
        ( pp(X0)
        | ( fFalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_36])]) ).

tff(f666,plain,
    ( spl21_19
  <=> pp(fTrue) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_19])]) ).

tff(f730,plain,
    ( ! [X0: bool] :
        ( pp(X0)
        | ( fFalse = X0 ) )
    | ~ spl21_19
    | ~ spl21_29 ),
    inference(superposition,[],[f668,f711]) ).

tff(f668,plain,
    ( pp(fTrue)
    | ~ spl21_19 ),
    inference(avatar_component_clause,[],[f666]) ).

tff(f740,plain,
    spl21_35,
    inference(avatar_split_clause,[],[f397,f738]) ).

tff(f738,plain,
    ( spl21_35
  <=> ! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_35])]) ).

tff(f397,plain,
    ! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)),
    inference(cnf_transformation,[],[f135]) ).

tff(f135,plain,
    ! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)),
    inference(rectify,[],[f59]) ).

tff(f59,axiom,
    ! [X51: nat] : ~ ord_less(int,semiring_1_of_nat(int,X51),zero_zero(int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_int__less__0__conv) ).

tff(f736,plain,
    spl21_34,
    inference(avatar_split_clause,[],[f387,f733]) ).

tff(f387,plain,
    zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)),
    inference(cnf_transformation,[],[f77]) ).

tff(f77,axiom,
    zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_int__0) ).

tff(f728,plain,
    spl21_33,
    inference(avatar_split_clause,[],[f490,f726]) ).

tff(f490,plain,
    ! [X0: $tType,X2: nat,X1: X0] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1)),
    inference(cnf_transformation,[],[f192]) ).

tff(f192,plain,
    ! [X0: $tType,X1: X0,X2: nat] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1)),
    inference(rectify,[],[f22]) ).

tff(f22,axiom,
    ! [X0: $tType,X17: X0,X30: nat] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X30,X17)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_consistent_Osimps_I1_J) ).

tff(f724,plain,
    spl21_32,
    inference(avatar_split_clause,[],[f442,f722]) ).

tff(f722,plain,
    ( spl21_32
  <=> ! [X1: $tType,X0: $tType] :
        ( preorder(fun(X0,X1))
        | ~ preorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_32])]) ).

tff(f442,plain,
    ! [X1: $tType,X0: $tType] :
      ( preorder(fun(X0,X1))
      | ~ preorder(X1) ),
    inference(cnf_transformation,[],[f247]) ).

tff(f247,plain,
    ! [X0: $tType,X1: $tType] :
      ( preorder(fun(X0,X1))
      | ~ preorder(X1) ),
    inference(ennf_transformation,[],[f164]) ).

tff(f164,plain,
    ! [X0: $tType,X1: $tType] :
      ( preorder(X1)
     => preorder(fun(X0,X1)) ),
    inference(rectify,[],[f100]) ).

tff(f100,axiom,
    ! [X68: $tType,X69: $tType] :
      ( preorder(X69)
     => preorder(fun(X68,X69)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).

tff(f720,plain,
    spl21_31,
    inference(avatar_split_clause,[],[f441,f718]) ).

tff(f718,plain,
    ( spl21_31
  <=> ! [X1: $tType,X0: $tType] :
        ( ord(fun(X0,X1))
        | ~ ord(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_31])]) ).

tff(f441,plain,
    ! [X1: $tType,X0: $tType] :
      ( ord(fun(X0,X1))
      | ~ ord(X1) ),
    inference(cnf_transformation,[],[f246]) ).

tff(f246,plain,
    ! [X0: $tType,X1: $tType] :
      ( ord(fun(X0,X1))
      | ~ ord(X1) ),
    inference(ennf_transformation,[],[f163]) ).

tff(f163,plain,
    ! [X0: $tType,X1: $tType] :
      ( ord(X1)
     => ord(fun(X0,X1)) ),
    inference(rectify,[],[f101]) ).

tff(f101,axiom,
    ! [X68: $tType,X69: $tType] :
      ( ord(X69)
     => ord(fun(X68,X69)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).

tff(f716,plain,
    spl21_30,
    inference(avatar_split_clause,[],[f418,f714]) ).

tff(f418,plain,
    ! [X0: $tType,X1: X0] :
      ( ord_less_eq(X0,X1,X1)
      | ~ preorder(X0) ),
    inference(cnf_transformation,[],[f240]) ).

tff(f240,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ord_less_eq(X0,X1,X1)
      | ~ preorder(X0) ),
    inference(ennf_transformation,[],[f150]) ).

tff(f150,plain,
    ! [X0: $tType] :
      ( preorder(X0)
     => ! [X1: X0] : ord_less_eq(X0,X1,X1) ),
    inference(rectify,[],[f97]) ).

tff(f97,axiom,
    ! [X0: $tType] :
      ( preorder(X0)
     => ! [X42: X0] : ord_less_eq(X0,X42,X42) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_order__refl) ).

tff(f712,plain,
    spl21_29,
    inference(avatar_split_clause,[],[f400,f710]) ).

tff(f400,plain,
    ! [X0: bool] :
      ( ( fFalse = X0 )
      | ( fTrue = X0 ) ),
    inference(cnf_transformation,[],[f138]) ).

tff(f138,plain,
    ! [X0: bool] :
      ( ( fFalse = X0 )
      | ( fTrue = X0 ) ),
    inference(rectify,[],[f121]) ).

tff(f121,axiom,
    ! [X70: bool] :
      ( ( fFalse = X70 )
      | ( fTrue = X70 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).

tff(f708,plain,
    spl21_28,
    inference(avatar_split_clause,[],[f386,f705]) ).

tff(f386,plain,
    ord_less_eq(int,zero_zero(int),zero_zero(int)),
    inference(cnf_transformation,[],[f88]) ).

tff(f88,axiom,
    ord_less_eq(int,zero_zero(int),zero_zero(int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).

tff(f703,plain,
    spl21_27,
    inference(avatar_split_clause,[],[f395,f701]) ).

tff(f701,plain,
    ( spl21_27
  <=> ! [X0: nat] : ord_less_eq(nat,zero_zero(nat),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_27])]) ).

tff(f395,plain,
    ! [X0: nat] : ord_less_eq(nat,zero_zero(nat),X0),
    inference(cnf_transformation,[],[f133]) ).

tff(f133,plain,
    ! [X0: nat] : ord_less_eq(nat,zero_zero(nat),X0),
    inference(rectify,[],[f57]) ).

tff(f57,axiom,
    ! [X20: nat] : ord_less_eq(nat,zero_zero(nat),X20),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_le0) ).

tff(f699,plain,
    spl21_26,
    inference(avatar_split_clause,[],[f392,f697]) ).

tff(f392,plain,
    ! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
    inference(cnf_transformation,[],[f130]) ).

tff(f130,plain,
    ! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
    inference(rectify,[],[f14]) ).

tff(f14,axiom,
    ! [X20: nat] : ~ ord_less(nat,X20,zero_zero(nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_not__less0) ).

tff(f695,plain,
    ( spl21_24
    | ~ spl21_25 ),
    inference(avatar_split_clause,[],[f364,f692,f687]) ).

tff(f364,plain,
    ( ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) != huffma1401021291ibling(a1,t_2,a) )
    | member(a1,a,huffma675207370phabet(a1,t_1)) ),
    inference(cnf_transformation,[],[f227]) ).

tff(f227,plain,
    ( ( ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) != huffma1401021291ibling(a1,t_2,a) )
      & ~ member(a1,a,huffma675207370phabet(a1,t_1)) )
    | ( ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) != huffma1401021291ibling(a1,t_1,a) )
      & member(a1,a,huffma675207370phabet(a1,t_1)) ) ),
    inference(ennf_transformation,[],[f126]) ).

tff(f126,negated_conjecture,
    ~ ( ( ~ member(a1,a,huffma675207370phabet(a1,t_1))
       => ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) = huffma1401021291ibling(a1,t_2,a) ) )
      & ( member(a1,a,huffma675207370phabet(a1,t_1))
       => ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) = huffma1401021291ibling(a1,t_1,a) ) ) ),
    inference(negated_conjecture,[],[f125]) ).

tff(f125,conjecture,
    ( ( ~ member(a1,a,huffma675207370phabet(a1,t_1))
     => ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) = huffma1401021291ibling(a1,t_2,a) ) )
    & ( member(a1,a,huffma675207370phabet(a1,t_1))
     => ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) = huffma1401021291ibling(a1,t_1,a) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).

tff(f690,plain,
    ( ~ spl21_23
    | ~ spl21_24 ),
    inference(avatar_split_clause,[],[f363,f687,f683]) ).

tff(f363,plain,
    ( ~ member(a1,a,huffma675207370phabet(a1,t_1))
    | ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) != huffma1401021291ibling(a1,t_1,a) ) ),
    inference(cnf_transformation,[],[f227]) ).

tff(f681,plain,
    spl21_22,
    inference(avatar_split_clause,[],[f559,f679]) ).

tff(f679,plain,
    ( spl21_22
  <=> ! [X1: int] : ~ ord_less(int,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_22])]) ).

tff(f559,plain,
    ! [X1: int] : ~ ord_less(int,X1,X1),
    inference(equality_resolution,[],[f469]) ).

tff(f469,plain,
    ! [X0: int,X1: int] :
      ( ( X0 != X1 )
      | ~ ord_less(int,X1,X0) ),
    inference(cnf_transformation,[],[f338]) ).

tff(f677,plain,
    spl21_21,
    inference(avatar_split_clause,[],[f391,f675]) ).

tff(f391,plain,
    ! [X0: nat] : ord_less_eq(nat,X0,X0),
    inference(cnf_transformation,[],[f129]) ).

tff(f129,plain,
    ! [X0: nat] : ord_less_eq(nat,X0,X0),
    inference(rectify,[],[f70]) ).

tff(f70,axiom,
    ! [X20: nat] : ord_less_eq(nat,X20,X20),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_le__refl) ).

tff(f673,plain,
    spl21_20,
    inference(avatar_split_clause,[],[f389,f671]) ).

tff(f389,plain,
    ! [X0: nat] : ~ ord_less(nat,X0,X0),
    inference(cnf_transformation,[],[f127]) ).

tff(f127,plain,
    ! [X0: nat] : ~ ord_less(nat,X0,X0),
    inference(rectify,[],[f36]) ).

tff(f36,axiom,
    ! [X20: nat] : ~ ord_less(nat,X20,X20),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_less__not__refl) ).

tff(f669,plain,
    spl21_19,
    inference(avatar_split_clause,[],[f385,f666]) ).

tff(f385,plain,
    pp(fTrue),
    inference(cnf_transformation,[],[f123]) ).

tff(f123,axiom,
    pp(fTrue),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).

tff(f664,plain,
    spl21_18,
    inference(avatar_split_clause,[],[f384,f661]) ).

tff(f384,plain,
    ord(nat),
    inference(cnf_transformation,[],[f114]) ).

tff(f114,axiom,
    ord(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).

tff(f659,plain,
    spl21_17,
    inference(avatar_split_clause,[],[f383,f656]) ).

tff(f656,plain,
    ( spl21_17
  <=> preorder(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_17])]) ).

tff(f383,plain,
    preorder(nat),
    inference(cnf_transformation,[],[f111]) ).

tff(f111,axiom,
    preorder(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).

tff(f654,plain,
    spl21_16,
    inference(avatar_split_clause,[],[f382,f651]) ).

tff(f651,plain,
    ( spl21_16
  <=> preorder(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_16])]) ).

tff(f382,plain,
    preorder(int),
    inference(cnf_transformation,[],[f104]) ).

tff(f104,axiom,
    preorder(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Opreorder) ).

tff(f649,plain,
    spl21_15,
    inference(avatar_split_clause,[],[f381,f646]) ).

tff(f381,plain,
    ord(int),
    inference(cnf_transformation,[],[f107]) ).

tff(f107,axiom,
    ord(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oord) ).

tff(f644,plain,
    spl21_14,
    inference(avatar_split_clause,[],[f380,f641]) ).

tff(f380,plain,
    ord(bool),
    inference(cnf_transformation,[],[f118]) ).

tff(f118,axiom,
    ord(bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).

tff(f639,plain,
    spl21_13,
    inference(avatar_split_clause,[],[f379,f636]) ).

tff(f636,plain,
    ( spl21_13
  <=> preorder(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_13])]) ).

tff(f379,plain,
    preorder(bool),
    inference(cnf_transformation,[],[f116]) ).

tff(f116,axiom,
    preorder(bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).

tff(f634,plain,
    spl21_12,
    inference(avatar_split_clause,[],[f378,f631]) ).

tff(f631,plain,
    ( spl21_12
  <=> linorder(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_12])]) ).

tff(f378,plain,
    linorder(nat),
    inference(cnf_transformation,[],[f112]) ).

tff(f112,axiom,
    linorder(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).

tff(f629,plain,
    spl21_11,
    inference(avatar_split_clause,[],[f377,f626]) ).

tff(f377,plain,
    linorder(int),
    inference(cnf_transformation,[],[f105]) ).

tff(f105,axiom,
    linorder(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).

tff(f624,plain,
    spl21_10,
    inference(avatar_split_clause,[],[f376,f621]) ).

tff(f621,plain,
    ( spl21_10
  <=> linorder(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_10])]) ).

tff(f376,plain,
    linorder(bool),
    inference(cnf_transformation,[],[f117]) ).

tff(f117,axiom,
    linorder(bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).

tff(f619,plain,
    spl21_9,
    inference(avatar_split_clause,[],[f375,f616]) ).

tff(f375,plain,
    linordered_semidom(nat),
    inference(cnf_transformation,[],[f109]) ).

tff(f109,axiom,
    linordered_semidom(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).

tff(f614,plain,
    spl21_8,
    inference(avatar_split_clause,[],[f374,f611]) ).

tff(f611,plain,
    ( spl21_8
  <=> linordered_semidom(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_8])]) ).

tff(f374,plain,
    linordered_semidom(int),
    inference(cnf_transformation,[],[f102]) ).

tff(f102,axiom,
    linordered_semidom(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).

tff(f609,plain,
    spl21_7,
    inference(avatar_split_clause,[],[f373,f606]) ).

tff(f606,plain,
    ( spl21_7
  <=> zero(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_7])]) ).

tff(f373,plain,
    zero(nat),
    inference(cnf_transformation,[],[f115]) ).

tff(f115,axiom,
    zero(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).

tff(f604,plain,
    spl21_6,
    inference(avatar_split_clause,[],[f372,f601]) ).

tff(f601,plain,
    ( spl21_6
  <=> semiring_char_0(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_6])]) ).

tff(f372,plain,
    semiring_char_0(nat),
    inference(cnf_transformation,[],[f110]) ).

tff(f110,axiom,
    semiring_char_0(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).

tff(f599,plain,
    spl21_5,
    inference(avatar_split_clause,[],[f371,f596]) ).

tff(f371,plain,
    semiring_1(nat),
    inference(cnf_transformation,[],[f113]) ).

tff(f113,axiom,
    semiring_1(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).

tff(f594,plain,
    spl21_4,
    inference(avatar_split_clause,[],[f370,f591]) ).

tff(f591,plain,
    ( spl21_4
  <=> semiring_char_0(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_4])]) ).

tff(f370,plain,
    semiring_char_0(int),
    inference(cnf_transformation,[],[f103]) ).

tff(f103,axiom,
    semiring_char_0(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).

tff(f589,plain,
    spl21_3,
    inference(avatar_split_clause,[],[f369,f586]) ).

tff(f586,plain,
    ( spl21_3
  <=> semiring_1(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_3])]) ).

tff(f369,plain,
    semiring_1(int),
    inference(cnf_transformation,[],[f106]) ).

tff(f106,axiom,
    semiring_1(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).

tff(f584,plain,
    spl21_2,
    inference(avatar_split_clause,[],[f368,f581]) ).

tff(f581,plain,
    ( spl21_2
  <=> zero(int) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_2])]) ).

tff(f368,plain,
    zero(int),
    inference(cnf_transformation,[],[f108]) ).

tff(f108,axiom,
    zero(int),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).

tff(f579,plain,
    ~ spl21_1,
    inference(avatar_split_clause,[],[f367,f576]) ).

tff(f576,plain,
    ( spl21_1
  <=> pp(fFalse) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_1])]) ).

tff(f367,plain,
    ~ pp(fFalse),
    inference(cnf_transformation,[],[f122]) ).

tff(f122,axiom,
    ~ pp(fFalse),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SWW542_5 : TPTP v8.2.0. Released v6.0.0.
% 0.03/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33  % Computer : n007.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sat May 18 20:54:37 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.33  % (25397)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.35  % (25400)WARNING: value z3 for option sas not known
% 0.18/0.36  % (25401)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.18/0.36  % (25399)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.18/0.36  % (25398)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.18/0.36  % (25402)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)
% 0.18/0.36  % (25403)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)
% 0.18/0.36  % (25400)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)
% 0.18/0.36  % (25404)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)
% 0.18/0.36  % (25404)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.18/0.36  % Exception at run slice level% Exception at run slice level
% 0.18/0.36  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.36  % Exception at run slice level
% 0.18/0.36  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.36  
% 0.18/0.36  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.38  % (25406)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)
% 0.18/0.38  % (25407)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)
% 0.18/0.38  % (25405)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.18/0.38  % (25405)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.18/0.38  % (25406)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.18/0.38  % Exception at run slice level
% 0.18/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.39  % (25408)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)
% 3.88/0.89  % (25402)First to succeed.
% 3.88/0.93  % (25402)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-25397"
% 3.88/0.93  % (25402)Refutation found. Thanks to Tanya!
% 3.88/0.93  % SZS status Theorem for theBenchmark
% 3.88/0.93  % SZS output start Proof for theBenchmark
% See solution above
% 4.24/0.95  % (25402)------------------------------
% 4.24/0.95  % (25402)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 4.24/0.95  % (25402)Termination reason: Refutation
% 4.24/0.95  
% 4.24/0.95  % (25402)Memory used [KB]: 5850
% 4.24/0.95  % (25402)Time elapsed: 0.574 s
% 4.24/0.95  % (25402)Instructions burned: 1082 (million)
% 4.24/0.95  % (25397)Success in time 0.603 s
%------------------------------------------------------------------------------