TSTP Solution File: SWW533_5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWW533_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 11:41:16 EDT 2024

% Result   : Theorem 0.22s 0.43s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :  268
% Syntax   : Number of formulae    :  642 ( 214 unt;  74 typ;   0 def)
%            Number of atoms       : 1220 ( 345 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives : 1087 ( 435   ~; 397   |;  60   &)
%                                         ( 133 <=>;  62  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    7 (   1 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   87 (  53   >;  34   *;   0   +;   0  <<)
%            Number of predicates  :  124 ( 122 usr; 108 prp; 0-3 aty)
%            Number of functors    :   56 (  56 usr;   4 con; 0-5 aty)
%            Number of variables   : 1062 ( 974   !;  13   ?;1062   :)
%                                         (  75  !>;   0  ?*;   0  @-;   0  @+)

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

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

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

tff(type_def_8,type,
    list: $tType > $tType ).

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

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

tff(type_def_11,type,
    product_prod: ( $tType * $tType ) > $tType ).

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

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

tff(func_def_2,type,
    combk: 
      !>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).

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

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

tff(func_def_5,type,
    huffma675207370phabet: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > fun(X0,bool) ) ).

tff(func_def_6,type,
    huffma1516701463abet_F: 
      !>[X0: $tType] : ( list(huffma1450048681e_tree(X0)) > fun(X0,bool) ) ).

tff(func_def_7,type,
    huffma410068972_depth: 
      !>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * X0 ) > nat ) ).

tff(func_def_8,type,
    huffma1352802255e_freq: 
      !>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * X0 ) > nat ) ).

tff(func_def_9,type,
    huffma409467474freq_F: 
      !>[X0: $tType] : ( ( list(huffma1450048681e_tree(X0)) * X0 ) > nat ) ).

tff(func_def_10,type,
    huffma945805758height: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).

tff(func_def_11,type,
    huffma632063779ight_F: 
      !>[X0: $tType] : ( list(huffma1450048681e_tree(X0)) > nat ) ).

tff(func_def_12,type,
    huffma1146269203erNode: 
      !>[X0: $tType] : ( ( nat * huffma1450048681e_tree(X0) * huffma1450048681e_tree(X0) ) > huffma1450048681e_tree(X0) ) ).

tff(func_def_13,type,
    huffma2021818691e_Leaf: 
      !>[X0: $tType] : ( ( nat * X0 ) > huffma1450048681e_tree(X0) ) ).

tff(func_def_14,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_15,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_16,type,
    inf_inf: 
      !>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).

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

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

tff(func_def_19,type,
    linord467138063of_set: 
      !>[X0: $tType] : ( fun(X0,bool) > list(X0) ) ).

tff(func_def_20,type,
    nil: 
      !>[X0: $tType] : list(X0) ).

tff(func_def_21,type,
    list_case: 
      !>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).

tff(func_def_22,type,
    list_rec: 
      !>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),fun(X0,X0))) * list(X1) ) > X0 ) ).

tff(func_def_23,type,
    list_size: 
      !>[X0: $tType] : ( ( fun(X0,nat) * list(X0) ) > nat ) ).

tff(func_def_24,type,
    set: 
      !>[X0: $tType] : ( list(X0) > fun(X0,bool) ) ).

tff(func_def_25,type,
    size_size: 
      !>[X0: $tType] : ( X0 > nat ) ).

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

tff(func_def_27,type,
    collect: 
      !>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).

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

tff(func_def_29,type,
    fFalse: bool ).

tff(func_def_30,type,
    fTrue: bool ).

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

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

tff(func_def_33,type,
    a1: a ).

tff(func_def_34,type,
    sK0: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).

tff(func_def_35,type,
    sK1: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_36,type,
    sK2: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).

tff(func_def_37,type,
    sK3: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > huffma1450048681e_tree(X0) ) ).

tff(func_def_38,type,
    sK4: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > huffma1450048681e_tree(X0) ) ).

tff(func_def_39,type,
    sK5: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).

tff(func_def_40,type,
    sK6: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).

tff(func_def_41,type,
    sK7: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_42,type,
    sK8: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_43,type,
    sK9: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_44,type,
    sK10: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_45,type,
    sK11: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).

tff(func_def_46,type,
    sK12: 
      !>[X0: $tType] : ( ( list(X0) * fun(X0,bool) * X0 ) > X0 ) ).

tff(func_def_47,type,
    sK13: 
      !>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > X0 ) ).

tff(func_def_48,type,
    sK14: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).

tff(func_def_49,type,
    sK15: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).

tff(func_def_50,type,
    sK16: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

tff(func_def_51,type,
    sK17: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) * list(X0) ) > X0 ) ).

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

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

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

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

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

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

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

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

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

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

tff(pred_def_11,type,
    huffma1518433673istent: 
      !>[X0: $tType] : ( huffma1450048681e_tree(X0) > $o ) ).

tff(pred_def_12,type,
    huffma594769176tent_F: 
      !>[X0: $tType] : ( list(huffma1450048681e_tree(X0)) > $o ) ).

tff(pred_def_13,type,
    list_ex1: 
      !>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).

tff(pred_def_14,type,
    ord_less: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(pred_def_15,type,
    pp: bool > $o ).

tff(f1227,plain,
    $false,
    inference(avatar_sat_refutation,[],[f598,f603,f608,f613,f618,f623,f628,f633,f638,f643,f648,f653,f658,f663,f668,f673,f678,f683,f688,f692,f696,f700,f704,f708,f712,f716,f720,f724,f728,f732,f736,f740,f744,f748,f755,f760,f764,f769,f773,f781,f786,f794,f799,f803,f807,f811,f815,f819,f823,f835,f839,f843,f848,f852,f856,f860,f864,f868,f872,f882,f886,f890,f906,f910,f914,f922,f927,f936,f940,f945,f949,f953,f957,f961,f995,f999,f1003,f1007,f1012,f1017,f1022,f1027,f1041,f1048,f1052,f1056,f1064,f1069,f1073,f1078,f1083,f1091,f1095,f1099,f1104,f1109,f1113,f1123,f1127,f1153,f1163,f1169,f1177,f1181,f1185,f1219,f1226]) ).

tff(f1226,plain,
    ( spl18_1
    | ~ spl18_58
    | ~ spl18_61
    | ~ spl18_65
    | ~ spl18_68
    | ~ spl18_99
    | ~ spl18_103
    | ~ spl18_107 ),
    inference(avatar_split_clause,[],[f1225,f1216,f1167,f1121,f925,f908,f880,f862,f595]) ).

tff(f595,plain,
    ( spl18_1
  <=> pp(fFalse) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_1])]) ).

tff(f862,plain,
    ( spl18_58
  <=> ! [X1: $tType,X0: $tType,X3: X1,X2: X0] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_58])]) ).

tff(f880,plain,
    ( spl18_61
  <=> ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = set(X0,nil(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_61])]) ).

tff(f908,plain,
    ( spl18_65
  <=> ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = huffma1516701463abet_F(X0,nil(huffma1450048681e_tree(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_65])]) ).

tff(f925,plain,
    ( spl18_68
  <=> ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_68])]) ).

tff(f1121,plain,
    ( spl18_99
  <=> ! [X0: $tType,X1: fun(X0,bool)] :
        ( ( combk(bool,X0,fFalse) = X1 )
        | pp(aa(X0,bool,X1,sK7(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_99])]) ).

tff(f1167,plain,
    ( spl18_103
  <=> ! [X0: $tType,X1: X0] : ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_103])]) ).

tff(f1216,plain,
    ( spl18_107
  <=> pp(aa(fun(a,bool),bool,aa(a,fun(fun(a,bool),bool),member(a),a1),huffma1516701463abet_F(a,nil(huffma1450048681e_tree(a))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_107])]) ).

tff(f1225,plain,
    ( pp(fFalse)
    | ~ spl18_58
    | ~ spl18_61
    | ~ spl18_65
    | ~ spl18_68
    | ~ spl18_99
    | ~ spl18_103
    | ~ spl18_107 ),
    inference(forward_demodulation,[],[f1224,f863]) ).

tff(f863,plain,
    ( ! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 )
    | ~ spl18_58 ),
    inference(avatar_component_clause,[],[f862]) ).

tff(f1224,plain,
    ( pp(aa(a,bool,combk(bool,a,fFalse),a1))
    | ~ spl18_61
    | ~ spl18_65
    | ~ spl18_68
    | ~ spl18_99
    | ~ spl18_103
    | ~ spl18_107 ),
    inference(forward_demodulation,[],[f1223,f1170]) ).

tff(f1170,plain,
    ( ! [X0: $tType] : ( combk(bool,X0,fFalse) = combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse)) )
    | ~ spl18_99
    | ~ spl18_103 ),
    inference(resolution,[],[f1168,f1122]) ).

tff(f1122,plain,
    ( ! [X0: $tType,X1: fun(X0,bool)] :
        ( pp(aa(X0,bool,X1,sK7(X0,X1)))
        | ( combk(bool,X0,fFalse) = X1 ) )
    | ~ spl18_99 ),
    inference(avatar_component_clause,[],[f1121]) ).

tff(f1168,plain,
    ( ! [X0: $tType,X1: X0] : ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse)),X1))
    | ~ spl18_103 ),
    inference(avatar_component_clause,[],[f1167]) ).

tff(f1223,plain,
    ( pp(aa(a,bool,combc(a,fun(a,bool),bool,member(a),combk(bool,a,fFalse)),a1))
    | ~ spl18_61
    | ~ spl18_65
    | ~ spl18_68
    | ~ spl18_107 ),
    inference(forward_demodulation,[],[f1222,f928]) ).

tff(f928,plain,
    ( ! [X0: $tType] : ( set(X0,nil(X0)) = combk(bool,X0,fFalse) )
    | ~ spl18_61
    | ~ spl18_68 ),
    inference(superposition,[],[f926,f881]) ).

tff(f881,plain,
    ( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = set(X0,nil(X0)) )
    | ~ spl18_61 ),
    inference(avatar_component_clause,[],[f880]) ).

tff(f926,plain,
    ( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse) )
    | ~ spl18_68 ),
    inference(avatar_component_clause,[],[f925]) ).

tff(f1222,plain,
    ( pp(aa(a,bool,combc(a,fun(a,bool),bool,member(a),set(a,nil(a))),a1))
    | ~ spl18_61
    | ~ spl18_65
    | ~ spl18_107 ),
    inference(forward_demodulation,[],[f1221,f881]) ).

tff(f1221,plain,
    ( pp(aa(a,bool,combc(a,fun(a,bool),bool,member(a),bot_bot(fun(a,bool))),a1))
    | ~ spl18_65
    | ~ spl18_107 ),
    inference(forward_demodulation,[],[f1220,f909]) ).

tff(f909,plain,
    ( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = huffma1516701463abet_F(X0,nil(huffma1450048681e_tree(X0))) )
    | ~ spl18_65 ),
    inference(avatar_component_clause,[],[f908]) ).

tff(f1220,plain,
    ( pp(aa(a,bool,combc(a,fun(a,bool),bool,member(a),huffma1516701463abet_F(a,nil(huffma1450048681e_tree(a)))),a1))
    | ~ spl18_107 ),
    inference(forward_demodulation,[],[f1218,f548]) ).

tff(f548,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
    inference(cnf_transformation,[],[f244]) ).

tff(f244,plain,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
    inference(rectify,[],[f128]) ).

tff(f128,axiom,
    ! [X0: $tType,X2: $tType,X1: $tType,X60: X0,X61: X1,X62: fun(X0,fun(X1,X2))] : ( aa(X0,X2,combc(X0,X1,X2,X62,X61),X60) = aa(X1,X2,aa(X0,fun(X1,X2),X62,X60),X61) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).

tff(f1218,plain,
    ( pp(aa(fun(a,bool),bool,aa(a,fun(fun(a,bool),bool),member(a),a1),huffma1516701463abet_F(a,nil(huffma1450048681e_tree(a)))))
    | ~ spl18_107 ),
    inference(avatar_component_clause,[],[f1216]) ).

tff(f1219,plain,
    spl18_107,
    inference(avatar_split_clause,[],[f405,f1216]) ).

tff(f405,plain,
    pp(aa(fun(a,bool),bool,aa(a,fun(fun(a,bool),bool),member(a),a1),huffma1516701463abet_F(a,nil(huffma1450048681e_tree(a))))),
    inference(cnf_transformation,[],[f3]) ).

tff(f3,axiom,
    pp(aa(fun(a,bool),bool,aa(a,fun(fun(a,bool),bool),member(a),a1),huffma1516701463abet_F(a,nil(huffma1450048681e_tree(a))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Nil_I3_J) ).

tff(f1185,plain,
    spl18_106,
    inference(avatar_split_clause,[],[f545,f1183]) ).

tff(f1183,plain,
    ( spl18_106
  <=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X1,X0),X4: fun(X2,X1),X3: X2] : ( aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_106])]) ).

tff(f545,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
    inference(cnf_transformation,[],[f241]) ).

tff(f241,plain,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
    inference(rectify,[],[f127]) ).

tff(f127,axiom,
    ! [X2: $tType,X1: $tType,X0: $tType,X60: X0,X61: fun(X0,X1),X62: fun(X1,X2)] : ( aa(X0,X2,combb(X1,X2,X0,X62,X61),X60) = aa(X1,X2,X62,aa(X0,X1,X61,X60)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).

tff(f1181,plain,
    spl18_105,
    inference(avatar_split_clause,[],[f491,f1179]) ).

tff(f1179,plain,
    ( spl18_105
  <=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X2,inf_inf(fun(X0,bool),X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_105])]) ).

tff(f491,plain,
    ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X2,inf_inf(fun(X0,bool),X2,X1)) ),
    inference(cnf_transformation,[],[f208]) ).

tff(f208,plain,
    ! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X2,inf_inf(fun(X0,bool),X2,X1)) ),
    inference(rectify,[],[f84]) ).

tff(f84,axiom,
    ! [X1: $tType,X47: fun(X1,bool),X39: fun(X1,bool)] : ( inf_inf(fun(X1,bool),X39,X47) = inf_inf(fun(X1,bool),X39,inf_inf(fun(X1,bool),X39,X47)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Int__left__absorb) ).

tff(f1177,plain,
    spl18_104,
    inference(avatar_split_clause,[],[f456,f1175]) ).

tff(f1175,plain,
    ( spl18_104
  <=> ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] : ( lexn(X0,X1,zero_zero(nat)) = bot_bot(fun(product_prod(list(X0),list(X0)),bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_104])]) ).

tff(f456,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] : ( lexn(X0,X1,zero_zero(nat)) = bot_bot(fun(product_prod(list(X0),list(X0)),bool)) ),
    inference(cnf_transformation,[],[f180]) ).

tff(f180,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] : ( lexn(X0,X1,zero_zero(nat)) = bot_bot(fun(product_prod(list(X0),list(X0)),bool)) ),
    inference(rectify,[],[f46]) ).

tff(f46,axiom,
    ! [X1: $tType,X41: fun(product_prod(X1,X1),bool)] : ( lexn(X1,X41,zero_zero(nat)) = bot_bot(fun(product_prod(list(X1),list(X1)),bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_lexn_Osimps_I1_J) ).

tff(f1169,plain,
    ( spl18_103
    | ~ spl18_68
    | ~ spl18_102 ),
    inference(avatar_split_clause,[],[f1165,f1161,f925,f1167]) ).

tff(f1161,plain,
    ( spl18_102
  <=> ! [X0: $tType,X1: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_102])]) ).

tff(f1165,plain,
    ( ! [X0: $tType,X1: X0] : ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse)),X1))
    | ~ spl18_68
    | ~ spl18_102 ),
    inference(forward_demodulation,[],[f1164,f926]) ).

tff(f1164,plain,
    ( ! [X0: $tType,X1: X0] : ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))),X1))
    | ~ spl18_102 ),
    inference(forward_demodulation,[],[f1162,f548]) ).

tff(f1162,plain,
    ( ! [X0: $tType,X1: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool))))
    | ~ spl18_102 ),
    inference(avatar_component_clause,[],[f1161]) ).

tff(f1163,plain,
    spl18_102,
    inference(avatar_split_clause,[],[f454,f1161]) ).

tff(f454,plain,
    ! [X0: $tType,X1: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))),
    inference(cnf_transformation,[],[f178]) ).

tff(f178,plain,
    ! [X0: $tType,X1: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))),
    inference(rectify,[],[f36]) ).

tff(f36,axiom,
    ! [X1: $tType,X38: X1] : ~ pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X38),bot_bot(fun(X1,bool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_empty__iff) ).

tff(f1153,plain,
    spl18_101,
    inference(avatar_split_clause,[],[f503,f1151]) ).

tff(f1151,plain,
    ( spl18_101
  <=> ! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
        ( ( nil(X0) = dropWhile(X0,X2,X1) )
        | ~ pp(aa(X0,bool,X2,sK13(X0,X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_101])]) ).

tff(f503,plain,
    ! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
      ( ( nil(X0) = dropWhile(X0,X2,X1) )
      | ~ pp(aa(X0,bool,X2,sK13(X0,X1,X2))) ),
    inference(cnf_transformation,[],[f360]) ).

tff(f360,plain,
    ! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
      ( ( ( nil(X0) = dropWhile(X0,X2,X1) )
        | ( ~ pp(aa(X0,bool,X2,sK13(X0,X1,X2)))
          & pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK13(X0,X1,X2)),set(X0,X1))) ) )
      & ( ! [X4: X0] :
            ( pp(aa(X0,bool,X2,X4))
            | ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),set(X0,X1))) )
        | ( nil(X0) != dropWhile(X0,X2,X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f358,f359]) ).

tff(f359,plain,
    ! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
      ( ? [X3: X0] :
          ( ~ pp(aa(X0,bool,X2,X3))
          & pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) )
     => ( ~ pp(aa(X0,bool,X2,sK13(X0,X1,X2)))
        & pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK13(X0,X1,X2)),set(X0,X1))) ) ),
    introduced(choice_axiom,[]) ).

tff(f358,plain,
    ! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
      ( ( ( nil(X0) = dropWhile(X0,X2,X1) )
        | ? [X3: X0] :
            ( ~ pp(aa(X0,bool,X2,X3))
            & pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) ) )
      & ( ! [X4: X0] :
            ( pp(aa(X0,bool,X2,X4))
            | ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),set(X0,X1))) )
        | ( nil(X0) != dropWhile(X0,X2,X1) ) ) ),
    inference(rectify,[],[f357]) ).

tff(f357,plain,
    ! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
      ( ( ( nil(X0) = dropWhile(X0,X2,X1) )
        | ? [X3: X0] :
            ( ~ pp(aa(X0,bool,X2,X3))
            & pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) ) )
      & ( ! [X3: X0] :
            ( pp(aa(X0,bool,X2,X3))
            | ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) )
        | ( nil(X0) != dropWhile(X0,X2,X1) ) ) ),
    inference(nnf_transformation,[],[f302]) ).

tff(f302,plain,
    ! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
      ( ( nil(X0) = dropWhile(X0,X2,X1) )
    <=> ! [X3: X0] :
          ( pp(aa(X0,bool,X2,X3))
          | ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) ) ),
    inference(ennf_transformation,[],[f216]) ).

tff(f216,plain,
    ! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
      ( ( nil(X0) = dropWhile(X0,X2,X1) )
    <=> ! [X3: X0] :
          ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1)))
         => pp(aa(X0,bool,X2,X3)) ) ),
    inference(rectify,[],[f17]) ).

tff(f17,axiom,
    ! [X1: $tType,X19: list(X1),X20: fun(X1,bool)] :
      ( ( dropWhile(X1,X20,X19) = nil(X1) )
    <=> ! [X21: X1] :
          ( pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X21),set(X1,X19)))
         => pp(aa(X1,bool,X20,X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_dropWhile__eq__Nil__conv) ).

tff(f1127,plain,
    ( spl18_100
    | ~ spl18_68
    | ~ spl18_96 ),
    inference(avatar_split_clause,[],[f1105,f1102,f925,f1125]) ).

tff(f1125,plain,
    ( spl18_100
  <=> ! [X0: $tType,X1: fun(X0,bool)] :
        ( ( combk(bool,X0,fFalse) = X1 )
        | pp(aa(X0,bool,X1,sK8(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_100])]) ).

tff(f1102,plain,
    ( spl18_96
  <=> ! [X0: $tType,X1: fun(X0,bool)] :
        ( ( bot_bot(fun(X0,bool)) = X1 )
        | pp(aa(X0,bool,X1,sK8(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_96])]) ).

tff(f1105,plain,
    ( ! [X0: $tType,X1: fun(X0,bool)] :
        ( ( combk(bool,X0,fFalse) = X1 )
        | pp(aa(X0,bool,X1,sK8(X0,X1))) )
    | ~ spl18_68
    | ~ spl18_96 ),
    inference(forward_demodulation,[],[f1103,f926]) ).

tff(f1103,plain,
    ( ! [X0: $tType,X1: fun(X0,bool)] :
        ( ( bot_bot(fun(X0,bool)) = X1 )
        | pp(aa(X0,bool,X1,sK8(X0,X1))) )
    | ~ spl18_96 ),
    inference(avatar_component_clause,[],[f1102]) ).

tff(f1123,plain,
    ( spl18_99
    | ~ spl18_68
    | ~ spl18_95 ),
    inference(avatar_split_clause,[],[f1100,f1097,f925,f1121]) ).

tff(f1097,plain,
    ( spl18_95
  <=> ! [X0: $tType,X1: fun(X0,bool)] :
        ( ( bot_bot(fun(X0,bool)) = X1 )
        | pp(aa(X0,bool,X1,sK7(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_95])]) ).

tff(f1100,plain,
    ( ! [X0: $tType,X1: fun(X0,bool)] :
        ( ( combk(bool,X0,fFalse) = X1 )
        | pp(aa(X0,bool,X1,sK7(X0,X1))) )
    | ~ spl18_68
    | ~ spl18_95 ),
    inference(forward_demodulation,[],[f1098,f926]) ).

tff(f1098,plain,
    ( ! [X0: $tType,X1: fun(X0,bool)] :
        ( ( bot_bot(fun(X0,bool)) = X1 )
        | pp(aa(X0,bool,X1,sK7(X0,X1))) )
    | ~ spl18_95 ),
    inference(avatar_component_clause,[],[f1097]) ).

tff(f1113,plain,
    ( spl18_98
    | ~ spl18_68
    | ~ spl18_90 ),
    inference(avatar_split_clause,[],[f1074,f1071,f925,f1111]) ).

tff(f1111,plain,
    ( spl18_98
  <=> ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),combk(bool,X0,fFalse),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_98])]) ).

tff(f1071,plain,
    ( spl18_90
  <=> ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),bot_bot(fun(X0,bool)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_90])]) ).

tff(f1074,plain,
    ( ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),combk(bool,X0,fFalse),X1) )
    | ~ spl18_68
    | ~ spl18_90 ),
    inference(forward_demodulation,[],[f1072,f926]) ).

tff(f1072,plain,
    ( ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),bot_bot(fun(X0,bool)),X1) )
    | ~ spl18_90 ),
    inference(avatar_component_clause,[],[f1071]) ).

tff(f1109,plain,
    ( spl18_97
    | ~ spl18_68
    | ~ spl18_88 ),
    inference(avatar_split_clause,[],[f1065,f1062,f925,f1107]) ).

tff(f1107,plain,
    ( spl18_97
  <=> ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),X1,combk(bool,X0,fFalse)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_97])]) ).

tff(f1062,plain,
    ( spl18_88
  <=> ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X1,bot_bot(fun(X0,bool))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_88])]) ).

tff(f1065,plain,
    ( ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),X1,combk(bool,X0,fFalse)) )
    | ~ spl18_68
    | ~ spl18_88 ),
    inference(forward_demodulation,[],[f1063,f926]) ).

tff(f1063,plain,
    ( ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X1,bot_bot(fun(X0,bool))) )
    | ~ spl18_88 ),
    inference(avatar_component_clause,[],[f1062]) ).

tff(f1104,plain,
    spl18_96,
    inference(avatar_split_clause,[],[f586,f1102]) ).

tff(f586,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ( bot_bot(fun(X0,bool)) = X1 )
      | pp(aa(X0,bool,X1,sK8(X0,X1))) ),
    inference(forward_demodulation,[],[f481,f447]) ).

tff(f447,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f171]) ).

tff(f171,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
    inference(rectify,[],[f77]) ).

tff(f77,axiom,
    ! [X1: $tType,X20: fun(X1,bool)] : ( collect(X1,X20) = X20 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Collect__def) ).

tff(f481,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
      | pp(aa(X0,bool,X1,sK8(X0,X1))) ),
    inference(cnf_transformation,[],[f344]) ).

tff(f344,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
        | pp(aa(X0,bool,X1,sK8(X0,X1))) )
      & ( ! [X3: X0] : ~ pp(aa(X0,bool,X1,X3))
        | ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f342,f343]) ).

tff(f343,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ? [X2: X0] : pp(aa(X0,bool,X1,X2))
     => pp(aa(X0,bool,X1,sK8(X0,X1))) ),
    introduced(choice_axiom,[]) ).

tff(f342,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
        | ? [X2: X0] : pp(aa(X0,bool,X1,X2)) )
      & ( ! [X3: X0] : ~ pp(aa(X0,bool,X1,X3))
        | ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
    inference(rectify,[],[f341]) ).

tff(f341,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
        | ? [X2: X0] : pp(aa(X0,bool,X1,X2)) )
      & ( ! [X2: X0] : ~ pp(aa(X0,bool,X1,X2))
        | ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
    inference(nnf_transformation,[],[f200]) ).

tff(f200,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
    <=> ! [X2: X0] : ~ pp(aa(X0,bool,X1,X2)) ),
    inference(rectify,[],[f35]) ).

tff(f35,axiom,
    ! [X1: $tType,X20: fun(X1,bool)] :
      ( ( bot_bot(fun(X1,bool)) = collect(X1,X20) )
    <=> ! [X21: X1] : ~ pp(aa(X1,bool,X20,X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_Collect__empty__eq) ).

tff(f1099,plain,
    spl18_95,
    inference(avatar_split_clause,[],[f584,f1097]) ).

tff(f584,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ( bot_bot(fun(X0,bool)) = X1 )
      | pp(aa(X0,bool,X1,sK7(X0,X1))) ),
    inference(forward_demodulation,[],[f479,f447]) ).

tff(f479,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
      | pp(aa(X0,bool,X1,sK7(X0,X1))) ),
    inference(cnf_transformation,[],[f340]) ).

tff(f340,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
        | pp(aa(X0,bool,X1,sK7(X0,X1))) )
      & ( ! [X3: X0] : ~ pp(aa(X0,bool,X1,X3))
        | ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f338,f339]) ).

tff(f339,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ? [X2: X0] : pp(aa(X0,bool,X1,X2))
     => pp(aa(X0,bool,X1,sK7(X0,X1))) ),
    introduced(choice_axiom,[]) ).

tff(f338,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
        | ? [X2: X0] : pp(aa(X0,bool,X1,X2)) )
      & ( ! [X3: X0] : ~ pp(aa(X0,bool,X1,X3))
        | ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
    inference(rectify,[],[f337]) ).

tff(f337,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
        | ? [X2: X0] : pp(aa(X0,bool,X1,X2)) )
      & ( ! [X2: X0] : ~ pp(aa(X0,bool,X1,X2))
        | ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
    inference(nnf_transformation,[],[f199]) ).

tff(f199,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
    <=> ! [X2: X0] : ~ pp(aa(X0,bool,X1,X2)) ),
    inference(rectify,[],[f37]) ).

tff(f37,axiom,
    ! [X1: $tType,X20: fun(X1,bool)] :
      ( ( bot_bot(fun(X1,bool)) = collect(X1,X20) )
    <=> ! [X21: X1] : ~ pp(aa(X1,bool,X20,X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_empty__Collect__eq) ).

tff(f1095,plain,
    spl18_94,
    inference(avatar_split_clause,[],[f554,f1093]) ).

tff(f1093,plain,
    ( spl18_94
  <=> ! [X0: $tType,X2: huffma1450048681e_tree(X0),X6: nat,X4: huffma1450048681e_tree(X0),X3: nat,X5: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
        ( ( X1 = X4 )
        | ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_94])]) ).

tff(f554,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,[],[f382]) ).

tff(f382,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,[],[f381]) ).

tff(f381,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,[],[f248]) ).

tff(f248,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,[],[f18]) ).

tff(f18,axiom,
    ! [X1: $tType,X22: huffma1450048681e_tree(X1),X23: huffma1450048681e_tree(X1),X5: nat,X24: huffma1450048681e_tree(X1),X25: huffma1450048681e_tree(X1),X7: nat] :
      ( ( huffma1146269203erNode(X1,X7,X25,X24) = huffma1146269203erNode(X1,X5,X23,X22) )
    <=> ( ( X22 = X24 )
        & ( X23 = X25 )
        & ( X5 = X7 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_tree_Osimps_I2_J) ).

tff(f1091,plain,
    spl18_93,
    inference(avatar_split_clause,[],[f553,f1089]) ).

tff(f1089,plain,
    ( spl18_93
  <=> ! [X0: $tType,X6: nat,X4: huffma1450048681e_tree(X0),X3: nat,X5: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
        ( ( X2 = X5 )
        | ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_93])]) ).

tff(f553,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,[],[f382]) ).

tff(f1083,plain,
    ( spl18_92
    | ~ spl18_91 ),
    inference(avatar_split_clause,[],[f1079,f1076,f1081]) ).

tff(f1081,plain,
    ( spl18_92
  <=> ! [X0: bool,X1: bool] :
        ( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
        | ~ pp(X0)
        | ~ pp(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_92])]) ).

tff(f1076,plain,
    ( spl18_91
  <=> ! [X0: bool,X1: bool] :
        ( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
        | ~ pp(X0)
        | ~ pp(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_91])]) ).

tff(f1079,plain,
    ( ! [X0: bool,X1: bool] :
        ( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
        | ~ pp(X0)
        | ~ pp(X1) )
    | ~ spl18_91 ),
    inference(forward_demodulation,[],[f1077,f548]) ).

tff(f1077,plain,
    ( ! [X0: bool,X1: bool] :
        ( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
        | ~ pp(X0)
        | ~ pp(X1) )
    | ~ spl18_91 ),
    inference(avatar_component_clause,[],[f1076]) ).

tff(f1078,plain,
    spl18_91,
    inference(avatar_split_clause,[],[f457,f1076]) ).

tff(f457,plain,
    ! [X0: bool,X1: bool] :
      ( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
      | ~ pp(X0)
      | ~ pp(X1) ),
    inference(cnf_transformation,[],[f181]) ).

tff(f181,plain,
    ! [X0: bool,X1: bool] :
      ( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
      | ~ pp(X0)
      | ~ pp(X1) ),
    inference(rectify,[],[f131]) ).

tff(f131,axiom,
    ! [X61: bool,X62: bool] :
      ( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X62),X61))
      | ~ pp(X61)
      | ~ pp(X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

tff(f1073,plain,
    spl18_90,
    inference(avatar_split_clause,[],[f453,f1071]) ).

tff(f453,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),bot_bot(fun(X0,bool)),X1) ),
    inference(cnf_transformation,[],[f177]) ).

tff(f177,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),bot_bot(fun(X0,bool)),X1) ),
    inference(rectify,[],[f59]) ).

tff(f59,axiom,
    ! [X1: $tType,X47: fun(X1,bool)] : ( bot_bot(fun(X1,bool)) = inf_inf(fun(X1,bool),bot_bot(fun(X1,bool)),X47) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Int__empty__left) ).

tff(f1069,plain,
    ( ~ spl18_16
    | spl18_89
    | ~ spl18_36
    | ~ spl18_76 ),
    inference(avatar_split_clause,[],[f1033,f992,f758,f1067,f670]) ).

tff(f670,plain,
    ( spl18_16
  <=> bot(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_16])]) ).

tff(f1067,plain,
    ( spl18_89
  <=> ! [X0: bool] : ~ ord_less(bool,X0,fFalse) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_89])]) ).

tff(f758,plain,
    ( spl18_36
  <=> ! [X0: $tType,X1: X0] :
        ( ~ ord_less(X0,X1,bot_bot(X0))
        | ~ bot(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_36])]) ).

tff(f992,plain,
    ( spl18_76
  <=> ( fFalse = bot_bot(bool) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_76])]) ).

tff(f1033,plain,
    ( ! [X0: bool] :
        ( ~ ord_less(bool,X0,fFalse)
        | ~ bot(bool) )
    | ~ spl18_36
    | ~ spl18_76 ),
    inference(superposition,[],[f759,f994]) ).

tff(f994,plain,
    ( ( fFalse = bot_bot(bool) )
    | ~ spl18_76 ),
    inference(avatar_component_clause,[],[f992]) ).

tff(f759,plain,
    ( ! [X0: $tType,X1: X0] :
        ( ~ ord_less(X0,X1,bot_bot(X0))
        | ~ bot(X0) )
    | ~ spl18_36 ),
    inference(avatar_component_clause,[],[f758]) ).

tff(f1064,plain,
    spl18_88,
    inference(avatar_split_clause,[],[f452,f1062]) ).

tff(f452,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X1,bot_bot(fun(X0,bool))) ),
    inference(cnf_transformation,[],[f176]) ).

tff(f176,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X1,bot_bot(fun(X0,bool))) ),
    inference(rectify,[],[f58]) ).

tff(f58,axiom,
    ! [X1: $tType,X39: fun(X1,bool)] : ( bot_bot(fun(X1,bool)) = inf_inf(fun(X1,bool),X39,bot_bot(fun(X1,bool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Int__empty__right) ).

tff(f1056,plain,
    spl18_87,
    inference(avatar_split_clause,[],[f552,f1054]) ).

tff(f1054,plain,
    ( spl18_87
  <=> ! [X0: $tType,X5: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X6: nat,X3: nat,X1: huffma1450048681e_tree(X0)] :
        ( ( X3 = X6 )
        | ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_87])]) ).

tff(f552,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,[],[f382]) ).

tff(f1052,plain,
    spl18_86,
    inference(avatar_split_clause,[],[f490,f1050]) ).

tff(f1050,plain,
    ( spl18_86
  <=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_86])]) ).

tff(f490,plain,
    ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X1,X2) ),
    inference(cnf_transformation,[],[f207]) ).

tff(f207,plain,
    ! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X1,X2) ),
    inference(rectify,[],[f86]) ).

tff(f86,axiom,
    ! [X1: $tType,X47: fun(X1,bool),X39: fun(X1,bool)] : ( inf_inf(fun(X1,bool),X39,X47) = inf_inf(fun(X1,bool),X47,X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Int__commute) ).

tff(f1048,plain,
    spl18_85,
    inference(avatar_split_clause,[],[f474,f1046]) ).

tff(f1046,plain,
    ( spl18_85
  <=> ! [X0: $tType,X1: list(X0)] :
        ( ( nil(X0) = X1 )
        | ( bot_bot(fun(X0,bool)) != set(X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_85])]) ).

tff(f474,plain,
    ! [X0: $tType,X1: list(X0)] :
      ( ( nil(X0) = X1 )
      | ( bot_bot(fun(X0,bool)) != set(X0,X1) ) ),
    inference(cnf_transformation,[],[f335]) ).

tff(f335,plain,
    ! [X0: $tType,X1: list(X0)] :
      ( ( ( bot_bot(fun(X0,bool)) = set(X0,X1) )
        | ( nil(X0) != X1 ) )
      & ( ( nil(X0) = X1 )
        | ( bot_bot(fun(X0,bool)) != set(X0,X1) ) ) ),
    inference(nnf_transformation,[],[f197]) ).

tff(f197,plain,
    ! [X0: $tType,X1: list(X0)] :
      ( ( bot_bot(fun(X0,bool)) = set(X0,X1) )
    <=> ( nil(X0) = X1 ) ),
    inference(rectify,[],[f30]) ).

tff(f30,axiom,
    ! [X1: $tType,X19: list(X1)] :
      ( ( set(X1,X19) = bot_bot(fun(X1,bool)) )
    <=> ( nil(X1) = X19 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_set__empty2) ).

tff(f1041,plain,
    ( spl18_84
    | ~ spl18_68
    | ~ spl18_83 ),
    inference(avatar_split_clause,[],[f1028,f1025,f925,f1039]) ).

tff(f1039,plain,
    ( spl18_84
  <=> ! [X0: $tType,X1: fun(X0,bool),X3: X0] :
        ( ( combk(bool,X0,fFalse) != X1 )
        | ~ pp(aa(X0,bool,X1,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_84])]) ).

tff(f1025,plain,
    ( spl18_83
  <=> ! [X0: $tType,X1: fun(X0,bool),X3: X0] :
        ( ( bot_bot(fun(X0,bool)) != X1 )
        | ~ pp(aa(X0,bool,X1,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_83])]) ).

tff(f1028,plain,
    ( ! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
        ( ( combk(bool,X0,fFalse) != X1 )
        | ~ pp(aa(X0,bool,X1,X3)) )
    | ~ spl18_68
    | ~ spl18_83 ),
    inference(forward_demodulation,[],[f1026,f926]) ).

tff(f1026,plain,
    ( ! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
        ( ( bot_bot(fun(X0,bool)) != X1 )
        | ~ pp(aa(X0,bool,X1,X3)) )
    | ~ spl18_83 ),
    inference(avatar_component_clause,[],[f1025]) ).

tff(f1027,plain,
    spl18_83,
    inference(avatar_split_clause,[],[f585,f1025]) ).

tff(f585,plain,
    ! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
      ( ( bot_bot(fun(X0,bool)) != X1 )
      | ~ pp(aa(X0,bool,X1,X3)) ),
    inference(forward_demodulation,[],[f478,f447]) ).

tff(f478,plain,
    ! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
      ( ~ pp(aa(X0,bool,X1,X3))
      | ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ),
    inference(cnf_transformation,[],[f340]) ).

tff(f1022,plain,
    ( spl18_82
    | ~ spl18_81 ),
    inference(avatar_split_clause,[],[f1018,f1015,f1020]) ).

tff(f1020,plain,
    ( spl18_82
  <=> ! [X0: bool,X1: bool] :
        ( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
        | pp(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_82])]) ).

tff(f1015,plain,
    ( spl18_81
  <=> ! [X0: bool,X1: bool] :
        ( pp(X1)
        | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_81])]) ).

tff(f1018,plain,
    ( ! [X0: bool,X1: bool] :
        ( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
        | pp(X1) )
    | ~ spl18_81 ),
    inference(forward_demodulation,[],[f1016,f548]) ).

tff(f1016,plain,
    ( ! [X0: bool,X1: bool] :
        ( pp(X1)
        | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
    | ~ spl18_81 ),
    inference(avatar_component_clause,[],[f1015]) ).

tff(f1017,plain,
    spl18_81,
    inference(avatar_split_clause,[],[f459,f1015]) ).

tff(f459,plain,
    ! [X0: bool,X1: bool] :
      ( pp(X1)
      | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
    inference(cnf_transformation,[],[f183]) ).

tff(f183,plain,
    ! [X0: bool,X1: bool] :
      ( pp(X1)
      | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
    inference(rectify,[],[f132]) ).

tff(f132,axiom,
    ! [X61: bool,X62: bool] :
      ( pp(X62)
      | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X62),X61)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

tff(f1012,plain,
    ( spl18_80
    | ~ spl18_79 ),
    inference(avatar_split_clause,[],[f1008,f1005,f1010]) ).

tff(f1010,plain,
    ( spl18_80
  <=> ! [X0: bool,X1: bool] :
        ( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
        | pp(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_80])]) ).

tff(f1005,plain,
    ( spl18_79
  <=> ! [X0: bool,X1: bool] :
        ( pp(X0)
        | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_79])]) ).

tff(f1008,plain,
    ( ! [X0: bool,X1: bool] :
        ( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
        | pp(X0) )
    | ~ spl18_79 ),
    inference(forward_demodulation,[],[f1006,f548]) ).

tff(f1006,plain,
    ( ! [X0: bool,X1: bool] :
        ( pp(X0)
        | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
    | ~ spl18_79 ),
    inference(avatar_component_clause,[],[f1005]) ).

tff(f1007,plain,
    spl18_79,
    inference(avatar_split_clause,[],[f458,f1005]) ).

tff(f458,plain,
    ! [X0: bool,X1: bool] :
      ( pp(X0)
      | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
    inference(cnf_transformation,[],[f182]) ).

tff(f182,plain,
    ! [X0: bool,X1: bool] :
      ( pp(X0)
      | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
    inference(rectify,[],[f133]) ).

tff(f133,axiom,
    ! [X61: bool,X62: bool] :
      ( pp(X61)
      | ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X62),X61)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

tff(f1003,plain,
    spl18_78,
    inference(avatar_split_clause,[],[f443,f1001]) ).

tff(f1001,plain,
    ( spl18_78
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
        ( ord_less(X0,X3,X1)
        | ~ ord_less(X0,X2,X1)
        | ~ ord_less(X0,X3,X2)
        | ~ preorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_78])]) ).

tff(f443,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
      ( ord_less(X0,X3,X1)
      | ~ ord_less(X0,X2,X1)
      | ~ ord_less(X0,X3,X2)
      | ~ preorder(X0) ),
    inference(cnf_transformation,[],[f281]) ).

tff(f281,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less(X0,X3,X1)
          | ~ ord_less(X0,X2,X1)
          | ~ ord_less(X0,X3,X2) )
      | ~ preorder(X0) ),
    inference(flattening,[],[f280]) ).

tff(f280,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less(X0,X3,X1)
          | ~ ord_less(X0,X2,X1)
          | ~ ord_less(X0,X3,X2) )
      | ~ preorder(X0) ),
    inference(ennf_transformation,[],[f168]) ).

tff(f168,plain,
    ! [X0: $tType] :
      ( preorder(X0)
     => ! [X1: X0,X2: X0,X3: X0] :
          ( ord_less(X0,X3,X2)
         => ( ord_less(X0,X2,X1)
           => ord_less(X0,X3,X1) ) ) ),
    inference(rectify,[],[f66]) ).

tff(f66,axiom,
    ! [X0: $tType] :
      ( preorder(X0)
     => ! [X50: X0,X30: X0,X49: X0] :
          ( ord_less(X0,X49,X30)
         => ( ord_less(X0,X30,X50)
           => ord_less(X0,X49,X50) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_order__less__trans) ).

tff(f999,plain,
    spl18_77,
    inference(avatar_split_clause,[],[f428,f997]) ).

tff(f997,plain,
    ( spl18_77
  <=> ! [X0: $tType,X2: X0,X1: X0] :
        ( ( inf_inf(X0,X2,X1) = inf_inf(X0,X2,inf_inf(X0,X2,X1)) )
        | ~ semilattice_inf(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_77])]) ).

tff(f428,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( inf_inf(X0,X2,X1) = inf_inf(X0,X2,inf_inf(X0,X2,X1)) )
      | ~ semilattice_inf(X0) ),
    inference(cnf_transformation,[],[f263]) ).

tff(f263,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] : ( inf_inf(X0,X2,X1) = inf_inf(X0,X2,inf_inf(X0,X2,X1)) )
      | ~ semilattice_inf(X0) ),
    inference(ennf_transformation,[],[f154]) ).

tff(f154,plain,
    ! [X0: $tType] :
      ( semilattice_inf(X0)
     => ! [X1: X0,X2: X0] : ( inf_inf(X0,X2,X1) = inf_inf(X0,X2,inf_inf(X0,X2,X1)) ) ),
    inference(rectify,[],[f99]) ).

tff(f99,axiom,
    ! [X0: $tType] :
      ( semilattice_inf(X0)
     => ! [X30: X0,X49: X0] : ( inf_inf(X0,X49,X30) = inf_inf(X0,X49,inf_inf(X0,X49,X30)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_inf__left__idem) ).

tff(f995,plain,
    ( spl18_76
    | ~ spl18_16
    | ~ spl18_58
    | ~ spl18_68
    | ~ spl18_70 ),
    inference(avatar_split_clause,[],[f984,f938,f925,f862,f670,f992]) ).

tff(f938,plain,
    ( spl18_70
  <=> ! [X1: $tType,X0: $tType,X2: X0] :
        ( ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) )
        | ~ bot(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_70])]) ).

tff(f984,plain,
    ( ( fFalse = bot_bot(bool) )
    | ~ spl18_16
    | ~ spl18_58
    | ~ spl18_68
    | ~ spl18_70 ),
    inference(forward_demodulation,[],[f983,f863]) ).

tff(f983,plain,
    ( ! [X0: $tType,X1: X0] : ( bot_bot(bool) = aa(X0,bool,combk(bool,X0,fFalse),X1) )
    | ~ spl18_16
    | ~ spl18_68
    | ~ spl18_70 ),
    inference(forward_demodulation,[],[f980,f926]) ).

tff(f980,plain,
    ( ! [X0: $tType,X1: X0] : ( bot_bot(bool) = aa(X0,bool,bot_bot(fun(X0,bool)),X1) )
    | ~ spl18_16
    | ~ spl18_70 ),
    inference(resolution,[],[f939,f672]) ).

tff(f672,plain,
    ( bot(bool)
    | ~ spl18_16 ),
    inference(avatar_component_clause,[],[f670]) ).

tff(f939,plain,
    ( ! [X1: $tType,X0: $tType,X2: X0] :
        ( ~ bot(X1)
        | ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) ) )
    | ~ spl18_70 ),
    inference(avatar_component_clause,[],[f938]) ).

tff(f961,plain,
    spl18_75,
    inference(avatar_split_clause,[],[f541,f959]) ).

tff(f959,plain,
    ( spl18_75
  <=> ! [X0: $tType,X2: nat,X4: nat,X3: X0,X1: X0] :
        ( ( X1 = X3 )
        | ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_75])]) ).

tff(f541,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,[],[f380]) ).

tff(f380,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,[],[f379]) ).

tff(f379,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,[],[f238]) ).

tff(f238,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,[],[f4]) ).

tff(f4,axiom,
    ! [X1: $tType,X4: X1,X5: nat,X6: X1,X7: nat] :
      ( ( huffma2021818691e_Leaf(X1,X7,X6) = huffma2021818691e_Leaf(X1,X5,X4) )
    <=> ( ( X4 = X6 )
        & ( X5 = X7 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_tree_Osimps_I1_J) ).

tff(f957,plain,
    spl18_74,
    inference(avatar_split_clause,[],[f540,f955]) ).

tff(f955,plain,
    ( spl18_74
  <=> ! [X0: $tType,X4: nat,X3: X0,X2: nat,X1: X0] :
        ( ( X2 = X4 )
        | ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_74])]) ).

tff(f540,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,[],[f380]) ).

tff(f953,plain,
    spl18_73,
    inference(avatar_split_clause,[],[f517,f951]) ).

tff(f951,plain,
    ( spl18_73
  <=> ! [X0: $tType,X3: X0,X2: X0,X1: nat] :
        ( ( zero_zero(nat) = huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) )
        | ( X2 = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_73])]) ).

tff(f517,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: nat] :
      ( ( zero_zero(nat) = huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) )
      | ( X2 = X3 ) ),
    inference(cnf_transformation,[],[f304]) ).

tff(f304,plain,
    ! [X0: $tType,X1: nat,X2: X0,X3: X0] :
      ( ( ( zero_zero(nat) = huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) )
        | ( X2 = X3 ) )
      & ( ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) = X1 )
        | ( X2 != X3 ) ) ),
    inference(ennf_transformation,[],[f225]) ).

tff(f225,plain,
    ! [X0: $tType,X1: nat,X2: X0,X3: X0] :
      ( ( ( X2 != X3 )
       => ( zero_zero(nat) = huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) ) )
      & ( ( X2 = X3 )
       => ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) = X1 ) ) ),
    inference(rectify,[],[f13]) ).

tff(f13,axiom,
    ! [X0: $tType,X13: nat,X12: X0,X8: X0] :
      ( ( ( X8 != X12 )
       => ( zero_zero(nat) = huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X13,X12),X8) ) )
      & ( ( X8 = X12 )
       => ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X13,X12),X8) = X13 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_freq_Osimps_I1_J) ).

tff(f949,plain,
    spl18_72,
    inference(avatar_split_clause,[],[f471,f947]) ).

tff(f947,plain,
    ( spl18_72
  <=> ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
        ( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,sK0(X0,X1)) )
        | ~ huffma1518433673istent(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_72])]) ).

tff(f471,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,sK0(X0,X1)) )
      | ~ huffma1518433673istent(X0,X1) ),
    inference(cnf_transformation,[],[f328]) ).

tff(f328,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,sK0(X0,X1)) )
        & pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK0(X0,X1)),huffma675207370phabet(X0,X1))) )
      | ~ huffma1518433673istent(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f292,f327]) ).

tff(f327,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ? [X2: X0] :
          ( ( huffma410068972_depth(X0,X1,X2) = huffma945805758height(X0,X1) )
          & pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),huffma675207370phabet(X0,X1))) )
     => ( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,sK0(X0,X1)) )
        & pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK0(X0,X1)),huffma675207370phabet(X0,X1))) ) ),
    introduced(choice_axiom,[]) ).

tff(f292,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( ? [X2: X0] :
          ( ( huffma410068972_depth(X0,X1,X2) = huffma945805758height(X0,X1) )
          & pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),huffma675207370phabet(X0,X1))) )
      | ~ huffma1518433673istent(X0,X1) ),
    inference(ennf_transformation,[],[f194]) ).

tff(f194,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
      ( huffma1518433673istent(X0,X1)
     => ? [X2: X0] :
          ( ( huffma410068972_depth(X0,X1,X2) = huffma945805758height(X0,X1) )
          & pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),huffma675207370phabet(X0,X1))) ) ),
    inference(rectify,[],[f47]) ).

tff(f47,axiom,
    ! [X1: $tType,X42: huffma1450048681e_tree(X1)] :
      ( huffma1518433673istent(X1,X42)
     => ? [X29: X1] :
          ( ( huffma410068972_depth(X1,X42,X29) = huffma945805758height(X1,X42) )
          & pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X29),huffma675207370phabet(X1,X42))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_exists__at__height) ).

tff(f945,plain,
    ( ~ spl18_71
    | spl18_43
    | ~ spl18_68 ),
    inference(avatar_split_clause,[],[f929,f925,f791,f942]) ).

tff(f942,plain,
    ( spl18_71
  <=> pp(aa(huffma1450048681e_tree(a),bool,combc(huffma1450048681e_tree(a),fun(huffma1450048681e_tree(a),bool),bool,member(huffma1450048681e_tree(a)),combk(bool,huffma1450048681e_tree(a),fFalse)),huffma2021818691e_Leaf(a,zero_zero(nat),a1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_71])]) ).

tff(f791,plain,
    ( spl18_43
  <=> pp(aa(huffma1450048681e_tree(a),bool,combc(huffma1450048681e_tree(a),fun(huffma1450048681e_tree(a),bool),bool,member(huffma1450048681e_tree(a)),bot_bot(fun(huffma1450048681e_tree(a),bool))),huffma2021818691e_Leaf(a,zero_zero(nat),a1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_43])]) ).

tff(f929,plain,
    ( ~ pp(aa(huffma1450048681e_tree(a),bool,combc(huffma1450048681e_tree(a),fun(huffma1450048681e_tree(a),bool),bool,member(huffma1450048681e_tree(a)),combk(bool,huffma1450048681e_tree(a),fFalse)),huffma2021818691e_Leaf(a,zero_zero(nat),a1)))
    | spl18_43
    | ~ spl18_68 ),
    inference(superposition,[],[f793,f926]) ).

tff(f793,plain,
    ( ~ pp(aa(huffma1450048681e_tree(a),bool,combc(huffma1450048681e_tree(a),fun(huffma1450048681e_tree(a),bool),bool,member(huffma1450048681e_tree(a)),bot_bot(fun(huffma1450048681e_tree(a),bool))),huffma2021818691e_Leaf(a,zero_zero(nat),a1)))
    | spl18_43 ),
    inference(avatar_component_clause,[],[f791]) ).

tff(f940,plain,
    spl18_70,
    inference(avatar_split_clause,[],[f467,f938]) ).

tff(f467,plain,
    ! [X1: $tType,X0: $tType,X2: X0] :
      ( ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) )
      | ~ bot(X1) ),
    inference(cnf_transformation,[],[f289]) ).

tff(f289,plain,
    ! [X0: $tType,X1: $tType] :
      ( ! [X2: X0] : ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) )
      | ~ bot(X1) ),
    inference(ennf_transformation,[],[f191]) ).

tff(f191,plain,
    ! [X0: $tType,X1: $tType] :
      ( bot(X1)
     => ! [X2: X0] : ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) ) ),
    inference(rectify,[],[f43]) ).

tff(f43,axiom,
    ! [X1: $tType,X2: $tType] :
      ( bot(X2)
     => ! [X8: X1] : ( aa(X1,X2,bot_bot(fun(X1,X2)),X8) = bot_bot(X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_bot__fun__def) ).

tff(f936,plain,
    spl18_69,
    inference(avatar_split_clause,[],[f417,f934]) ).

tff(f934,plain,
    ( spl18_69
  <=> ! [X0: $tType,X2: X0,X1: X0] :
        ( ord_less(X0,X1,X2)
        | ( X1 = X2 )
        | ord_less(X0,X2,X1)
        | ~ linorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_69])]) ).

tff(f417,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ord_less(X0,X1,X2)
      | ( X1 = X2 )
      | ord_less(X0,X2,X1)
      | ~ linorder(X0) ),
    inference(cnf_transformation,[],[f255]) ).

tff(f255,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ord_less(X0,X1,X2)
          | ( X1 = X2 )
          | ord_less(X0,X2,X1) )
      | ~ linorder(X0) ),
    inference(ennf_transformation,[],[f148]) ).

tff(f148,plain,
    ! [X0: $tType] :
      ( linorder(X0)
     => ! [X1: X0,X2: X0] :
          ( ord_less(X0,X1,X2)
          | ( X1 = X2 )
          | ord_less(X0,X2,X1) ) ),
    inference(rectify,[],[f85]) ).

tff(f85,axiom,
    ! [X0: $tType] :
      ( linorder(X0)
     => ! [X30: X0,X49: X0] :
          ( ord_less(X0,X30,X49)
          | ( X30 = X49 )
          | ord_less(X0,X49,X30) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_linorder__less__linear) ).

tff(f927,plain,
    ( spl18_68
    | ~ spl18_37
    | ~ spl18_67 ),
    inference(avatar_split_clause,[],[f923,f920,f762,f925]) ).

tff(f762,plain,
    ( spl18_37
  <=> ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_37])]) ).

tff(f920,plain,
    ( spl18_67
  <=> ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_67])]) ).

tff(f923,plain,
    ( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse) )
    | ~ spl18_37
    | ~ spl18_67 ),
    inference(forward_demodulation,[],[f921,f763]) ).

tff(f763,plain,
    ( ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 )
    | ~ spl18_37 ),
    inference(avatar_component_clause,[],[f762]) ).

tff(f921,plain,
    ( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) )
    | ~ spl18_67 ),
    inference(avatar_component_clause,[],[f920]) ).

tff(f922,plain,
    spl18_67,
    inference(avatar_split_clause,[],[f411,f920]) ).

tff(f411,plain,
    ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) ),
    inference(cnf_transformation,[],[f143]) ).

tff(f143,plain,
    ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) ),
    inference(rectify,[],[f40]) ).

tff(f40,axiom,
    ! [X1: $tType] : ( bot_bot(fun(X1,bool)) = collect(X1,combk(bool,X1,fFalse)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_empty__def) ).

tff(f914,plain,
    spl18_66,
    inference(avatar_split_clause,[],[f416,f912]) ).

tff(f912,plain,
    ( spl18_66
  <=> ! [X0: $tType] :
        ( ( nil(X0) = linord467138063of_set(X0,bot_bot(fun(X0,bool))) )
        | ~ linorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_66])]) ).

tff(f416,plain,
    ! [X0: $tType] :
      ( ( nil(X0) = linord467138063of_set(X0,bot_bot(fun(X0,bool))) )
      | ~ linorder(X0) ),
    inference(cnf_transformation,[],[f254]) ).

tff(f254,plain,
    ! [X0: $tType] :
      ( ( nil(X0) = linord467138063of_set(X0,bot_bot(fun(X0,bool))) )
      | ~ linorder(X0) ),
    inference(ennf_transformation,[],[f147]) ).

tff(f147,plain,
    ! [X0: $tType] :
      ( linorder(X0)
     => ( nil(X0) = linord467138063of_set(X0,bot_bot(fun(X0,bool))) ) ),
    inference(rectify,[],[f44]) ).

tff(f44,axiom,
    ! [X1: $tType] :
      ( linorder(X1)
     => ( nil(X1) = linord467138063of_set(X1,bot_bot(fun(X1,bool))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_sorted__list__of__set__empty) ).

tff(f910,plain,
    spl18_65,
    inference(avatar_split_clause,[],[f410,f908]) ).

tff(f410,plain,
    ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = huffma1516701463abet_F(X0,nil(huffma1450048681e_tree(X0))) ),
    inference(cnf_transformation,[],[f142]) ).

tff(f142,plain,
    ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = huffma1516701463abet_F(X0,nil(huffma1450048681e_tree(X0))) ),
    inference(rectify,[],[f28]) ).

tff(f28,axiom,
    ! [X1: $tType] : ( huffma1516701463abet_F(X1,nil(huffma1450048681e_tree(X1))) = bot_bot(fun(X1,bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_alphabet_092_060_094isub_062F_Osimps_I1_J) ).

tff(f906,plain,
    ( spl18_64
    | ~ spl18_3
    | ~ spl18_51 ),
    inference(avatar_split_clause,[],[f873,f833,f605,f904]) ).

tff(f904,plain,
    ( spl18_64
  <=> ! [X0: bool] : ( bot_bot(bool) = inf_inf(bool,X0,bot_bot(bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_64])]) ).

tff(f605,plain,
    ( spl18_3
  <=> bounded_lattice_bot(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_3])]) ).

tff(f833,plain,
    ( spl18_51
  <=> ! [X0: $tType,X1: X0] :
        ( ( bot_bot(X0) = inf_inf(X0,X1,bot_bot(X0)) )
        | ~ bounded_lattice_bot(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_51])]) ).

tff(f873,plain,
    ( ! [X0: bool] : ( bot_bot(bool) = inf_inf(bool,X0,bot_bot(bool)) )
    | ~ spl18_3
    | ~ spl18_51 ),
    inference(resolution,[],[f834,f607]) ).

tff(f607,plain,
    ( bounded_lattice_bot(bool)
    | ~ spl18_3 ),
    inference(avatar_component_clause,[],[f605]) ).

tff(f834,plain,
    ( ! [X0: $tType,X1: X0] :
        ( ~ bounded_lattice_bot(X0)
        | ( bot_bot(X0) = inf_inf(X0,X1,bot_bot(X0)) ) )
    | ~ spl18_51 ),
    inference(avatar_component_clause,[],[f833]) ).

tff(f890,plain,
    spl18_63,
    inference(avatar_split_clause,[],[f543,f888]) ).

tff(f888,plain,
    ( spl18_63
  <=> ! [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,[spl18_63])]) ).

tff(f543,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,[],[f239]) ).

tff(f239,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,[],[f16]) ).

tff(f16,axiom,
    ! [X0: $tType,X12: X0,X14: nat,X16: huffma1450048681e_tree(X0),X17: huffma1450048681e_tree(X0),X18: nat] : ( huffma2021818691e_Leaf(X0,X14,X12) != huffma1146269203erNode(X0,X18,X17,X16) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_tree_Osimps_I4_J) ).

tff(f886,plain,
    spl18_62,
    inference(avatar_split_clause,[],[f435,f884]) ).

tff(f884,plain,
    ( spl18_62
  <=> ! [X0: $tType,X1: X0] :
        ( ord_less(X0,bot_bot(X0),X1)
        | ( bot_bot(X0) = X1 )
        | ~ bot(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_62])]) ).

tff(f435,plain,
    ! [X0: $tType,X1: X0] :
      ( ord_less(X0,bot_bot(X0),X1)
      | ( bot_bot(X0) = X1 )
      | ~ bot(X0) ),
    inference(cnf_transformation,[],[f325]) ).

tff(f325,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] :
          ( ( ( bot_bot(X0) != X1 )
            | ~ ord_less(X0,bot_bot(X0),X1) )
          & ( ord_less(X0,bot_bot(X0),X1)
            | ( bot_bot(X0) = X1 ) ) )
      | ~ bot(X0) ),
    inference(nnf_transformation,[],[f272]) ).

tff(f272,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] :
          ( ( bot_bot(X0) != X1 )
        <=> ord_less(X0,bot_bot(X0),X1) )
      | ~ bot(X0) ),
    inference(ennf_transformation,[],[f161]) ).

tff(f161,plain,
    ! [X0: $tType] :
      ( bot(X0)
     => ! [X1: X0] :
          ( ( bot_bot(X0) != X1 )
        <=> ord_less(X0,bot_bot(X0),X1) ) ),
    inference(rectify,[],[f60]) ).

tff(f60,axiom,
    ! [X1: $tType] :
      ( bot(X1)
     => ! [X6: X1] :
          ( ( bot_bot(X1) != X6 )
        <=> ord_less(X1,bot_bot(X1),X6) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_bot__less) ).

tff(f882,plain,
    spl18_61,
    inference(avatar_split_clause,[],[f409,f880]) ).

tff(f409,plain,
    ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = set(X0,nil(X0)) ),
    inference(cnf_transformation,[],[f141]) ).

tff(f141,plain,
    ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = set(X0,nil(X0)) ),
    inference(rectify,[],[f29]) ).

tff(f29,axiom,
    ! [X1: $tType] : ( bot_bot(fun(X1,bool)) = set(X1,nil(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_List_Oset_Osimps_I1_J) ).

tff(f872,plain,
    spl18_60,
    inference(avatar_split_clause,[],[f527,f870]) ).

tff(f870,plain,
    ( spl18_60
  <=> ! [X0: $tType,X3: nat,X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
        ( huffma1518433673istent(X0,X1)
        | ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_60])]) ).

tff(f527,plain,
    ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] :
      ( huffma1518433673istent(X0,X1)
      | ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ),
    inference(cnf_transformation,[],[f370]) ).

tff(f370,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat] :
      ( ( huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
        | ( bot_bot(fun(X0,bool)) != inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
        | ~ huffma1518433673istent(X0,X1)
        | ~ huffma1518433673istent(X0,X2) )
      & ( ( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
          & huffma1518433673istent(X0,X1)
          & huffma1518433673istent(X0,X2) )
        | ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ) ),
    inference(flattening,[],[f369]) ).

tff(f369,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat] :
      ( ( huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
        | ( bot_bot(fun(X0,bool)) != inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
        | ~ huffma1518433673istent(X0,X1)
        | ~ huffma1518433673istent(X0,X2) )
      & ( ( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
          & huffma1518433673istent(X0,X1)
          & huffma1518433673istent(X0,X2) )
        | ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ) ),
    inference(nnf_transformation,[],[f233]) ).

tff(f233,plain,
    ! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat] :
      ( huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
    <=> ( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
        & huffma1518433673istent(X0,X1)
        & huffma1518433673istent(X0,X2) ) ),
    inference(rectify,[],[f50]) ).

tff(f50,axiom,
    ! [X1: $tType,X43: huffma1450048681e_tree(X1),X44: huffma1450048681e_tree(X1),X45: nat] :
      ( huffma1518433673istent(X1,huffma1146269203erNode(X1,X45,X44,X43))
    <=> ( ( bot_bot(fun(X1,bool)) = inf_inf(fun(X1,bool),huffma675207370phabet(X1,X44),huffma675207370phabet(X1,X43)) )
        & huffma1518433673istent(X1,X43)
        & huffma1518433673istent(X1,X44) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_consistent_Osimps_I2_J) ).

tff(f868,plain,
    spl18_59,
    inference(avatar_split_clause,[],[f526,f866]) ).

tff(f866,plain,
    ( spl18_59
  <=> ! [X0: $tType,X3: nat,X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
        ( huffma1518433673istent(X0,X2)
        | ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_59])]) ).

tff(f526,plain,
    ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] :
      ( huffma1518433673istent(X0,X2)
      | ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ),
    inference(cnf_transformation,[],[f370]) ).

tff(f864,plain,
    spl18_58,
    inference(avatar_split_clause,[],[f513,f862]) ).

tff(f513,plain,
    ! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
    inference(cnf_transformation,[],[f222]) ).

tff(f222,plain,
    ! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
    inference(rectify,[],[f129]) ).

tff(f129,axiom,
    ! [X1: $tType,X0: $tType,X61: X1,X62: X0] : ( aa(X1,X0,combk(X0,X1,X62),X61) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).

tff(f860,plain,
    spl18_57,
    inference(avatar_split_clause,[],[f512,f858]) ).

tff(f858,plain,
    ( spl18_57
  <=> ! [X0: $tType,X3: nat,X2: X0,X1: X0] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_57])]) ).

tff(f512,plain,
    ! [X0: $tType,X2: X0,X3: nat,X1: X0] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) ),
    inference(cnf_transformation,[],[f221]) ).

tff(f221,plain,
    ! [X0: $tType,X1: X0,X2: X0,X3: nat] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) ),
    inference(rectify,[],[f14]) ).

tff(f14,axiom,
    ! [X0: $tType,X12: X0,X15: X0,X13: nat] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X13,X15),X12) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_depth_Osimps_I1_J) ).

tff(f856,plain,
    spl18_56,
    inference(avatar_split_clause,[],[f489,f854]) ).

tff(f854,plain,
    ( spl18_56
  <=> ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_56])]) ).

tff(f489,plain,
    ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X2,X1)) ),
    inference(cnf_transformation,[],[f206]) ).

tff(f206,plain,
    ! [X0: $tType,X1: X0,X2: nat] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X2,X1)) ),
    inference(rectify,[],[f12]) ).

tff(f12,axiom,
    ! [X0: $tType,X12: X0,X14: nat] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X14,X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_tree_Osize_I3_J) ).

tff(f852,plain,
    spl18_55,
    inference(avatar_split_clause,[],[f451,f850]) ).

tff(f850,plain,
    ( spl18_55
  <=> ! [X0: $tType,X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X1,X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_55])]) ).

tff(f451,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X1,X1) = X1 ),
    inference(cnf_transformation,[],[f175]) ).

tff(f175,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X1,X1) = X1 ),
    inference(rectify,[],[f88]) ).

tff(f88,axiom,
    ! [X1: $tType,X39: fun(X1,bool)] : ( inf_inf(fun(X1,bool),X39,X39) = X39 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_Int__absorb) ).

tff(f848,plain,
    ( ~ spl18_15
    | spl18_54
    | ~ spl18_36
    | ~ spl18_44 ),
    inference(avatar_split_clause,[],[f829,f797,f758,f845,f665]) ).

tff(f665,plain,
    ( spl18_15
  <=> bot(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_15])]) ).

tff(f845,plain,
    ( spl18_54
  <=> ( zero_zero(nat) = bot_bot(nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_54])]) ).

tff(f797,plain,
    ( spl18_44
  <=> ! [X0: nat] :
        ( ord_less(nat,zero_zero(nat),X0)
        | ( zero_zero(nat) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_44])]) ).

tff(f829,plain,
    ( ( zero_zero(nat) = bot_bot(nat) )
    | ~ bot(nat)
    | ~ spl18_36
    | ~ spl18_44 ),
    inference(resolution,[],[f798,f759]) ).

tff(f798,plain,
    ( ! [X0: nat] :
        ( ord_less(nat,zero_zero(nat),X0)
        | ( zero_zero(nat) = X0 ) )
    | ~ spl18_44 ),
    inference(avatar_component_clause,[],[f797]) ).

tff(f843,plain,
    spl18_53,
    inference(avatar_split_clause,[],[f438,f841]) ).

tff(f841,plain,
    ( spl18_53
  <=> ! [X0: $tType,X2: X0,X1: X0] :
        ( ~ ord_less(X0,X1,X2)
        | ~ ord_less(X0,X2,X1)
        | ~ preorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_53])]) ).

tff(f438,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ~ ord_less(X0,X1,X2)
      | ~ ord_less(X0,X2,X1)
      | ~ preorder(X0) ),
    inference(cnf_transformation,[],[f274]) ).

tff(f274,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ~ ord_less(X0,X1,X2)
          | ~ ord_less(X0,X2,X1) )
      | ~ preorder(X0) ),
    inference(ennf_transformation,[],[f163]) ).

tff(f163,plain,
    ! [X0: $tType] :
      ( preorder(X0)
     => ! [X1: X0,X2: X0] :
          ( ord_less(X0,X2,X1)
         => ~ ord_less(X0,X1,X2) ) ),
    inference(rectify,[],[f73]) ).

tff(f73,axiom,
    ! [X0: $tType] :
      ( preorder(X0)
     => ! [X30: X0,X49: X0] :
          ( ord_less(X0,X49,X30)
         => ~ ord_less(X0,X30,X49) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_order__less__imp__not__less) ).

tff(f839,plain,
    spl18_52,
    inference(avatar_split_clause,[],[f426,f837]) ).

tff(f837,plain,
    ( spl18_52
  <=> ! [X0: $tType,X2: X0,X1: X0] :
        ( ~ ord_less(X0,X2,X1)
        | ~ ord_less(X0,X1,X2)
        | ~ linorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_52])]) ).

tff(f426,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ~ ord_less(X0,X2,X1)
      | ~ ord_less(X0,X1,X2)
      | ~ linorder(X0) ),
    inference(cnf_transformation,[],[f324]) ).

tff(f324,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ( ~ ord_less(X0,X2,X1)
            | ( ( X1 != X2 )
              & ~ ord_less(X0,X1,X2) ) )
          & ( ( X1 = X2 )
            | ord_less(X0,X1,X2)
            | ord_less(X0,X2,X1) ) )
      | ~ linorder(X0) ),
    inference(flattening,[],[f323]) ).

tff(f323,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ( ~ ord_less(X0,X2,X1)
            | ( ( X1 != X2 )
              & ~ ord_less(X0,X1,X2) ) )
          & ( ( X1 = X2 )
            | ord_less(X0,X1,X2)
            | ord_less(X0,X2,X1) ) )
      | ~ linorder(X0) ),
    inference(nnf_transformation,[],[f262]) ).

tff(f262,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ~ ord_less(X0,X2,X1)
        <=> ( ( X1 = X2 )
            | ord_less(X0,X1,X2) ) )
      | ~ linorder(X0) ),
    inference(ennf_transformation,[],[f153]) ).

tff(f153,plain,
    ! [X0: $tType] :
      ( linorder(X0)
     => ! [X1: X0,X2: X0] :
          ( ~ ord_less(X0,X2,X1)
        <=> ( ( X1 = X2 )
            | ord_less(X0,X1,X2) ) ) ),
    inference(rectify,[],[f89]) ).

tff(f89,axiom,
    ! [X1: $tType] :
      ( linorder(X1)
     => ! [X52: X1,X37: X1] :
          ( ~ ord_less(X1,X37,X52)
        <=> ( ( X37 = X52 )
            | ord_less(X1,X52,X37) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_not__less__iff__gr__or__eq) ).

tff(f835,plain,
    spl18_51,
    inference(avatar_split_clause,[],[f415,f833]) ).

tff(f415,plain,
    ! [X0: $tType,X1: X0] :
      ( ( bot_bot(X0) = inf_inf(X0,X1,bot_bot(X0)) )
      | ~ bounded_lattice_bot(X0) ),
    inference(cnf_transformation,[],[f253]) ).

tff(f253,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ( bot_bot(X0) = inf_inf(X0,X1,bot_bot(X0)) )
      | ~ bounded_lattice_bot(X0) ),
    inference(ennf_transformation,[],[f146]) ).

tff(f146,plain,
    ! [X0: $tType] :
      ( bounded_lattice_bot(X0)
     => ! [X1: X0] : ( bot_bot(X0) = inf_inf(X0,X1,bot_bot(X0)) ) ),
    inference(rectify,[],[f98]) ).

tff(f98,axiom,
    ! [X0: $tType] :
      ( bounded_lattice_bot(X0)
     => ! [X49: X0] : ( bot_bot(X0) = inf_inf(X0,X49,bot_bot(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_inf__bot__right) ).

tff(f823,plain,
    spl18_50,
    inference(avatar_split_clause,[],[f575,f821]) ).

tff(f821,plain,
    ( spl18_50
  <=> ! [X0: $tType,X1: nat,X3: X0] : ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X3),X3) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_50])]) ).

tff(f575,plain,
    ! [X0: $tType,X3: X0,X1: 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] :
      ( ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) = X1 )
      | ( X2 != X3 ) ),
    inference(cnf_transformation,[],[f304]) ).

tff(f819,plain,
    spl18_49,
    inference(avatar_split_clause,[],[f511,f817]) ).

tff(f817,plain,
    ( spl18_49
  <=> ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X1] : ( list_case(X1,X0,X3,X2,nil(X0)) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_49])]) ).

tff(f511,plain,
    ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X1] : ( list_case(X1,X0,X3,X2,nil(X0)) = X3 ),
    inference(cnf_transformation,[],[f220]) ).

tff(f220,plain,
    ! [X0: $tType,X1: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X1] : ( list_case(X1,X0,X3,X2,nil(X0)) = X3 ),
    inference(rectify,[],[f24]) ).

tff(f24,axiom,
    ! [X2: $tType,X1: $tType,X9: fun(X2,fun(list(X2),X1)),X10: X1] : ( list_case(X1,X2,X10,X9,nil(X2)) = X10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_list_Osimps_I4_J) ).

tff(f815,plain,
    spl18_48,
    inference(avatar_split_clause,[],[f510,f813]) ).

tff(f813,plain,
    ( spl18_48
  <=> ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),fun(X1,X1))),X3: X1] : ( list_rec(X1,X0,X3,X2,nil(X0)) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_48])]) ).

tff(f510,plain,
    ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),fun(X1,X1))),X3: X1] : ( list_rec(X1,X0,X3,X2,nil(X0)) = X3 ),
    inference(cnf_transformation,[],[f219]) ).

tff(f219,plain,
    ! [X0: $tType,X1: $tType,X2: fun(X0,fun(list(X0),fun(X1,X1))),X3: X1] : ( list_rec(X1,X0,X3,X2,nil(X0)) = X3 ),
    inference(rectify,[],[f48]) ).

tff(f48,axiom,
    ! [X2: $tType,X1: $tType,X9: fun(X2,fun(list(X2),fun(X1,X1))),X10: X1] : ( list_rec(X1,X2,X10,X9,nil(X2)) = X10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_list_Orecs_I1_J) ).

tff(f811,plain,
    spl18_47,
    inference(avatar_split_clause,[],[f488,f809]) ).

tff(f809,plain,
    ( spl18_47
  <=> ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_47])]) ).

tff(f488,plain,
    ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
    inference(cnf_transformation,[],[f205]) ).

tff(f205,plain,
    ! [X0: $tType,X1: X0,X2: nat] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
    inference(rectify,[],[f25]) ).

tff(f25,axiom,
    ! [X0: $tType,X12: X0,X13: nat] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X13,X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_height_Osimps_I1_J) ).

tff(f807,plain,
    spl18_46,
    inference(avatar_split_clause,[],[f450,f805]) ).

tff(f805,plain,
    ( spl18_46
  <=> ! [X0: $tType,X1: fun(X0,bool)] : ( nil(X0) = dropWhile(X0,X1,nil(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_46])]) ).

tff(f450,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : ( nil(X0) = dropWhile(X0,X1,nil(X0)) ),
    inference(cnf_transformation,[],[f174]) ).

tff(f174,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : ( nil(X0) = dropWhile(X0,X1,nil(X0)) ),
    inference(rectify,[],[f19]) ).

tff(f19,axiom,
    ! [X1: $tType,X20: fun(X1,bool)] : ( nil(X1) = dropWhile(X1,X20,nil(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_dropWhile_Osimps_I1_J) ).

tff(f803,plain,
    spl18_45,
    inference(avatar_split_clause,[],[f449,f801]) ).

tff(f801,plain,
    ( spl18_45
  <=> ! [X0: $tType,X1: X0] : ( zero_zero(nat) = huffma409467474freq_F(X0,nil(huffma1450048681e_tree(X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_45])]) ).

tff(f449,plain,
    ! [X0: $tType,X1: X0] : ( zero_zero(nat) = huffma409467474freq_F(X0,nil(huffma1450048681e_tree(X0)),X1) ),
    inference(cnf_transformation,[],[f173]) ).

tff(f173,plain,
    ! [X0: $tType,X1: X0] : ( zero_zero(nat) = huffma409467474freq_F(X0,nil(huffma1450048681e_tree(X0)),X1) ),
    inference(rectify,[],[f6]) ).

tff(f6,axiom,
    ! [X0: $tType,X8: X0] : ( zero_zero(nat) = huffma409467474freq_F(X0,nil(huffma1450048681e_tree(X0)),X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_freq_092_060_094isub_062F_Osimps_I1_J) ).

tff(f799,plain,
    spl18_44,
    inference(avatar_split_clause,[],[f444,f797]) ).

tff(f444,plain,
    ! [X0: nat] :
      ( ord_less(nat,zero_zero(nat),X0)
      | ( zero_zero(nat) = X0 ) ),
    inference(cnf_transformation,[],[f326]) ).

tff(f326,plain,
    ! [X0: nat] :
      ( ( ( zero_zero(nat) != X0 )
        | ~ ord_less(nat,zero_zero(nat),X0) )
      & ( ord_less(nat,zero_zero(nat),X0)
        | ( zero_zero(nat) = X0 ) ) ),
    inference(nnf_transformation,[],[f169]) ).

tff(f169,plain,
    ! [X0: nat] :
      ( ( zero_zero(nat) != X0 )
    <=> ord_less(nat,zero_zero(nat),X0) ),
    inference(rectify,[],[f97]) ).

tff(f97,axiom,
    ! [X57: nat] :
      ( ( zero_zero(nat) != X57 )
    <=> ord_less(nat,zero_zero(nat),X57) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_neq0__conv) ).

tff(f794,plain,
    ( ~ spl18_43
    | spl18_42 ),
    inference(avatar_split_clause,[],[f789,f783,f791]) ).

tff(f783,plain,
    ( spl18_42
  <=> pp(aa(fun(huffma1450048681e_tree(a),bool),bool,aa(huffma1450048681e_tree(a),fun(fun(huffma1450048681e_tree(a),bool),bool),member(huffma1450048681e_tree(a)),huffma2021818691e_Leaf(a,huffma409467474freq_F(a,nil(huffma1450048681e_tree(a)),a1),a1)),set(huffma1450048681e_tree(a),nil(huffma1450048681e_tree(a))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_42])]) ).

tff(f789,plain,
    ( ~ pp(aa(huffma1450048681e_tree(a),bool,combc(huffma1450048681e_tree(a),fun(huffma1450048681e_tree(a),bool),bool,member(huffma1450048681e_tree(a)),bot_bot(fun(huffma1450048681e_tree(a),bool))),huffma2021818691e_Leaf(a,zero_zero(nat),a1)))
    | spl18_42 ),
    inference(forward_demodulation,[],[f788,f409]) ).

tff(f788,plain,
    ( ~ pp(aa(huffma1450048681e_tree(a),bool,combc(huffma1450048681e_tree(a),fun(huffma1450048681e_tree(a),bool),bool,member(huffma1450048681e_tree(a)),set(huffma1450048681e_tree(a),nil(huffma1450048681e_tree(a)))),huffma2021818691e_Leaf(a,zero_zero(nat),a1)))
    | spl18_42 ),
    inference(forward_demodulation,[],[f787,f449]) ).

tff(f787,plain,
    ( ~ pp(aa(huffma1450048681e_tree(a),bool,combc(huffma1450048681e_tree(a),fun(huffma1450048681e_tree(a),bool),bool,member(huffma1450048681e_tree(a)),set(huffma1450048681e_tree(a),nil(huffma1450048681e_tree(a)))),huffma2021818691e_Leaf(a,huffma409467474freq_F(a,nil(huffma1450048681e_tree(a)),a1),a1)))
    | spl18_42 ),
    inference(forward_demodulation,[],[f785,f548]) ).

tff(f785,plain,
    ( ~ pp(aa(fun(huffma1450048681e_tree(a),bool),bool,aa(huffma1450048681e_tree(a),fun(fun(huffma1450048681e_tree(a),bool),bool),member(huffma1450048681e_tree(a)),huffma2021818691e_Leaf(a,huffma409467474freq_F(a,nil(huffma1450048681e_tree(a)),a1),a1)),set(huffma1450048681e_tree(a),nil(huffma1450048681e_tree(a)))))
    | spl18_42 ),
    inference(avatar_component_clause,[],[f783]) ).

tff(f786,plain,
    ~ spl18_42,
    inference(avatar_split_clause,[],[f383,f783]) ).

tff(f383,plain,
    ~ pp(aa(fun(huffma1450048681e_tree(a),bool),bool,aa(huffma1450048681e_tree(a),fun(fun(huffma1450048681e_tree(a),bool),bool),member(huffma1450048681e_tree(a)),huffma2021818691e_Leaf(a,huffma409467474freq_F(a,nil(huffma1450048681e_tree(a)),a1),a1)),set(huffma1450048681e_tree(a),nil(huffma1450048681e_tree(a))))),
    inference(cnf_transformation,[],[f138]) ).

tff(f138,plain,
    ~ pp(aa(fun(huffma1450048681e_tree(a),bool),bool,aa(huffma1450048681e_tree(a),fun(fun(huffma1450048681e_tree(a),bool),bool),member(huffma1450048681e_tree(a)),huffma2021818691e_Leaf(a,huffma409467474freq_F(a,nil(huffma1450048681e_tree(a)),a1),a1)),set(huffma1450048681e_tree(a),nil(huffma1450048681e_tree(a))))),
    inference(flattening,[],[f137]) ).

tff(f137,negated_conjecture,
    ~ pp(aa(fun(huffma1450048681e_tree(a),bool),bool,aa(huffma1450048681e_tree(a),fun(fun(huffma1450048681e_tree(a),bool),bool),member(huffma1450048681e_tree(a)),huffma2021818691e_Leaf(a,huffma409467474freq_F(a,nil(huffma1450048681e_tree(a)),a1),a1)),set(huffma1450048681e_tree(a),nil(huffma1450048681e_tree(a))))),
    inference(negated_conjecture,[],[f136]) ).

tff(f136,conjecture,
    pp(aa(fun(huffma1450048681e_tree(a),bool),bool,aa(huffma1450048681e_tree(a),fun(fun(huffma1450048681e_tree(a),bool),bool),member(huffma1450048681e_tree(a)),huffma2021818691e_Leaf(a,huffma409467474freq_F(a,nil(huffma1450048681e_tree(a)),a1),a1)),set(huffma1450048681e_tree(a),nil(huffma1450048681e_tree(a))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(f781,plain,
    ( spl18_40
    | ~ spl18_41
    | ~ spl18_22 ),
    inference(avatar_split_clause,[],[f751,f698,f778,f775]) ).

tff(f775,plain,
    ( spl18_40
  <=> ! [X0: bool] : ( fTrue = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_40])]) ).

tff(f778,plain,
    ( spl18_41
  <=> ( fFalse = fTrue ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_41])]) ).

tff(f698,plain,
    ( spl18_22
  <=> ! [X0: bool] :
        ( ( fFalse = X0 )
        | ( fTrue = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_22])]) ).

tff(f751,plain,
    ( ! [X0: bool] :
        ( ( fFalse != fTrue )
        | ( fTrue = X0 ) )
    | ~ spl18_22 ),
    inference(equality_factoring,[],[f699]) ).

tff(f699,plain,
    ( ! [X0: bool] :
        ( ( fFalse = X0 )
        | ( fTrue = X0 ) )
    | ~ spl18_22 ),
    inference(avatar_component_clause,[],[f698]) ).

tff(f773,plain,
    spl18_39,
    inference(avatar_split_clause,[],[f448,f771]) ).

tff(f771,plain,
    ( spl18_39
  <=> ! [X0: $tType,X1: fun(X0,nat)] : ( zero_zero(nat) = list_size(X0,X1,nil(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_39])]) ).

tff(f448,plain,
    ! [X0: $tType,X1: fun(X0,nat)] : ( zero_zero(nat) = list_size(X0,X1,nil(X0)) ),
    inference(cnf_transformation,[],[f172]) ).

tff(f172,plain,
    ! [X0: $tType,X1: fun(X0,nat)] : ( zero_zero(nat) = list_size(X0,X1,nil(X0)) ),
    inference(rectify,[],[f26]) ).

tff(f26,axiom,
    ! [X1: $tType,X35: fun(X1,nat)] : ( zero_zero(nat) = list_size(X1,X35,nil(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_list_Osize_I1_J) ).

tff(f769,plain,
    spl18_38,
    inference(avatar_split_clause,[],[f408,f767]) ).

tff(f767,plain,
    ( spl18_38
  <=> ! [X0: $tType] : ( zero_zero(nat) = huffma632063779ight_F(X0,nil(huffma1450048681e_tree(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_38])]) ).

tff(f408,plain,
    ! [X0: $tType] : ( zero_zero(nat) = huffma632063779ight_F(X0,nil(huffma1450048681e_tree(X0))) ),
    inference(cnf_transformation,[],[f7]) ).

tff(f7,axiom,
    ! [X0: $tType] : ( zero_zero(nat) = huffma632063779ight_F(X0,nil(huffma1450048681e_tree(X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_height_092_060_094isub_062F_Osimps_I1_J) ).

tff(f764,plain,
    spl18_37,
    inference(avatar_split_clause,[],[f447,f762]) ).

tff(f760,plain,
    spl18_36,
    inference(avatar_split_clause,[],[f434,f758]) ).

tff(f434,plain,
    ! [X0: $tType,X1: X0] :
      ( ~ ord_less(X0,X1,bot_bot(X0))
      | ~ bot(X0) ),
    inference(cnf_transformation,[],[f271]) ).

tff(f271,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ~ ord_less(X0,X1,bot_bot(X0))
      | ~ bot(X0) ),
    inference(ennf_transformation,[],[f160]) ).

tff(f160,plain,
    ! [X0: $tType] :
      ( bot(X0)
     => ! [X1: X0] : ~ ord_less(X0,X1,bot_bot(X0)) ),
    inference(rectify,[],[f61]) ).

tff(f61,axiom,
    ! [X0: $tType] :
      ( bot(X0)
     => ! [X12: X0] : ~ ord_less(X0,X12,bot_bot(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_not__less__bot) ).

tff(f755,plain,
    ( spl18_35
    | spl18_1
    | ~ spl18_22 ),
    inference(avatar_split_clause,[],[f750,f698,f595,f753]) ).

tff(f753,plain,
    ( spl18_35
  <=> ! [X0: bool] :
        ( ~ pp(X0)
        | ( fTrue = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_35])]) ).

tff(f750,plain,
    ( ! [X0: bool] :
        ( ~ pp(X0)
        | ( fTrue = X0 ) )
    | spl18_1
    | ~ spl18_22 ),
    inference(superposition,[],[f597,f699]) ).

tff(f597,plain,
    ( ~ pp(fFalse)
    | spl18_1 ),
    inference(avatar_component_clause,[],[f595]) ).

tff(f748,plain,
    spl18_34,
    inference(avatar_split_clause,[],[f564,f746]) ).

tff(f746,plain,
    ( spl18_34
  <=> ! [X0: $tType,X2: X0] :
        ( ~ ord_less(X0,X2,X2)
        | ~ order(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_34])]) ).

tff(f564,plain,
    ! [X0: $tType,X2: X0] :
      ( ~ ord_less(X0,X2,X2)
      | ~ order(X0) ),
    inference(equality_resolution,[],[f431]) ).

tff(f431,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( X1 != X2 )
      | ~ ord_less(X0,X2,X1)
      | ~ order(X0) ),
    inference(cnf_transformation,[],[f268]) ).

tff(f268,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ( X1 != X2 )
          | ~ ord_less(X0,X2,X1) )
      | ~ order(X0) ),
    inference(ennf_transformation,[],[f157]) ).

tff(f157,plain,
    ! [X0: $tType] :
      ( order(X0)
     => ! [X1: X0,X2: X0] :
          ( ord_less(X0,X2,X1)
         => ( X1 != X2 ) ) ),
    inference(rectify,[],[f78]) ).

tff(f78,axiom,
    ! [X0: $tType] :
      ( order(X0)
     => ! [X30: X0,X49: X0] :
          ( ord_less(X0,X49,X30)
         => ( X30 != X49 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_less__imp__neq) ).

tff(f744,plain,
    spl18_33,
    inference(avatar_split_clause,[],[f559,f742]) ).

tff(f742,plain,
    ( spl18_33
  <=> ! [X0: $tType,X2: X0] :
        ( ~ ord_less(X0,X2,X2)
        | ~ linorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_33])]) ).

tff(f559,plain,
    ! [X0: $tType,X2: X0] :
      ( ~ ord_less(X0,X2,X2)
      | ~ linorder(X0) ),
    inference(equality_resolution,[],[f424]) ).

tff(f424,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( X1 != X2 )
      | ~ ord_less(X0,X1,X2)
      | ~ linorder(X0) ),
    inference(cnf_transformation,[],[f322]) ).

tff(f322,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ( ( X1 != X2 )
            | ( ~ ord_less(X0,X1,X2)
              & ~ ord_less(X0,X2,X1) ) )
          & ( ord_less(X0,X1,X2)
            | ord_less(X0,X2,X1)
            | ( X1 = X2 ) ) )
      | ~ linorder(X0) ),
    inference(flattening,[],[f321]) ).

tff(f321,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ( ( X1 != X2 )
            | ( ~ ord_less(X0,X1,X2)
              & ~ ord_less(X0,X2,X1) ) )
          & ( ord_less(X0,X1,X2)
            | ord_less(X0,X2,X1)
            | ( X1 = X2 ) ) )
      | ~ linorder(X0) ),
    inference(nnf_transformation,[],[f261]) ).

tff(f261,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ( X1 != X2 )
        <=> ( ord_less(X0,X1,X2)
            | ord_less(X0,X2,X1) ) )
      | ~ linorder(X0) ),
    inference(ennf_transformation,[],[f152]) ).

tff(f152,plain,
    ! [X0: $tType] :
      ( linorder(X0)
     => ! [X1: X0,X2: X0] :
          ( ( X1 != X2 )
        <=> ( ord_less(X0,X1,X2)
            | ord_less(X0,X2,X1) ) ) ),
    inference(rectify,[],[f90]) ).

tff(f90,axiom,
    ! [X1: $tType] :
      ( linorder(X1)
     => ! [X52: X1,X37: X1] :
          ( ( X37 != X52 )
        <=> ( ord_less(X1,X52,X37)
            | ord_less(X1,X37,X52) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_linorder__neq__iff) ).

tff(f740,plain,
    spl18_32,
    inference(avatar_split_clause,[],[f487,f738]) ).

tff(f738,plain,
    ( spl18_32
  <=> ! [X0: $tType,X2: nat,X1: X0] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_32])]) ).

tff(f487,plain,
    ! [X0: $tType,X2: nat,X1: X0] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1)),
    inference(cnf_transformation,[],[f204]) ).

tff(f204,plain,
    ! [X0: $tType,X1: X0,X2: nat] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1)),
    inference(rectify,[],[f10]) ).

tff(f10,axiom,
    ! [X0: $tType,X12: X0,X13: nat] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X13,X12)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_consistent_Osimps_I1_J) ).

tff(f736,plain,
    spl18_31,
    inference(avatar_split_clause,[],[f469,f734]) ).

tff(f734,plain,
    ( spl18_31
  <=> ! [X1: $tType,X0: $tType] :
        ( preorder(fun(X0,X1))
        | ~ preorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_31])]) ).

tff(f469,plain,
    ! [X1: $tType,X0: $tType] :
      ( preorder(fun(X0,X1))
      | ~ preorder(X1) ),
    inference(cnf_transformation,[],[f291]) ).

tff(f291,plain,
    ! [X0: $tType,X1: $tType] :
      ( preorder(fun(X0,X1))
      | ~ preorder(X1) ),
    inference(ennf_transformation,[],[f193]) ).

tff(f193,plain,
    ! [X0: $tType,X1: $tType] :
      ( preorder(X1)
     => preorder(fun(X0,X1)) ),
    inference(rectify,[],[f107]) ).

tff(f107,axiom,
    ! [X58: $tType,X59: $tType] :
      ( preorder(X59)
     => preorder(fun(X58,X59)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).

tff(f732,plain,
    spl18_30,
    inference(avatar_split_clause,[],[f466,f730]) ).

tff(f730,plain,
    ( spl18_30
  <=> ! [X1: $tType,X0: $tType] :
        ( bot(fun(X0,X1))
        | ~ bot(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_30])]) ).

tff(f466,plain,
    ! [X1: $tType,X0: $tType] :
      ( bot(fun(X0,X1))
      | ~ bot(X1) ),
    inference(cnf_transformation,[],[f288]) ).

tff(f288,plain,
    ! [X0: $tType,X1: $tType] :
      ( bot(fun(X0,X1))
      | ~ bot(X1) ),
    inference(ennf_transformation,[],[f190]) ).

tff(f190,plain,
    ! [X0: $tType,X1: $tType] :
      ( bot(X1)
     => bot(fun(X0,X1)) ),
    inference(rectify,[],[f110]) ).

tff(f110,axiom,
    ! [X58: $tType,X59: $tType] :
      ( bot(X59)
     => bot(fun(X58,X59)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).

tff(f728,plain,
    spl18_29,
    inference(avatar_split_clause,[],[f465,f726]) ).

tff(f726,plain,
    ( spl18_29
  <=> ! [X1: $tType,X0: $tType] :
        ( order(fun(X0,X1))
        | ~ order(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_29])]) ).

tff(f465,plain,
    ! [X1: $tType,X0: $tType] :
      ( order(fun(X0,X1))
      | ~ order(X1) ),
    inference(cnf_transformation,[],[f287]) ).

tff(f287,plain,
    ! [X0: $tType,X1: $tType] :
      ( order(fun(X0,X1))
      | ~ order(X1) ),
    inference(ennf_transformation,[],[f189]) ).

tff(f189,plain,
    ! [X0: $tType,X1: $tType] :
      ( order(X1)
     => order(fun(X0,X1)) ),
    inference(rectify,[],[f108]) ).

tff(f108,axiom,
    ! [X58: $tType,X59: $tType] :
      ( order(X59)
     => order(fun(X58,X59)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).

tff(f724,plain,
    spl18_28,
    inference(avatar_split_clause,[],[f464,f722]) ).

tff(f722,plain,
    ( spl18_28
  <=> ! [X1: $tType,X0: $tType] :
        ( ord(fun(X0,X1))
        | ~ ord(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_28])]) ).

tff(f464,plain,
    ! [X1: $tType,X0: $tType] :
      ( ord(fun(X0,X1))
      | ~ ord(X1) ),
    inference(cnf_transformation,[],[f286]) ).

tff(f286,plain,
    ! [X0: $tType,X1: $tType] :
      ( ord(fun(X0,X1))
      | ~ ord(X1) ),
    inference(ennf_transformation,[],[f188]) ).

tff(f188,plain,
    ! [X0: $tType,X1: $tType] :
      ( ord(X1)
     => ord(fun(X0,X1)) ),
    inference(rectify,[],[f109]) ).

tff(f109,axiom,
    ! [X58: $tType,X59: $tType] :
      ( ord(X59)
     => ord(fun(X58,X59)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).

tff(f720,plain,
    spl18_27,
    inference(avatar_split_clause,[],[f463,f718]) ).

tff(f718,plain,
    ( spl18_27
  <=> ! [X1: $tType,X0: $tType] :
        ( lattice(fun(X0,X1))
        | ~ lattice(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_27])]) ).

tff(f463,plain,
    ! [X1: $tType,X0: $tType] :
      ( lattice(fun(X0,X1))
      | ~ lattice(X1) ),
    inference(cnf_transformation,[],[f285]) ).

tff(f285,plain,
    ! [X0: $tType,X1: $tType] :
      ( lattice(fun(X0,X1))
      | ~ lattice(X1) ),
    inference(ennf_transformation,[],[f187]) ).

tff(f187,plain,
    ! [X0: $tType,X1: $tType] :
      ( lattice(X1)
     => lattice(fun(X0,X1)) ),
    inference(rectify,[],[f104]) ).

tff(f104,axiom,
    ! [X58: $tType,X59: $tType] :
      ( lattice(X59)
     => lattice(fun(X58,X59)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Olattice) ).

tff(f716,plain,
    spl18_26,
    inference(avatar_split_clause,[],[f462,f714]) ).

tff(f714,plain,
    ( spl18_26
  <=> ! [X1: $tType,X0: $tType] :
        ( semilattice_inf(fun(X0,X1))
        | ~ lattice(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_26])]) ).

tff(f462,plain,
    ! [X1: $tType,X0: $tType] :
      ( semilattice_inf(fun(X0,X1))
      | ~ lattice(X1) ),
    inference(cnf_transformation,[],[f284]) ).

tff(f284,plain,
    ! [X0: $tType,X1: $tType] :
      ( semilattice_inf(fun(X0,X1))
      | ~ lattice(X1) ),
    inference(ennf_transformation,[],[f186]) ).

tff(f186,plain,
    ! [X0: $tType,X1: $tType] :
      ( lattice(X1)
     => semilattice_inf(fun(X0,X1)) ),
    inference(rectify,[],[f106]) ).

tff(f106,axiom,
    ! [X58: $tType,X59: $tType] :
      ( lattice(X59)
     => semilattice_inf(fun(X58,X59)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Osemilattice__inf) ).

tff(f712,plain,
    spl18_25,
    inference(avatar_split_clause,[],[f461,f710]) ).

tff(f710,plain,
    ( spl18_25
  <=> ! [X1: $tType,X0: $tType] :
        ( bounded_lattice(fun(X0,X1))
        | ~ bounded_lattice(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_25])]) ).

tff(f461,plain,
    ! [X1: $tType,X0: $tType] :
      ( bounded_lattice(fun(X0,X1))
      | ~ bounded_lattice(X1) ),
    inference(cnf_transformation,[],[f283]) ).

tff(f283,plain,
    ! [X0: $tType,X1: $tType] :
      ( bounded_lattice(fun(X0,X1))
      | ~ bounded_lattice(X1) ),
    inference(ennf_transformation,[],[f185]) ).

tff(f185,plain,
    ! [X0: $tType,X1: $tType] :
      ( bounded_lattice(X1)
     => bounded_lattice(fun(X0,X1)) ),
    inference(rectify,[],[f103]) ).

tff(f103,axiom,
    ! [X58: $tType,X59: $tType] :
      ( bounded_lattice(X59)
     => bounded_lattice(fun(X58,X59)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Obounded__lattice) ).

tff(f708,plain,
    spl18_24,
    inference(avatar_split_clause,[],[f460,f706]) ).

tff(f706,plain,
    ( spl18_24
  <=> ! [X1: $tType,X0: $tType] :
        ( bounded_lattice_bot(fun(X0,X1))
        | ~ bounded_lattice(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_24])]) ).

tff(f460,plain,
    ! [X1: $tType,X0: $tType] :
      ( bounded_lattice_bot(fun(X0,X1))
      | ~ bounded_lattice(X1) ),
    inference(cnf_transformation,[],[f282]) ).

tff(f282,plain,
    ! [X0: $tType,X1: $tType] :
      ( bounded_lattice_bot(fun(X0,X1))
      | ~ bounded_lattice(X1) ),
    inference(ennf_transformation,[],[f184]) ).

tff(f184,plain,
    ! [X0: $tType,X1: $tType] :
      ( bounded_lattice(X1)
     => bounded_lattice_bot(fun(X0,X1)) ),
    inference(rectify,[],[f105]) ).

tff(f105,axiom,
    ! [X58: $tType,X59: $tType] :
      ( bounded_lattice(X59)
     => bounded_lattice_bot(fun(X58,X59)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Obounded__lattice__bot) ).

tff(f704,plain,
    spl18_23,
    inference(avatar_split_clause,[],[f437,f702]) ).

tff(f702,plain,
    ( spl18_23
  <=> ! [X0: $tType,X1: X0] :
        ( ~ ord_less(X0,X1,X1)
        | ~ preorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_23])]) ).

tff(f437,plain,
    ! [X0: $tType,X1: X0] :
      ( ~ ord_less(X0,X1,X1)
      | ~ preorder(X0) ),
    inference(cnf_transformation,[],[f273]) ).

tff(f273,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ~ ord_less(X0,X1,X1)
      | ~ preorder(X0) ),
    inference(ennf_transformation,[],[f162]) ).

tff(f162,plain,
    ! [X0: $tType] :
      ( preorder(X0)
     => ! [X1: X0] : ~ ord_less(X0,X1,X1) ),
    inference(rectify,[],[f92]) ).

tff(f92,axiom,
    ! [X0: $tType] :
      ( preorder(X0)
     => ! [X49: X0] : ~ ord_less(X0,X49,X49) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_order__less__irrefl) ).

tff(f700,plain,
    spl18_22,
    inference(avatar_split_clause,[],[f412,f698]) ).

tff(f412,plain,
    ! [X0: bool] :
      ( ( fFalse = X0 )
      | ( fTrue = X0 ) ),
    inference(cnf_transformation,[],[f144]) ).

tff(f144,plain,
    ! [X0: bool] :
      ( ( fFalse = X0 )
      | ( fTrue = X0 ) ),
    inference(rectify,[],[f135]) ).

tff(f135,axiom,
    ! [X62: bool] :
      ( ( fFalse = X62 )
      | ( fTrue = X62 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).

tff(f696,plain,
    spl18_21,
    inference(avatar_split_clause,[],[f446,f694]) ).

tff(f694,plain,
    ( spl18_21
  <=> ! [X0: $tType,X1: fun(X0,bool)] : ~ list_ex1(X0,X1,nil(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_21])]) ).

tff(f446,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : ~ list_ex1(X0,X1,nil(X0)),
    inference(cnf_transformation,[],[f170]) ).

tff(f170,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : ~ list_ex1(X0,X1,nil(X0)),
    inference(rectify,[],[f27]) ).

tff(f27,axiom,
    ! [X1: $tType,X20: fun(X1,bool)] : ~ list_ex1(X1,X20,nil(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_list__ex1__simps_I1_J) ).

tff(f692,plain,
    spl18_20,
    inference(avatar_split_clause,[],[f406,f690]) ).

tff(f690,plain,
    ( spl18_20
  <=> ! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_20])]) ).

tff(f406,plain,
    ! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
    inference(cnf_transformation,[],[f139]) ).

tff(f139,plain,
    ! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
    inference(rectify,[],[f96]) ).

tff(f96,axiom,
    ! [X56: nat] : ~ ord_less(nat,X56,zero_zero(nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_less__nat__zero__code) ).

tff(f688,plain,
    spl18_19,
    inference(avatar_split_clause,[],[f403,f685]) ).

tff(f685,plain,
    ( spl18_19
  <=> pp(fTrue) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_19])]) ).

tff(f403,plain,
    pp(fTrue),
    inference(cnf_transformation,[],[f126]) ).

tff(f126,axiom,
    pp(fTrue),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).

tff(f683,plain,
    spl18_18,
    inference(avatar_split_clause,[],[f402,f680]) ).

tff(f680,plain,
    ( spl18_18
  <=> preorder(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_18])]) ).

tff(f402,plain,
    preorder(bool),
    inference(cnf_transformation,[],[f120]) ).

tff(f120,axiom,
    preorder(bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).

tff(f678,plain,
    spl18_17,
    inference(avatar_split_clause,[],[f401,f675]) ).

tff(f675,plain,
    ( spl18_17
  <=> preorder(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_17])]) ).

tff(f401,plain,
    preorder(nat),
    inference(cnf_transformation,[],[f112]) ).

tff(f112,axiom,
    preorder(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).

tff(f673,plain,
    spl18_16,
    inference(avatar_split_clause,[],[f400,f670]) ).

tff(f400,plain,
    bot(bool),
    inference(cnf_transformation,[],[f124]) ).

tff(f124,axiom,
    bot(bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).

tff(f668,plain,
    spl18_15,
    inference(avatar_split_clause,[],[f399,f665]) ).

tff(f399,plain,
    bot(nat),
    inference(cnf_transformation,[],[f116]) ).

tff(f116,axiom,
    bot(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Obot) ).

tff(f663,plain,
    spl18_14,
    inference(avatar_split_clause,[],[f398,f660]) ).

tff(f660,plain,
    ( spl18_14
  <=> order(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_14])]) ).

tff(f398,plain,
    order(bool),
    inference(cnf_transformation,[],[f122]) ).

tff(f122,axiom,
    order(bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).

tff(f658,plain,
    spl18_13,
    inference(avatar_split_clause,[],[f397,f655]) ).

tff(f655,plain,
    ( spl18_13
  <=> order(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_13])]) ).

tff(f397,plain,
    order(nat),
    inference(cnf_transformation,[],[f114]) ).

tff(f114,axiom,
    order(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).

tff(f653,plain,
    spl18_12,
    inference(avatar_split_clause,[],[f396,f650]) ).

tff(f650,plain,
    ( spl18_12
  <=> ord(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_12])]) ).

tff(f396,plain,
    ord(bool),
    inference(cnf_transformation,[],[f123]) ).

tff(f123,axiom,
    ord(bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).

tff(f648,plain,
    spl18_11,
    inference(avatar_split_clause,[],[f395,f645]) ).

tff(f645,plain,
    ( spl18_11
  <=> ord(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_11])]) ).

tff(f395,plain,
    ord(nat),
    inference(cnf_transformation,[],[f115]) ).

tff(f115,axiom,
    ord(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).

tff(f643,plain,
    spl18_10,
    inference(avatar_split_clause,[],[f394,f640]) ).

tff(f640,plain,
    ( spl18_10
  <=> lattice(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_10])]) ).

tff(f394,plain,
    lattice(bool),
    inference(cnf_transformation,[],[f101]) ).

tff(f101,axiom,
    lattice(bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Olattice) ).

tff(f638,plain,
    spl18_9,
    inference(avatar_split_clause,[],[f393,f635]) ).

tff(f635,plain,
    ( spl18_9
  <=> lattice(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_9])]) ).

tff(f393,plain,
    lattice(nat),
    inference(cnf_transformation,[],[f102]) ).

tff(f102,axiom,
    lattice(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Olattice) ).

tff(f633,plain,
    spl18_8,
    inference(avatar_split_clause,[],[f392,f630]) ).

tff(f630,plain,
    ( spl18_8
  <=> semilattice_inf(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_8])]) ).

tff(f392,plain,
    semilattice_inf(bool),
    inference(cnf_transformation,[],[f119]) ).

tff(f119,axiom,
    semilattice_inf(bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Osemilattice__inf) ).

tff(f628,plain,
    spl18_7,
    inference(avatar_split_clause,[],[f391,f625]) ).

tff(f625,plain,
    ( spl18_7
  <=> semilattice_inf(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_7])]) ).

tff(f391,plain,
    semilattice_inf(nat),
    inference(cnf_transformation,[],[f111]) ).

tff(f111,axiom,
    semilattice_inf(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Osemilattice__inf) ).

tff(f623,plain,
    spl18_6,
    inference(avatar_split_clause,[],[f390,f620]) ).

tff(f620,plain,
    ( spl18_6
  <=> linorder(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_6])]) ).

tff(f390,plain,
    linorder(bool),
    inference(cnf_transformation,[],[f121]) ).

tff(f121,axiom,
    linorder(bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).

tff(f618,plain,
    spl18_5,
    inference(avatar_split_clause,[],[f389,f615]) ).

tff(f615,plain,
    ( spl18_5
  <=> linorder(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_5])]) ).

tff(f389,plain,
    linorder(nat),
    inference(cnf_transformation,[],[f113]) ).

tff(f113,axiom,
    linorder(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).

tff(f613,plain,
    spl18_4,
    inference(avatar_split_clause,[],[f388,f610]) ).

tff(f610,plain,
    ( spl18_4
  <=> bounded_lattice(bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_4])]) ).

tff(f388,plain,
    bounded_lattice(bool),
    inference(cnf_transformation,[],[f100]) ).

tff(f100,axiom,
    bounded_lattice(bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice) ).

tff(f608,plain,
    spl18_3,
    inference(avatar_split_clause,[],[f387,f605]) ).

tff(f387,plain,
    bounded_lattice_bot(bool),
    inference(cnf_transformation,[],[f118]) ).

tff(f118,axiom,
    bounded_lattice_bot(bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice__bot) ).

tff(f603,plain,
    spl18_2,
    inference(avatar_split_clause,[],[f386,f600]) ).

tff(f600,plain,
    ( spl18_2
  <=> zero(nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_2])]) ).

tff(f386,plain,
    zero(nat),
    inference(cnf_transformation,[],[f117]) ).

tff(f117,axiom,
    zero(nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).

tff(f598,plain,
    ~ spl18_1,
    inference(avatar_split_clause,[],[f384,f595]) ).

tff(f384,plain,
    ~ pp(fFalse),
    inference(cnf_transformation,[],[f134]) ).

tff(f134,axiom,
    ~ pp(fFalse),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SWW533_5 : TPTP v8.1.2. Released v6.0.0.
% 0.11/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n013.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 19:25:38 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (18066)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39  % (18073)WARNING: value z3 for option sas not known
% 0.15/0.39  % (18074)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39  % (18071)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39  % (18075)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)
% 0.15/0.39  % (18072)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39  % (18073)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)
% 0.15/0.39  % (18076)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)
% 0.15/0.39  % (18077)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)
% 0.15/0.39  % (18077)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.39  % Exception at run slice level% Exception at run slice level
% 0.15/0.39  
% 0.15/0.39  % Exception at run slice levelUser error: User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39  Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39  
% 0.15/0.39  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.41  % (18088)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)
% 0.15/0.41  % (18089)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)
% 0.15/0.41  % (18087)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.41  % (18075)First to succeed.
% 0.22/0.42  % (18088)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.42  % (18087)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.42  % Exception at run slice level
% 0.22/0.42  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.42  % (18075)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-18066"
% 0.22/0.43  % (18075)Refutation found. Thanks to Tanya!
% 0.22/0.43  % SZS status Theorem for theBenchmark
% 0.22/0.43  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.43  % (18075)------------------------------
% 0.22/0.43  % (18075)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.43  % (18075)Termination reason: Refutation
% 0.22/0.43  
% 0.22/0.43  % (18075)Memory used [KB]: 1373
% 0.22/0.43  % (18075)Time elapsed: 0.037 s
% 0.22/0.43  % (18075)Instructions burned: 56 (million)
% 0.22/0.43  % (18066)Success in time 0.061 s
%------------------------------------------------------------------------------